Decoherence and einselection in equilibrium in an adapted Caldeira Leggett model

Andreas Albrecht Center for Quantum Mathematics and Physics (QMAP) and Department of Physics UC Davis

Quantum Entanglement in Cosmology IPMU May 21, 2019 Supported by the US Department of Energy

5/21/19 A. Albrecht IPMU talk 1 Outline

1. Motivations

2. Introduction to einselection and the toy model

3. Einselection in equilibrium (technical explorations and overall assessment)

4. Eigenstate Einselection Hypothesis (if there is time)

5. Conclusions

5/21/19 A. Albrecht IPMU talk 2 Outline

1. Motivations

2. Introduction to einselection and the toy model

3. Einselection in equilibrium (technical explorations and overall assessment)

4. Eigenstate Einselection Hypothesis (if there is time)

With A. Arrasmith 5. Conclusions

5/21/19 A. Albrecht IPMU talk 3 Outline

1. Motivations

2. Introduction to einselection and the toy model

3. Einselection in equilibrium (technical explorations and overall assessment)

4. Eigenstate Einselection Hypothesis (if there is time)

5. Conclusions

5/21/19 A. Albrecht IPMU talk 4 Comments on the arrow of time in cosmology (at board)

5/21/19 A. Albrecht IPMU talk 5 Q: What features of the universe are correlated with classicality? • Arrow of time? • Locality? • Etc.

5/21/19 A. Albrecht IPMU talk 6 Q: What features of the universe are correlated with classicality? • Arrow of time? • Locality? • Etc.

➔ Explore the process of einselection in a toy model, relate to AoT, etc.

5/21/19 A. Albrecht IPMU talk 7 Q: What features of the universe are correlated with classicality? • Arrow of time? • Locality? • Etc.Related to the emergence of classical ➔ Explore the process of einselection in a toy model, relate to AoT, etc.

5/21/19 A. Albrecht IPMU talk 8 Q: What features of the universe are correlated with classicality? • Arrow of time? • Locality? • Etc.Related to the Traditionally emergence of connected with classical arrow of time ➔ Explore the process of einselection in a toy model, relate to AoT, etc.

5/21/19 A. Albrecht IPMU talk 9 Q: What features of the universe are correlated with classicality? • Arrow of time? • Locality? • Etc.Related to the Traditionally emergence of connected with classical arrow of time ➔ Explore the process of einselection in a Buttoy whatmodel, about relate to AoT, etc. einselection in eqm?

5/21/19 A. Albrecht IPMU talk 10 This talk: a more focused Q: What features of the universe are correlatedtechnical with discussion in service of these big picture classicality? motivations • Arrow of time? • Locality? • Etc.Related to the Traditionally emergence of connected with classical arrow of time ➔ Explore the process of einselection in a Buttoy whatmodel, about relate to AoT, etc. einselection in eqm?

5/21/19 A. Albrecht IPMU talk 11 This talk: a more focused Q: What features of the universe are correlatedtechnical with discussion in service of these big picture classicality? motivations • Arrow of time? • Locality? • Etc.Related to the Traditionally emergence of connected with classical arrow of time ➔ Explore the process of einselection in a Buttoy whatmodel, about relate to AoT, etc. einselection in eqm?

If you are handed a theory, what are the classical degrees of freedom?

5/21/19 A. Albrecht IPMU talk 12 Outline

1. Motivations

2. Introduction to einselection and the toy model

3. Einselection in equilibrium (technical explorations and overall assessment)

4. Eigenstate Einselection Hypothesis (if there is time)

5. Conclusions

5/21/19 A. Albrecht IPMU talk 13 Outline

1. Motivations

2. Introduction to einselection and the toy model

3. Einselection in equilibrium (technical explorations and overall assessment)

4. Eigenstate Einselection Hypothesis (if there is time)

5. Conclusions

5/21/19 A. Albrecht IPMU talk 14 Einselection:

The preference of special “pointer” states of a system due to interactions with the environment

“Preference” ➔ • Stability of pointer states • Destruction of non-pointer states (including “Schrödinger cat” superpositions of pointer states) • Pure non-pointer states → mixtures of pointer states via entanglement with the environment.

