# Phase-space continuity equations for quantum decoherence, purity, von Neumann and Renyi entropies

@article{Bernardini2019PhasespaceCE, title={Phase-space continuity equations for quantum decoherence, purity, von Neumann and Renyi entropies}, author={Alex E. Bernardini and Orfeu Bertolami}, journal={Journal of Physics: Conference Series}, year={2019}, volume={1275} }

Phase-space features of the Wigner flow are examined so to provide a set of continuity equations that describe the flux of quantum information in the phase-space. The reported results suggest that the non-classicality profile of anharmonic (periodic) quantum systems can be consistently obtained in terms of the fluxes of probability, purity and von Neumann entropy. Extensions of the such phase-space quantifiers are also investigated in the context of the so-called Renyi entropy.

## 9 Citations

### Anharmonic effects on phase-space quantum profiles: an exact approach

- PhysicsJournal of Physics: Conference Series
- 2020

Given its well known spectral decomposition profile, the 1-dim harmonic oscillator potential modified by an inverse square (1-dim angular momentum-like) contribution works as an efficient platform…

### Noncommutative phase-space Lotka-Volterra dynamics: The quantum analog.

- PhysicsPhysical review. E
- 2022

The Lotka-Volterra (LV) dynamics is investigated in the framework of the Weyl-Wigner (WW) quantum mechanics extended to one-dimensional Hamiltonian systems, H(x,k) constrained by the ∂^{2}H/∂x∂k=0…

### Generalized phase-space description of nonlinear Hamiltonian systems and Harper-like dynamics

- PhysicsPhysical Review A
- 2022

Abstract Phase-space features of the Wigner flow for generic 1-dim systems with Hamiltonian, HW (q, p), constrained by the ∂2HW /∂q∂p = 0 condition are analytically obtained in terms of Wigner…

### Phase space formulation of the Abelian and non-Abelian quantum geometric tensor

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2020

The geometry of the parameter space is encoded by the quantum geometric tensor, which captures fundamental information about quantum states and contains both the quantum metric tensor and the…

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

- PhysicsPhysical Review Research
- 2022

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 about…

### Chiral magnetic effect out of equilibrium

- PhysicsPhysical Review D
- 2022

We consider relativistic fermionic systems in lattice regularization out of equilibrium. The chiral magnetic conductivity σ CME is calculated in spatially inﬁnite system for the case when the chiral…

## References

SHOWING 1-10 OF 13 REFERENCES

### Non-classicality from the phase-space flow analysis of the Weyl-Wigner quantum mechanics

- Physics
- 2017

A fluid analog of the information flux in the phase-space associated to purity and von Neumann entropy is identified in the Weyl-Wigner formalism of quantum mechanics. Once constrained by symmetry…

### Testing nonclassicality with exact Wigner currents for an anharmonic quantum system

- PhysicsPhysical Review A
- 2018

Phase-space features of the Wigner flow for an anharmonic quantum system driven by the harmonic oscillator potential modified by the addition of an inverse square (one-dimensional Coulomb-like)…

### Wigner flow reveals topological order in quantum phase space dynamics.

- PhysicsPhysical review letters
- 2013

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.

### Quantum to classical transition in the Hořava-Lifshitz quantum cosmology

- Physics
- 2018

A quasi-Gaussian quantum superposition of Hořava-Lifshitz (HL) stationary states is built in order to describe the transition of the quantum cosmological problem to the related classical dynamics.…

### Nonclassicality criteria from phase-space representations and information-theoretical constraints are maximally inequivalent.

- PhysicsPhysical review letters
- 2012

It is proved that the two defining criteria for defining the nonclassicality of bipartite bosonic quantum systems are maximally inequivalent, and suggested that there are other quantum correlations in nature than those revealed by entanglement and quantum discord.

### Quantum tunneling using entangled classical trajectories.

- PhysicsPhysical review letters
- 2001

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.

### On the quantum correction for thermodynamic equilibrium

- Mathematics
- 1932

The probability of a configuration is given in classical theory by the Boltzmann formula exp [— V/hT] where V is the potential energy of this configuration. For high temperatures this of course also…

### Quantum mechanics as a statistical theory

- PhysicsMathematical 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…

### Wigner functions and Weyl transforms for pedestrians

- Physics
- 2008

Wigner functions and Weyl transforms of operators offer a formulation of quantum mechanics that is equivalent to the standard approach given by the Schrodinger equation. We give a short introduction…

### Generation of nonclassical motional states of a trapped atom.

- PhysicsPhysical review letters
- 1996

The creation of thermal, Fock, coherent, and squeezed states of motion of a harmonically bound Be ion, which is trapped in the regime where the coupling between its motional and internal states can be described by a Jaynes-Cummings-type interaction.