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Quantum Simulation Entanglement Theory Quantum Correlations Open Quantum Systems Decoherence Quantum State Preparation Representation

The Quantum Liouville Equation is non-Liouvillian

arXiv
Authors: Dimitris Kakofengitis, Ole Steuernagel

Year

2014

Paper ID

46956

Status

Preprint

Abstract Read

~2 min

Abstract Words

110

Citations

N/A

Abstract

The Hamiltonian flow of a classical, time-independent, conservative system is incompressible, it is Liouvillian. The analog of Hamilton's equations of motion for a quantum-mechanical system is the quantum-Liouville equation. It is shown that its associated quantum flow in phase space, Wigner flow, is not incompressible. It gives rise to a quantum analog of classical Hamiltonian vector fields: the Wigner phase space velocity field bm w, the divergence of which can be unbounded. The loci of such unbounded divergence form lines in phase space which coincide with the lines of zero of the Wigner function. Along these lines exist characteristic pinch points which coincide with stagnation points of the Wigner flow.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • The Hamiltonian flow of a classical, time-independent, conservative system is incompressible, it is Liouvillian.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1410.4367 [2] arXiv https://arxiv.org/abs/1410.4367 [3] Publisher https://arxiv.org/abs/1410.4367

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