5/21/19 A. Albrecht IPMU talk 15 Einselection:

The preference of special “pointer” states of a system due to interactions with the environment

“Preference” ➔ • Stability of pointer states • Destruction of non-pointer states (including “Schrödinger cat” superpositions of pointer states) • Pure non-pointer states → mixtures of pointer states via entanglement with the environment.

5/21/19 A. Albrecht IPMU talk 16 Einselection:

The preference of special “pointer” states of a system due to interactions with the environment

“Preference” ➔ • Stability of pointer states • Destruction of non-pointer states (including “Schrödinger cat” superpositions of pointer states) • Pure non-pointer states → mixtures of pointer states via entanglement with the environment.

About to illustrate this with our toy model 5/21/19 A. Albrecht IPMU talk 17 Einselection:

The preference of special “pointer” states of a system due to interactions with the environment

“Preference” ➔ • Stability of pointer states • Destruction of non-pointer states (including “Schrödinger cat” superpositions of pointer states) • Pure non-pointer states → mixtures of pointer states via entanglement with the environment.

About to illustrate this Important for with our toy the emergence of model classicality 5/21/19 A. Albrecht IPMU talk 18 The Caldeira-Leggett Model:

WSE= “Environment” “World” “System” (SHO)

5/21/19 A. Albrecht IPMU talk 19 The Caldeira-Leggett Model: WSE=

SEESE H= HSHO 11 + q SHO H I +  H

Self- Hamiltonian of System

5/21/19 A. Albrecht IPMU talk 20 The Caldeira-Leggett Model: WSE=

SEESE H= HSHO 11 + q SHO H I +  H

Self- Interaction Hamiltonian Hamiltonian of System

5/21/19 A. Albrecht IPMU talk 21 The Caldeira-Leggett Model: WSE=

SEESE H= HSHO 11 + q SHO H I +  H

Self- Interaction Self- Hamiltonian Hamiltonian Hamiltonian of of System Environment

5/21/19 A. Albrecht IPMU talk 22 The Caldeira-Leggett Model: WSE=

Different (non- commuting) H’s

SEESE H= HSHO 11 + q SHO H I +  H

Self- Interaction Self- Hamiltonian Hamiltonian Hamiltonian of of System Environment

5/21/19 A. Albrecht IPMU talk 23 The Caldeira-Leggett Model:

Different (non- commuting) H’s

SEESE H= HSHO 11 + q SHO H I +  H CL: i) Model E as an infinite set of SHOs with different frequencies ii) Take special (order of) limits and parameter choices to get an (irreversible) stochastic equation that describes this (unitary) evolution under certain conditions (including AoT) iii) Demonstrate einselection etc. (CL and others) 5/21/19 A. Albrecht IPMU talk 24 The Caldeira-Leggett Model:

Different (non- commuting) H’s

SEESE H= HSHO 11 + q SHO H I +  H

Adapted CL: Random Hermitian matrices i) Model E as finite system ii) Solve full unitary evolution in all regimes (numerical) iii) Demonstrate Einselection under certain conditions (AoT) iv) Explore scope of einselection (eqm?)

5/21/19 A. Albrecht IPMU talk 25 Introducing the toy model

E • No interaction case (H I = 0 )

• Model SHO with d=30 Hilbert space

SEESE H= HSHO 11 + q SHO H I +  H

5/21/19 A. Albrecht IPMU talk 26 Introducing the toy model

E • No interaction case (H I = 0 )

• Model SHO with d=30 Hilbert space

SEESE H= HSHO 11 + q SHO H I +  H

“Movie” A (Isolated SHO)

5/21/19 A. Albrecht IPMU talk 27 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 28  q → Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 29  q → Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 30  q → Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 31 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 32 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 33 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 34 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 35 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 36 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 37 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 38 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 39 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 40 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 41 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 42 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 43 Introducing the toy model

E • No interaction case (H I = 0 )

• Model SHO with d=30 Hilbert space

Nice stable behavior Numerical noise not an issue

5/21/19 A. Albrecht IPMU talk 44 Introducing the Schrödinger cat

E • No interaction case (H I = 0 )

• Model SHO with d=30 Hilbert space

Show Movie B

5/21/19 A. Albrecht IPMU talk 45 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 46 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 47 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 48 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 49 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 50 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 51 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 52 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 53 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 54 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 55 Isolated SHO

