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Decoherence and Einselection in Equilibrium in an Adapted Caldeira Leggett Model 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 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) 4/4/19 A. Albrecht Nottingham seminar 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?) 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 ) 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, 4/4/19 A.
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