Anharmonic quantum mechanical systems do not feature phase space trajectories

@article{Oliva2018AnharmonicQM,
  title={Anharmonic quantum mechanical systems do not feature phase space trajectories},
  author={Maxime Oliva and Dimitris Kakofengitis and Ole Steuernagel},
  journal={Physica A: Statistical Mechanics and its Applications},
  year={2018}
}

Figures from this paper

Joint quantum–classical Hamilton variational principle in the phase space

We show that the dynamics of a closed quantum system obeys the Hamilton variational principle. Even though quantum particles lack well-defined trajectories, their evolution in the Husimi

Dynamic Shear Suppression in Quantum Phase Space.

Classical phase space flow is inviscid. Here we show that in quantum phase space Wigner's probability current J can be effectively viscous. This results in shear suppression in quantum phase space

A kinetic theory for quantum information transport

In this work we build a theoretical framework for the transport of information in quantum systems. This is a framework aimed at describing how out of equilibrium open quantum systems move information

Quantum and semiclassical dynamics as fluid theories where gauge matters

The family of trajectories-based approximations employed in computational quantum physics and chemistry is very diverse. For instance, Bohmian and Heller's frozen Gaussian semiclassical trajectories

Entropy nonconservation and boundary conditions for Hamiltonian dynamical systems.

TLDR
It is shown that the boundary conditions for a tunneling quantum system become the criteria for entropy preservation in the classical limit, highlighting how boundary effects drastically change the nature of a system.

Classical Propagation in the Quantum Inverted Oscillator

We emphasize the fact the evolution of quantum states in the inverted oscillator (IO) is reduced to classical equations of motion, stressing that the corresponding tunnelling and reflexion

Long-time semiclassical evolution of spinlike systems from Majorana sampling

We propose an approach to the analysis of the semiclassical evolution of spinlike systems. We show that an appropriate discretization of distributions in classical phase space (in this case the

Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems

TLDR
The semi-classical limit of the generalized SO(3) map is applied for representation of variable-spin systems in a four-dimensional symplectic manifold and one of the classical dynamic variables is “quantized” and a discretized version of the Truncated Wigner Approximation is introduced.

Entropy transfer from a quantum particle to a classical coherent light field

In the field of light-matter interactions, it is often assumed that a classical light field that interacts with a quantum particle remains almost unchanged and thus contains nearly no information

References

SHOWING 1-10 OF 104 REFERENCES

Wigner flow reveals topological order in quantum phase space dynamics.

TLDR
The flow that is the quantum analog of classical particle flow along phase portrait lines is identified, which reveals hidden features of quantum dynamics and extra complexity and reveals fundamental topological order in quantum dynamics that has so far gone unnoticed.

Tunneling Dynamics Using Classical-like Trajectories with an Effective Quantum Force

We develop an effective quantum force to propagate trajectories in Wigner phase space. In this way, the quantum entanglement between trajectories is represented by the effective quantum force, which

Simulation of quantum processes using entangled trajectory molecular dynamics

In this paper, we describe a new method for simulating quantum processes using classical-like molecular dynamics. The approach is based on solving the quantum Liouville equation in the Wigner

Quantum tunneling using entangled classical trajectories.

TLDR
A new method for simulating quantum processes in the context of classical molecular dynamics simulations based on solving numerically the quantum Liouville equation in the Wigner representation using ensembles of classical trajectories yields excellent agreement with exact quantum calculations.

Wigner’s quantum phase-space current in weakly-anharmonic weakly-excited two-state systems

Abstract.There are no phase-space trajectories for anharmonic quantum systems, but Wigner’s phase-space representation of quantum mechanics features Wigner current J . This current reveals fine

Phase Space Descriptions of Quantum Phenomena

In this paper we show the deep connection between the WignerMoyal approach and the Bohm approach to quantum mechanics. We point out that the key equations used in the Bohm approach were already

Time-dependent quantum-mechanical methods for molecular dynamics

The basic framework of time-dependent quantum-mechanical methods for molecular dynamics calculations is described. The central problem addressed by computational methods is a discrete representation

Quantum collision theory with phase-space distributions

Quantum-mechanical phase-space distributions, introduced by Wigner in 1932, provide an intuitive alternative to the usual wave-function approach to problems in scattering and reaction theory. The aim

Quantum mechanics as a statistical theory

  • J. E. Moyal
  • Physics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1949
An attempt is made to interpret quantum mechanics as a statistical theory, or more exactly as a form of non-deterministic statistical dynamics. The paper falls into three parts. In the first, the
...