=  2  Im ( )  Re( )

5/21/19 A. Albrecht IPMU talk 56 Schrödinger cat interacting with the environment:

E • Interactions turned on (H I  0 )

SEESE H= HSHO 11 + q SHO H I +  H

This evolution will take an initial product state into a mixed state:

=→    ij WSESE ij ij,

5/21/19 A. Albrecht IPMU talk 57 Schrödinger cat interacting with the environment:

E • Interactions turned on (H I  0 )

SEESE H= HSHO 11 + q SHO H I +  H

This evolution will take an initial product state into a mixed state: Pure (product) =→    ij WSESE ij ij,

5/21/19 A. Albrecht IPMU talk 58 Schrödinger cat interacting with the environment:

E • Interactions turned on (H I  0 )

SEESE H= HSHO 11 + q SHO H I +  H

This evolution will take an initial product state into a mixed state: Pure Entangled (product) =→    ij WSESE ij ij,

5/21/19 A. Albrecht IPMU talk 59 Schrödinger cat interacting with the environment:

E • Interactions turned on (H I  0 )

SEESE H= HSHO 11 + q SHO H I +  H

This evolution will take an initial product state into a mixed state: Pure Entangled (product) =→    ij WSESE ij ij,

Tr   =   → S SE( WWSS) more general

5/21/19 A. Albrecht IPMU talk 60 Some comments on entangled states

5/21/19 A. Albrecht IPMU talk 61 WAB=

Inclined to think: =   WAB

A state for each subsystem

5/21/19 A. Albrecht IPMU talk 62 WAB=

But the general case is: = ij WAB ij ij,

5/21/19 A. Albrecht IPMU talk 63 WAB=

But the general case is: = ij WAB ij ij,

Which gives:

 Tr   AB( WW )

 Tr   BA( WW )

A density matrix for each

5/21/19subsystem A. Albrecht IPMU talk 64 The expectation value of an observable which lives only in A can be written: ˆ OA= tr( A O A)  p i p i O p i i

Eigenvalues and eigenstates of  A

5/21/19 A. Albrecht IPMU talk 65 The expectation value of an observable which lives only in A can be written: ˆ OA= tr( A O A)  p i p i O p i i

Eigenvalues and eigenstates of  A

(“Schmidt states”)

5/21/19 A. Albrecht IPMU talk 66 The expectation value of an observable which lives only in A can be written: ˆ OA= tr( A O A)  p i p i O p i i

Eigenvalues and eigenstates of  A

A “classical mixture” of the eigenstates (no cross terms ➔ no “quantum coherence”)

5/21/19 A. Albrecht IPMU talk 67 The expectation value of an observable which lives only in A can be written: ˆ OA= tr( A O A)  p i p i O p i i

Eigenvalues and eigenstates of  A

A “classical mixture” of the eigenstates (no cross terms ➔ no “quantum coherence”)

Onset of entanglement ➔ decoherence

5/21/19 A. Albrecht IPMU talk 68 S tr (ln ) von Neumann entropy S  0 S = 0 =→    ij WABAB ij ij,

Decoherence ➔ increasing S ➔ arrow of time

5/21/19 A. Albrecht IPMU talk 69 • In general, the density matrix eigenstates might vary significantly from one moment to the next, producing a “classical mixture of random stuff”

5/21/19 A. Albrecht IPMU talk 70 • In general, the density matrix eigenstates might vary significantly from one moment to the next, producing a “classical mixture of random stuff”

• Special case: The nature of the interactions between A and B lead to a reliable preference for specific “pointer” eigenstates. This is Einselection

5/21/19 A. Albrecht IPMU talk 71 • In general, the density matrix eigenstates might vary significantly from one moment to the next, producing a “classical mixture of random stuff”

• Special case: The nature of the interactions between A and B lead to a reliable preference for specific “pointer” eigenstates. This is Einselection

Discuss pendulum interacting with the air, leading to localized wave packed pointer states.

