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
Seminar University of Nottingham April 4, 2019 Supported by the US Department of Energy
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 4 Comments on the arrow of time in cosmology (at board)
4/4/19 A. Albrecht Nottingham seminar 5 Q: What features of the universe are correlated with classicality? • Arrow of time? • Locality? • Etc.
4/4/19 A. Albrecht Nottingham seminar 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.
4/4/19 A. Albrecht Nottingham seminar 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.
4/4/19 A. Albrecht Nottingham seminar 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.
4/4/19 A. Albrecht Nottingham seminar 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?
4/4/19 A. Albrecht Nottingham seminar 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?
4/4/19 A. Albrecht Nottingham seminar 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?
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 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.
4/4/19 A. Albrecht Nottingham seminar 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.
4/4/19 A. Albrecht Nottingham seminar 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 4/4/19 A. Albrecht Nottingham seminar 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 4/4/19 A. Albrecht Nottingham seminar 18 The Caldeira-Leggett Model:
WSE= “Environment” “World” “System” (SHO)
4/4/19 A. Albrecht Nottingham seminar 19 The Caldeira-Leggett Model: WSE=
SEESE H= HSHO 11 + q SHO H I + H
Self- Hamiltonian of System
4/4/19 A. Albrecht Nottingham seminar 20 The Caldeira-Leggett Model: WSE=
SEESE H= HSHO 11 + q SHO H I + H
Self- Interaction Hamiltonian Hamiltonian of System
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 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) 4/4/19 A. Albrecht Nottingham seminar 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?)
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 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)
4/4/19 A. Albrecht Nottingham seminar 27 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 28 q → Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 29 q → Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 30 q → Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 31 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 32 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 33 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 34 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 35 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 36 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 37 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 38 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 39 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 40 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 41 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 42 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 44 Introducing the Schrödinger cat
E • No interaction case (H I = 0 )
• Model SHO with d=30 Hilbert space
Show Movie B
4/4/19 A. Albrecht Nottingham seminar 45 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 46 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 47 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 48 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 49 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 50 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 51 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 52 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 53 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 54 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 55 Isolated SHO
= 2 Im ( ) Re( )
4/4/19 A. Albrecht Nottingham seminar 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,
4/4/19 A. Albrecht Nottingham seminar 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,
4/4/19 A. Albrecht Nottingham seminar 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,
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 60 Some comments on entangled states
4/4/19 A. Albrecht Nottingham seminar 61 WAB=
Inclined to think: = WAB
A state for each subsystem
4/4/19 A. Albrecht Nottingham seminar 62 WAB=
But the general case is: = ij WAB ij ij,
4/4/19 A. Albrecht Nottingham seminar 63 WAB=
But the general case is: = ij WAB ij ij,
Which gives:
Tr AB( WW )
Tr BA( WW )
A density matrix for each
4/4/19subsystem A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 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”)
4/4/19 A. Albrecht Nottingham seminar 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”)
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 68 S tr (ln ) von Neumann entropy S 0 S = 0 =→ ij WABAB ij ij,
Decoherence ➔ increasing S ➔ arrow of time
4/4/19 A. Albrecht Nottingham seminar 69 • In general, the density matrix eigenstates might vary significantly from one moment to the next, producing a “classical mixture of random stuff”
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 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.
4/4/19 A. Albrecht Nottingham seminar 72 Schrödinger cat interacting with the environment:
E • Interactions turned on (H I 0 )
SEESE H= HSHO 11 + q SHO H I + H
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 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 4/4/19 A. Albrecht Nottingham seminar 78 Eigenvalues
First 2
Eigenstates
(Numerical garbage… only one nonzero eigenvalue at t=0)
4/4/19 A. Albrecht Nottingham seminar 79 Eigenvalues
First 2
Eigenstates
4/4/19 A. Albrecht Nottingham seminar 80 Eigenvalues
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Eigenstates q
4/4/19 A. Albrecht Nottingham seminar 81 Eigenvalues
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4/4/19 A. Albrecht Nottingham seminar 82 Eigenvalues
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4/4/19 A. Albrecht Nottingham seminar 83 Eigenvalues
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4/4/19 A. Albrecht Nottingham seminar 84 Eigenvalues
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4/4/19 A. Albrecht Nottingham seminar 85 Eigenvalues
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4/4/19 A. Albrecht Nottingham seminar 86 Eigenvalues
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4/4/19 A. Albrecht Nottingham seminar 87 Eigenvalues
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4/4/19 A. Albrecht Nottingham seminar 88 Eigenvalues
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4/4/19 A. Albrecht Nottingham seminar 89 Eigenvalues
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4/4/19 A. Albrecht Nottingham seminar 90 Eigenvalues
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4/4/19 A. Albrecht Nottingham seminar 91 Eigenvalues
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4/4/19 A. Albrecht Nottingham seminar 92 Eigenvalues
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4/4/19 A. Albrecht Nottingham seminar 93 Eigenvalues
