Time Scales and Manifestations of Chaos in Many-Body Quantum Dynamics by Lea F. Santos

PROGRAM

THERMALIZATION, MANY BODY LOCALIZATION AND HYDRODYNAMICS

ORGANIZERS: Dmitry Abanin, Abhishek Dhar, François Huveneers, Takahiro Sagawa, Keiji Saito, Herbert Spohn and Hal Tasaki

DATE : 11 November 2019 to 29 November 2019

VENUE: Ramanujan Lecture Hall, ICTS Bangalore

How do isolated quantum systems thermalize? This is a fundamental question that is related to the foundations of quantum statistical mechanics and also to the question of the arrow of time. The first study goes back to John von Neumann in 1929. Recently, this question was revived, fuelled by several new concepts in theory along with many relevant experiments. This question is now shared by many fields such as statistical physics, mathematical physics, quantum information and cold atomic systems, and the studies around this question have become interdisciplinary. In the broad context of this basic fundamental question, three closely related areas of research have emerged.

Thermalization
Many Body Localization (MBL)
Hydrodynamical description of many body systems
This three-week program aims to bring together researchers working in these areas to discuss recent progress in the field, and hopes to lead to collaborative efforts towards solution of some of the outstanding problems. Apart from technical talks spread throughout the period of the program, there will be sets of pedagogical lectures by leading experts on the following topics:

Benjamin Doyon (Integrable systems and generalized hydrodynamics)
Tomaz Prosen (Solvable models of diffusion and many-body chaos)
Peter Reimann (Analytical approaches on thermalization)
Marcos Rigol (Dynamics and generalized thermalization in integrable systems)
Wojciech De Roeck (Mechanisms of slow thermalization)
Maksym Serbyn (MBL and other mechanisms of ergodicity breaking)
Herbert Spohn (Hydrodynamic theory)
Romain Vasseur (MBL and measurement-induced transitions)
Registration is open to advanced graduate students, postdocs and other researchers working in these areas.

0:00:00 Time Scales and Manifestations of Chaos in Many-Body Quantum Dynamics
0:00:47 Time Scales and Self-Averaging
0:02:44 Coherent Evolution in Experiments
0:03:07 Equilibration
0:03:17 Time-independent Hamiltonian
0:04:33 Thermalization
0:05:13 Chaos in Realistic Many-Body Quantum Systems
0:05:25 Full Random Matrices vs Realistic Models
0:06:29 Full Random Matrices vs Two-Body Interaction
0:07:45 Dynamics and Time Scales
0:08:18 Dynamics
0:08:53 Models
0:11:16 Survival Probability
0:15:42 Full Random Matrices vs Two-Body Interaction
0:17:34 Initial Fast Decay
0:17:55 Power-law Decay
0:18:30 Survival Probability
0:20:24 Correlation Hole
0:21:07 Survival Probability
0:21:45 Survival Probability Time Scales
0:22:01 Time to Reach the Minimum of the Hole
0:23:37 Spread in the many-body space
0:25:15 Relaxation Time
0:25:36 Relaxation Time: Heisenberg Time
0:26:16 Realistic spin-I/2 model
0:26:50 Spin Autocorrelation Function
0:28:07 As the disorder increases
0:28:11 1D Disordered Spin-I/2 Model
0:28:20 Power-law exponent: energy bounds
0:28:29 Correlation Hole and Disorder Strength
0:29:00 Thouless Dimensionless Conductance
0:29:43 Why Thouless? Relation with the Thouless Energy
0:32:22 Summary
0:33:00 Self-Averaging
0:33:32 Non-Local in Time & Local in Time
0:36:17 Q&A