5/21/19 A. Albrecht IPMU talk 72 Schrödinger cat interacting with the environment:

E • Interactions turned on (H I  0 )

SEESE H= HSHO 11 + q SHO H I +  H

5/21/19 A. Albrecht IPMU talk 73 Schrödinger cat interacting with the environment: An illustration of • Interactions turned on (H E  0 ) I Einselection

SEESE H= HSHO 11 + q SHO H I +  H

5/21/19 A. Albrecht IPMU talk 74 Schrödinger cat interacting with the environment:

E • Interactions turned on (H I  0 )

SEESE H= HSHO 11 + q SHO H I +  H

This evolution will take an initial product state into a mixed state:

=→    ij WSESE ij ij,

Tr   =   → S SE( WWSS) more general

5/21/19 A. Albrecht IPMU talk 75 Schrödinger cat interacting with the environment:

E • Interactions turned on (H I  0 )

SEESE H= HSHO 11 + q SHO H I +  H Show This evolution will take an initial product state into a eigenstates mixed state: and =→    ij eigenvalues WSESE ij ij,

Tr   =   → S SE( WWSS) more general

5/21/19 A. Albrecht IPMU talk 76 Schrödinger cat interacting with the environment:

E • Interactions turned on (H I  0 )

SEESE H= HSHO 11 + q SHO H I +  H Show First 2 This evolution will take an initial product state into a eigenstates mixed state: and =→    ij eigenvalues WSESE ij ij,

Tr   =   → S SE( WWSS) more general

5/21/19 A. Albrecht IPMU talk 77 Schrödinger cat interacting with the environment:

E • Interactions turned on (H I  0 )

SEESE H= HSHO 11 + q SHO H I +  H Show First 2 This evolution will take an initial product state into a eigenstates mixed state: and =→    ij eigenvalues WSESE ij ij,

Tr   =   → S SE( WWSS) more general Show Movie C 5/21/19 A. Albrecht IPMU talk 78 Eigenvalues

First 2

Eigenstates

(Numerical garbage… only one nonzero eigenvalue at t=0)

5/21/19 A. Albrecht IPMU talk 79 Eigenvalues

First 2

Eigenstates

5/21/19 A. Albrecht IPMU talk 80 Eigenvalues

First 2

Eigenstates q

5/21/19 A. Albrecht IPMU talk 81 Eigenvalues

First 2

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5/21/19 A. Albrecht IPMU talk 82 Eigenvalues

First 2

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5/21/19 A. Albrecht IPMU talk 83 Eigenvalues

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5/21/19 A. Albrecht IPMU talk 84 Eigenvalues

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5/21/19 A. Albrecht IPMU talk 85 Eigenvalues

First 2

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5/21/19 A. Albrecht IPMU talk 86 Eigenvalues

First 2

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5/21/19 A. Albrecht IPMU talk 87 Eigenvalues

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5/21/19 A. Albrecht IPMU talk 88 Eigenvalues

First 2

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5/21/19 A. Albrecht IPMU talk 89 Eigenvalues

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5/21/19 A. Albrecht IPMU talk 90 Eigenvalues

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5/21/19 A. Albrecht IPMU talk 91 Eigenvalues

First 2

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5/21/19 A. Albrecht IPMU talk 92 Eigenvalues

First 2

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5/21/19 A. Albrecht IPMU talk 93 Eigenvalues

First 2

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5/21/19 A. Albrecht IPMU talk 94 Eigenvalues

First 2

Eigenstates

5/21/19 A. Albrecht IPMU talk 95 Schrödinger cat interacting with the environment:

E • Interactions turned on (H I  0 )

H= HSEESE 11 + q H +  H UPSHOT:SHO SHO I Show First 2 This evolution• The toy will model take an successfully initial product “einselects” state into a eigenstates mixed state:the “classical” wave packets from a and Schrödinger cat superposition =→    ij eigenvalues WSESE ij ij,

Tr   =   → S SE( WWSS) more general Show Movie C 5/21/19 A. Albrecht IPMU talk 96 Outline

1. Motivations

2. Introduction to einselection and the toy model

3. Einselection in equilibrium (technical explorations and overall assessment)

4. Eigenstate Einselection Hypothesis (if there is time)

5. Conclusions

5/21/19 A. Albrecht IPMU talk 97 Outline

1. Motivations

2. Introduction to einselection and the toy model

3. Einselection in equilibrium (technical explorations and overall assessment)

4. Eigenstate Einselection Hypothesis (if there is time)

5. Conclusions

5/21/19 A. Albrecht IPMU talk 98 The collapsing Schrödinger cat (Movie C) was in this time window

Entropy vs time

• Einselection associated with increasing entropy

5/21/19 A. Albrecht IPMU talk 99 The collapsing Schrödinger cat (Movie C) was in this time window

Entropy vs time

How do the density matrix eigenstates behave in eqm?