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4/4/19 A. Albrecht Nottingham seminar 94 Eigenvalues
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4/4/19 A. Albrecht Nottingham seminar 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 4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 98 The collapsing Schrödinger cat (Movie C) was in this time window
Entropy vs time
• Einselection associated with increasing entropy
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 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 4/4/19 A. Albrecht Nottingham seminar 101 Discuss “detailed balance” (wallowing) of everett worlds at board
4/4/19 A. Albrecht Nottingham seminar 102 SHO density matrix in eqm
Eigenvalues
First 2
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4/4/19 A. Albrecht Nottingham seminar 103 SHO density matrix in eqm
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4/4/19 A. Albrecht Nottingham seminar 104 SHO density matrix in eqm
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4/4/19 A. Albrecht Nottingham seminar 105 SHO density matrix in eqm
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4/4/19 A. Albrecht Nottingham seminar 106 SHO density matrix in eqm
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4/4/19 A. Albrecht Nottingham seminar 107 SHO density matrix in eqm
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4/4/19 A. Albrecht Nottingham seminar 108 SHO density matrix in eqm
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4/4/19 A. Albrecht Nottingham seminar 109 SHO density matrix in eqm
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4/4/19 A. Albrecht Nottingham seminar 110 SHO density matrix in eqm
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4/4/19 A. Albrecht Nottingham seminar 111 SHO density matrix in eqm
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4/4/19 A. Albrecht Nottingham seminar 112 SHO density matrix in eqm
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4/4/19 A. Albrecht Nottingham seminar 113 SHO density matrix in eqm
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4/4/19 A. Albrecht Nottingham seminar 114 SHO density matrix in eqm
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4/4/19 A. Albrecht Nottingham seminar 115 SHO density matrix in eqm
Eigenvalues Pretty noisy (as one First 2 might expect)
Eigenstates
4/4/19 A. Albrecht Nottingham seminar 116 SHO density matrix in eqm
Eigenvalues Pretty noisy (as one First 2 might expect)
Eigenstates “Colliding (wallowing?) Everett worlds”
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 118 Strong
Weak
Next movie shows weak coupling case, starting here
Show Movie E 4/4/19 A. Albrecht Nottingham seminar 119 SHO density matrix in eqm Weakly coupled case
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Weak
Next movie showsMovie weak E couplingshows the case, weakly startinginteracting here toy model in eqm phase
Show Movie E ➔ Some “noticeable” oscillatory 4/4/19 A. Albrechtbehavior Nottingham seminar 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 4/4/19 A. Albrechtbehavior Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 203 Power spectrum
( )
SHO frequency
4/4/19 A. Albrecht Nottingham seminar 204 Weak coupling
30 Power spectra by eigenstate
( ) Eigenstates 1,2,3,5,7…27, 29,30
1
Full system power spectra
4/4/19 A. Albrecht Nottingham seminar 205 Weak coupling
30 Power spectra by eigenstate
( ) Eigenstates 1,2,3,5,7…27, 29,30
1
Full system power spectra
4/4/194/2/19 A.A. Albrecht Albrecht Nottingham IC Theory seminar seminar 206 Now look at strong coupling, where Eqm seemed more noisy
4/4/19 A. Albrecht Nottingham seminar 207 Strong coupling
30 Power spectra by eigenstate
( ) Eigenstates 1,2,3,5,7…27, 29,30
1
Full system power spectra
4/4/194/2/19 A.A. Albrecht Albrecht Nottingham IC Theory seminar seminar 208 Strong coupling
30 Power spectra by eigenstate
( ) Eigenstates 1,2,3,5,7…27, 29,30
1
Full system power spectra
4/4/194/2/19 A.A. Albrecht Albrecht Nottingham IC Theory seminar seminar 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
4/4/194/2/19 A.A. Albrecht Albrecht Nottingham IC Theory seminar seminar 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.
4/4/19 A. Albrecht Nottingham seminar 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
4/4/19 A. Albrecht Nottingham seminar 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.
4/4/19 A. Albrecht Nottingham seminar 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.
4/4/19 A. Albrecht Nottingham seminar 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.
4/4/19 A. Albrecht Nottingham seminar 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.
4/4/19 A. Albrecht Nottingham seminar 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.
4/4/19 A. Albrecht Nottingham seminar 217 Fractional interference
4/4/19 Probability for Path 1
error frombuilt states. other Historiesbuiltfrom coherentstates A. Albrecht A. Nottingham seminar (green) degrademore slowly than histories 218 Fractional interference
4/4/19 Probability for Path 1
error frombuilt states. other Historiesbuiltfrom coherentstates But eventuallyBut coherent the statepaths degrade too. Regionpreviousshown in plot A. Albrecht A. Nottingham seminar (green) degrademore slowly than histories 219 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.
4/4/19 A. Albrecht Nottingham seminar 220 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
4/4/19 A. Albrecht Nottingham seminar 221 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
4/4/19 A. Albrecht Nottingham seminar 222 Similar power spectra to those shown above
Entropy vs time
Power spectra by eigenstate
( )
Full system power spectrum
4/4/19 A. Albrecht Nottingham seminar 223 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
4/4/19 A. Albrecht Nottingham seminar 224 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)
4/4/19 A. Albrecht Nottingham seminar 225 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
4/4/19 A. Albrecht Nottingham seminar 226 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
4/4/19 A. Albrecht Nottingham seminar 227 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.
4/4/19 A. Albrecht Nottingham seminar 228 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.
4/4/19 A. Albrecht Nottingham seminar 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.
4/4/19 A. Albrecht Nottingham seminar 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. 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.
4/4/19 A. Albrecht Nottingham seminar 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.
4/4/19 A. Albrecht Nottingham seminar 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.
➔ 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 4/4/19 A. Albrecht Nottingham seminar 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. 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 4/4/19 A. Albrecht Nottingham seminar 234