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Andreas Albrecht.Pdf 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 CL: SEESE i) ModelH= HE asSHO an infinite11 + qset SHO of H SHOs I + with different H 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 Adapted CL: SEESERandom Hermitian H= HSHO 11 + q SHO H I + H 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 ) This evolution will take an initial product state into a mixed state: SEESE H= HSHO 11 + q SHO H I + H =→ ij WSESE ij ij, 5/21/19 A.
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