• Einselection associated with increasing entropy

5/21/19 A. Albrecht IPMU talk 100 The collapsing Schrödinger cat (Movie C) was in this time window

Entropy vs time

How do the density matrix eigenstates behave in eqm?

• Einselection associated with increasing entropy Movie D starts here

Show Movie D 5/21/19 A. Albrecht IPMU talk 101 Discuss “detailed balance” (wallowing) of everett worlds at board

5/21/19 A. Albrecht IPMU talk 102 SHO density matrix in eqm

Eigenvalues

First 2

Eigenstates

5/21/19 A. Albrecht IPMU talk 103 SHO density matrix in eqm

Eigenvalues

First 2

Eigenstates

5/21/19 A. Albrecht IPMU talk 104 SHO density matrix in eqm

Eigenvalues

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5/21/19 A. Albrecht IPMU talk 105 SHO density matrix in eqm

Eigenvalues

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5/21/19 A. Albrecht IPMU talk 106 SHO density matrix in eqm

Eigenvalues

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5/21/19 A. Albrecht IPMU talk 107 SHO density matrix in eqm

Eigenvalues

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5/21/19 A. Albrecht IPMU talk 108 SHO density matrix in eqm

Eigenvalues

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5/21/19 A. Albrecht IPMU talk 109 SHO density matrix in eqm

Eigenvalues

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5/21/19 A. Albrecht IPMU talk 110 SHO density matrix in eqm

Eigenvalues

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5/21/19 A. Albrecht IPMU talk 111 SHO density matrix in eqm

Eigenvalues

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5/21/19 A. Albrecht IPMU talk 112 SHO density matrix in eqm

Eigenvalues

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5/21/19 A. Albrecht IPMU talk 113 SHO density matrix in eqm

Eigenvalues

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5/21/19 A. Albrecht IPMU talk 114 SHO density matrix in eqm

Eigenvalues

First 2

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5/21/19 A. Albrecht IPMU talk 115 SHO density matrix in eqm

Eigenvalues Pretty noisy (as one First 2 might expect)

Eigenstates

5/21/19 A. Albrecht IPMU talk 116 SHO density matrix in eqm

Eigenvalues Pretty noisy (as one First 2 might expect)

Eigenstates “Colliding (wallowing?) Everett worlds”

5/21/19 A. Albrecht IPMU talk 117 SHO density matrix in eqm

However, when the Eigenvalues coupling strength is reduced, things getPretty noisy (as one First 2 more interesting might expect)

Eigenstates

5/21/19 A. Albrecht IPMU talk 118 Strong

Weak

Next movie shows weak coupling case, starting here

Show Movie E 5/21/19 A. Albrecht IPMU talk 119 SHO density matrix in eqm Weakly coupled case

Eigenvalues

First 2

Eigenstates

5/21/19 A. Albrecht IPMU talk 120 SHO density matrix in eqm Weakly coupled case

Eigenvalues

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5/21/19 A. Albrecht IPMU talk 121 SHO density matrix in eqm Weakly coupled case

Eigenvalues

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5/21/19 A. Albrecht IPMU talk 122 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 123 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 124 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 125 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 126 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 127 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 128 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 129 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 130 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 131 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 132 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 133 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 134 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 135 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 136 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 137 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 138 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 139 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 140 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 141 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 142 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 143 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 144 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 145 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 146 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 147 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 148 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 149 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 150 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 151 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 152 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 153 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 154 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 155 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 156 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 157 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 158 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 159 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 160 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 161 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 162 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 163 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 164 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 165 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 166 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 167 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 168 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 169 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 170 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 171 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 172 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 173 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 174 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 175 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 176 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 177 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 178 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 179 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 180 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 181 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 182 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 183 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 184 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 185 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 186 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 187 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 188 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 189 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 190 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 191 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 192 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 193 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 194 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 196 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 197 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 198 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 199 SHO density matrix in eqm Weakly coupled case

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5/21/19 A. Albrecht IPMU talk 200 Strong

