When does a quantum mechanical system depend on the initial conditions of the system or the environment?

Details When does a quantum mechanical system depend on the initial conditions of the system or the environment? When does a quantum mechanical system depend on the initial conditions of the system or the environment?

2011-11-14

arxiv.org/abs/1111.3080v3

Physics

Quantum Physics

5+31 pages, 2 figures, revtex. v2: minor changes in notation

Scientific paper

Deriving rigorous bounds for the time scales that are needed for thermalization forms one of the most vexing problems when it comes to understanding statistical mechanics from the principles of quantum mechanics. One central aspect in obtaining such bounds is to determine how long a system retains memory of its initial conditions. By viewing this problem from an quantum information theory perspective, we are able to simplify part of this task in a very natural and easy way. We first show that for any interaction between the system and the environment, and almost all initial states of the system, the question of how long such memory lasts can be answered by studying the temporal evolution of just one special initial state. This special state thereby depends only on our knowledge of macroscopic parameters of the system. We provide a simple entropic inequality for this state that can be used to determine whether mosts states of the system have, or have not become independent of their initial conditions after time t. Analyzing the rate of entropy change over time for a particular kind of interaction then allows us to place rigorous bounds on such time scales. We make a similar statement for almost all initial states of the environment, and finally provide a sufficient condition for which a system never thermalizes, but remains close to its initial state for all times.

Affiliated with

Also associated with

No associations

Rating

When does a quantum mechanical system depend on the initial conditions of the system or the environment? does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with When does a quantum mechanical system depend on the initial conditions of the system or the environment?, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and When does a quantum mechanical system depend on the initial conditions of the system or the environment? will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-216494