Hi everyone,
Tomorrow Adrian Hutter will present his master's thesis.
--Frédéric
------------------------------------- Speaker: Adrian Hutter Title: How long does it take for a quantum mechanical system to forget about its initial state? Date/Time/Place: Tuesday, July 19, 17:00, HIT K52
Abstract: In recent years there has been enormous progress in understanding the foundations of statistical mechanics from first principles of quantum mechanics. Existing results are mainly concerned with long-time temporal averages. Finding the time scales on which thermalization happens remains an open problem. In this talk I will address the question of how long a quantum-mechanical system needs to become independent of its initial state. We approach this question by use of the decoupling technique, which was originally developed for quantum information-theoretical purposes. We find that we can draw conclusions about the evolution of almost all states of the system by studying the time evolution of just a single state. In particular, comparing the entropies in the system and in the environment for that particular state allows us to predict whether the system has halready “forgotten” about its initial state or not. This criterion is tight up to differences between smooth min- and max-entropies. We then proceed to study how fast these entropies can be changed. This allows us to find lower bounds on the times which are needed for the system to become independent of its initial state. These bounds hold with full generality and for any kind of interaction between the system and its environment. We discuss applications of our bound to the decoherence time of quantum memories. We conclude by presenting a converse result which shows that the system will stay close to its initial state for all times if the relevant energy eigenstates are sufficiently lowly entangled between the system and the environment.
Joint work with Stephanie Wehner.