Weak

Next movie showsMovie weak E couplingshows the case, weakly startinginteracting here toy model in eqm phase

Show Movie E ➔ Some “noticeable” oscillatory 5/21/19 behaviorA. Albrecht IPMU talk 201 Strong

Weak Next: Further explorations of oscillatory behavior

Next movie showsMovie weak E couplingshows the case, weakly startinginteracting here toy model in eqm phase

Show Movie E ➔ Some “noticeable” oscillatory 5/21/19 behaviorA. Albrecht IPMU talk 202 Further analysis:

Time-time correlation function

f t qˆ ( ) SHO t

 (t)  f( t) f( t +  t) dt t

 (t)

Max and Min p t eigenvectors

5/21/19 A. Albrecht IPMU talk 203 Power spectrum

( )

SHO  frequency

5/21/19 A. Albrecht IPMU talk 204 Weak coupling

30 Power spectra by  eigenstate

( ) Eigenstates 1,2,3,5,7…27, 29,30

1

Full system power spectra

5/21/19 A. Albrecht IPMU talk 205 Weak coupling

30 Power spectra by  eigenstate

( ) Eigenstates 1,2,3,5,7…27, 29,30

1

Full system power spectra

5/21/194/2/19 A. AlbrechtA. Albrecht IC Theory IPMU seminartalk 206 Now look at strong coupling, where Eqm seemed more noisy

5/21/19 A. Albrecht IPMU talk 207 Strong coupling

30 Power spectra by  eigenstate

( ) Eigenstates 1,2,3,5,7…27, 29,30

1

Full system power spectra

5/21/194/2/19 A. AlbrechtA. Albrecht IC Theory IPMU seminartalk 208 Strong coupling

30 Power spectra by  eigenstate

( ) Eigenstates 1,2,3,5,7…27, 29,30

1

Full system power spectra

5/21/194/2/19 A. AlbrechtA. Albrecht IC Theory IPMU seminartalk 209 Strong coupling

30 Power spectra by  eigenstate

( ) Note: Relatively strongEigenstates peak in total power1,2,3,5,7…27, spectrum (vs eigenstates),29,30 but very low amplitude oscillations (vs individual 1 eigenstates).

Full system power spectra

5/21/194/2/19 A. AlbrechtA. Albrecht IC Theory IPMU seminartalk 210 Upshot:

➔Strong oscillatory signal in for  eigenstates for weakly coupled case (despite messy overall wavefunction shapes)

➔No such signal for strongly coupled case

➔Both cases show strong oscillatory signal for q  but amplitude is small.

5/21/19 A. Albrecht IPMU talk 211 Upshot:

➔Strong oscillatory signal in for  eigenstates for weakly coupled case (despite messy overall wavefunction shapes)

➔No such signal for strongly coupled case

➔Both cases show strong oscillatory signal for q  but amplitude is small.

NEXT: A consistent histories approach

5/21/19 A. Albrecht IPMU talk 212 Consistent histories (CH):

➔Generally, in the path integral formulation of QM interference among paths plays an important role

➔CH formalism identifies paths where interferences effects are NOT important. These are the paths to which probabilities can be assigned, and which are classical in that sense.

➔We have found that the messiness of the eqm physics of our toy model shows up as histories that degrade after a couple of SHO periods

➔CH gives interesting test of “coherent state as most robust state” result from master equation work.

5/21/19 A. Albrecht IPMU talk 213 Consistent histories (CH):

➔Generally, in the path integral formulation of QM interference among paths plays an important role

➔CH formalism identifies paths where interferences effects are NOT important. These are the paths to which probabilities can be assigned, and which are classical in that sense.

➔We have found that the messiness of the eqm physics of our toy model shows up as histories that degrade after a couple of SHO periods

➔CH gives interesting test of “coherent state as most robust state” result from master equation work.

5/21/19 A. Albrecht IPMU talk 214 Consistent histories (CH):

➔Generally, in the path integral formulation of QM interference among paths plays an important role

➔CH formalism identifies paths where interferences effects are NOT important. These are the paths to which probabilities can be assigned, and which are classical in that sense. (Define histories on ➔ a discrete time We have found that the messiness of the eqm physics ofgrid) our toy model shows up as histories that degrade after a couple of SHO periods

➔CH gives interesting test of “coherent state as most robust state” result from master equation work.

