Quantum Fokker-Planck Dynamics
- URL: http://arxiv.org/abs/2106.05718v3
- Date: Thu, 14 Oct 2021 17:33:14 GMT
- Title: Quantum Fokker-Planck Dynamics
- Authors: Louis Labuschagne and W. Adam Majewski
- Abstract summary: This paper aims to obtain a quantum counterpart of Fokker-Planck dynamics.
Within this framework we present a quantization of the generalized Laplace operator.
We then construct and examine the behaviour of the corresponding Markov semigroups.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The Fokker-Planck equation is a partial differential equation which is a key
ingredient in many models in physics. This paper aims to obtain a quantum
counterpart of Fokker-Planck dynamics, as a means to describing quantum
Fokker-Planck dynamics. Given that relevant models relate to the description of
large systems, the quantization of the Fokker-Planck equation should be done in
a manner that respects this fact, and is therefore carried out within the
setting of non-commutative analysis based on general von Neumann algebras.
Within this framework we present a quantization of the generalized Laplace
operator, and then go on to incorporate a potential term conditioned to
noncommutative analysis. In closing we then construct and examine the
asymptotic behaviour of the corresponding Markov semigroups. We also present a
noncommutative Csiszar-Kullback inequality formulated in terms of a notion of
relative entropy, and show that for more general systems, good behaviour with
respect to this notion of entropy ensures similar asymptotic behaviour of the
relevant dynamics.
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