Quantum Fokker–Planck Dynamics

@article{Labuschagne2021QuantumFD,
  title={Quantum Fokker–Planck Dynamics},
  author={Louis E. Labuschagne and W. Adam Majewski},
  journal={Annales Henri Poincar{\'e}},
  year={2021}
}
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 noncommutative analysis based… 

References

SHOWING 1-10 OF 68 REFERENCES
An Analysis of Quantum Fokker-Planck Models: A Wigner Function Approach
The analysis of dissipative transport equations within the framework of open quantum systems with Fokker-Planck-type scattering is carried out from the perspective of a Wigner function approach. In
Dynamics on Noncommutative Orlicz Spaces
Quantum dynamical maps are defined and studied for quantum statistical physics based on Orlicz spaces. This complements earlier work [26] where we made a strong case for the assertion that
Dynamics and Potentials
For a system of spins and Fermions (satisfying graded commutation relations) on a lattice, a C*-dynamics can be associated with a potential, which has a natural convergence property and a very
A note on derivations of Murray–von Neumann algebras
TLDR
It is proved that the only derivation that maps a Murray–von Neumann algebra associated with a factor of type II1 into that factor is 0, and extensions of Singer’s seminal result answering a question of Kaplansky are applied to von Neumann algebras.
The role of type III factors in quantum field theory
Quantum Fokker-Planck models: the Lindblad and Wigner approaches
In this article we try to bridge the gap between the quantum dynamical semigroup and Wigner function approaches to quantum open systems. In particular we study stationary states and the long time
Diffusion for weakly coupled quantum oscillators
We construct a simple model which exhibits some of the properties discussed by van Hove in his study of the Pauli master equation. The model consists of an infinite chain of quantum oscillators which
Quasi-entropies for States of a von Neumann Algebra
In a general von Neumann algebra context the relative entropy of two states was defined and investigated by Araki ([3], see also [5]). When <p and w are normal states on a von Neuman algebra M the
ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
It is well known that the analysis of the large-time asymptotics of Fokker-Planck type equations by the entropy method is closely related to proving the validity of convex Sobolev inequalities. Here
On quantum statistical mechanics; A study guide
TLDR
The physical concepts and mathematical structures appearing in the analysis of large quantum systems, and their consequences include the emergence of algebraic approach and the necessity of employment of infinite dimensional structures are described.
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