5/21/19 A. Albrecht IPMU talk 215 Consistent histories (CH):

➔Generally, in the path integral formulation of QM interference among paths plays an important role

➔CH formalism identifies paths where interferences effects are NOT important. These are the paths to which probabilities can be assigned, and which are classical in that sense.

➔We have found that the messiness of the eqm physics of our toy model shows up as histories that degrade after a couple of SHO periods

➔CH gives interesting test of “coherent state as most robust state” result from master equation work.

5/21/19 A. Albrecht IPMU talk 216 Consistent histories (CH):

➔Generally, in the path integral formulation of QM interference among paths plays an important role

➔CH formalism identifies paths where interferences effects are NOT important. These are the paths to which probabilities can be assigned, and which are classical in that sense.

➔We have found that the messiness of the eqm physics of our toy model shows up as histories that degrade after a couple of SHO periods

➔CH gives interesting test of “coherent state as most robust state” result from master equation work.

5/21/19 A. Albrecht IPMU talk 217 Fractional interference

5/21/19 Probability for Path 1

error frombuilt states. other Historiesbuiltfrom coherentstates A. Albrecht A. talk IPMU (green) degrademore slowly than histories 218 Fractional interference

5/21/19 Probability for Path 1

error frombuilt states. other Historiesbuiltfrom coherentstates But eventuallyBut coherent the statepaths degrade too. Regionshownprevious in plot A. Albrecht A. talk IPMU (green) degrademore slowly than histories 219 Fractional interference

5/21/19 Probability for Path 1

error frombuilt states. other Historiesbuiltfrom coherentstates (consistent with existing lore about Lesson from consistent histories: coherent states are most robust Histories made by projecting on SHO inSHO an environment). A. Albrecht A. talk IPMU (green) degrademore slowly than histories 220 Fractional interference

5/21/19 Probability for Path 1

error frombuilt states. other Historiesbuiltfrom coherentstates (consistent with existing lore about Lesson from consistent histories: coherent states are most robust Histories made by projecting on SHO inSHO an environment). But But in EQM (detailed balance), even A. Albrecht A. talk IPMU coherent state histories degenerate on thescale of a coherence time (green) degrademore slowly than histories 221 Lessons from eqm studies in the adapted CL model:

➔Plenty of messiness in eqm (“wallowing or interfering Everett worlds”)

➔Still, some intriguing sign of “classicality” show up in the power spectra of density matrix eigenstates.

➔Consistent Histories formalism shows some classical behavior (which degrades after a couple of SHO periods)

➔Further discussion of implications at end of talk.

5/21/19 A. Albrecht IPMU talk 222 Outline

1. Motivations

2. Introduction to einselection and the toy model

3. Einselection in equilibrium (technical explorations and overall assessment)

4. Eigenstate Einselection Hypothesis (if there is time)

5. Conclusions

5/21/19 A. Albrecht IPMU talk 223 Outline

1. Motivations

2. Introduction to einselection and the toy model

3. Einselection in equilibrium (technical explorations and overall assessment)

4. Eigenstate Einselection Hypothesis (if there is time)

5. Conclusions

5/21/19 A. Albrecht IPMU talk 224 Similar power spectra to those shown above

Entropy vs time

Power spectra by eigenstate

( )

Full system power spectrum 

5/21/19 A. Albrecht IPMU talk 225 Randomized Same as previous slide, but calculated for a state that has the Similarphases power of the coefficients spectra to of thethose expansion shown in energy above eigenstates (of the whole system) randomized Entropy vs time

Power spectra by eigenstate

( )

Full system power spectrum 

5/21/19 A. Albrecht IPMU talk 226 Randomized Same as previous slide, but calculated for a state that has the Similarphases power of the coefficients spectra to of thethose expansion shown in energy above eigenstates (of the whole system) randomized Entropy vs time

Power spectra by eigenstate ➔ Interesting behavior of power spectra a reflection of intrinsic properties of (certain) energy ( ) eigenstates of the entire system

➔ Compare with “Eigenstate Thermalization Full system Hypothesis” (ETH) power spectrum ➔ “Eigenstate Einselection Hypothesis” (EEH) 

5/21/19 A. Albrecht IPMU talk 227 Outline

1. Motivations

2. Introduction to einselection and the toy model

3. Einselection in equilibrium (technical explorations and overall assessment)

4. Eigenstate Einselection Hypothesis (if there is time)

5. Conclusions

5/21/19 A. Albrecht IPMU talk 228 Outline

1. Motivations

2. Introduction to einselection and the toy model

3. Einselection in equilibrium (technical explorations and overall assessment)

4. Eigenstate Einselection Hypothesis (if there is time)

5. Conclusions

5/21/19 A. Albrecht IPMU talk 229 Conclusions

➔ The adapted CL (ACL) model reproduced results about decoherence and einselection known from the standard CL model

➔ The ACL allows the exploration of these phenomena under conditions not accessible to the CL model (specifically eqm.)

➔ We have found einselection phenomena are highly degraded in eqm., but not completely destroyed.

➔ A suggestion: Classical phenomena may persist in equilibrium on a time scale short compared to a decoherence time… interesting for cosmology.

5/21/19 A. Albrecht IPMU talk 230 Conclusions

➔ The adapted CL (ACL) model reproduced results about decoherence and einselection known from the standard CL model

➔ The ACL allows the exploration of these phenomena under conditions not accessible to the CL model (specifically eqm.)

➔ We have found einselection phenomena are highly degraded in eqm., but not completely destroyed.

➔ A suggestion: Classical phenomena may persist in equilibrium on a time scale short compared to a decoherence time… interesting for cosmology.

5/21/19 A. Albrecht IPMU talk 231 Conclusions

➔ The adapted CL (ACL) model reproduced results about decoherence and einselection known from the standard CL model

➔ The ACL allows the exploration of these phenomena under conditions not accessible to the CL model (specifically eqm.)

➔ We have found einselection phenomena are highly degraded in eqm., but not completely destroyed.

➔ A suggestion: Classical phenomena may persist in equilibrium on a time scale short compared to a decoherence time… interesting for cosmology.

5/21/19 A. Albrecht IPMU talk 232 Conclusions

➔ The adapted CL (ACL) model reproduced results about decoherence and einselection known from the standard CL model

➔ The ACL allows the exploration of these phenomena under conditions not accessible to the CL model (specifically eqm.)

➔ We have found einselection phenomena are highly degraded in eqm., but not completely destroyed. Interesting connection with cosmological motivations ➔ A suggestion: Classical phenomena may persist in equilibrium on a time scale short compared to a decoherence time… interesting for cosmology.

5/21/19 A. Albrecht IPMU talk 233 Conclusions

➔ The adapted CL (ACL) model reproduced results about decoherence and einselection known from the standard CL model

➔ The ACL allows the exploration of these phenomena under conditions not accessible to the CL model (specifically eqm.)

➔ We have found einselection phenomena are highly degraded in eqm., but not completely destroyed.

➔ A suggestion: Classical phenomena may persist in equilibrium on a time scale short compared to a decoherence time… interesting for cosmology.

5/21/19 A. Albrecht IPMU talk 234 Conclusions

➔ The adapted CL (ACL) model reproduced results about decoherence and einselection known from the standard CL model

➔ The ACL allows the exploration of these phenomena under conditions not accessible to the CL model (specifically eqm.)

➔ We have found einselection phenomena are highly degraded in eqm., but not completely destroyed.

➔ A suggestion: Classical phenomena may persist in equilibrium on a time scale short compared to a decoherence time… interesting for cosmology. “classical” features emerged in eqm when the decoherence time was extended (weak coupling) to be longer than the SHO period 5/21/19 A. Albrecht IPMU talk 235 Conclusions

➔ The adapted CL (ACL) model reproduced results about decoherence and einselection known from the standard CL model

➔ The ACL allows the exploration of these phenomena under conditions not accessible to the CL model (specifically eqm.)

➔ We have found einselection phenomena are highly degraded in eqm., but not completely destroyed. Compare with “de ➔ Sitter Equilibrium” A suggestion: Classical phenomena may persist in equilibriumscenario where on a time scale short compared to a decoherence time… decoherenceinteresting time for cosmology. is the age of the Universe “classical” features emerged in eqm when the decoherence time was extended (weak coupling) to be longer than the SHO period 5/21/19 A. Albrecht IPMU talk 236