Constant-temperature dynamics in the Wigner representation of quantum mechanics.

Valerian I. Tatarskii

Alessandro Sergi, Francesco Petruccione

Thermal fluctuations in time-dependent quantum processes are treated by a constant-temperature generalization of Wigner's formulation of quantum mechanics in phase space. To this end, quantum Nosè–Hoover dynamics is defined by generalizing the Moyal bracket. Computational applications of the formalism, together with further theoretical developments, are discussed.

Dimitris Kakofengitis, Ole Steuernagel

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 details of quantum dynamics —finer than is ordinarily thought accessible according to quantum folklore invoking Heisenberg’s uncertainty principle. Here, we focus on the simplest, most intuitive, and analytically accessible aspects of J. We investigate features of J for bound states of time-reversible, weakly-anharmonic one-dimensional quantum-mechanical systems which are weakly-excited. We establish that weakly-anharmonic potentials can be grouped into three distinct classes: hard, soft, and odd potentials. We stress connections between each other and the harmonic case. We show that their Wigner current fieldline patterns can be characterised by J’s discrete stagnation points, how these arise and how a quantum system’s dynamics is constrained by the stagnation points’ topological charge conservation. We additionally show that quantum dynamics in phase space, in the case of vanishing Planck constant ℏ or vanishing anharmonicity, does not pointwise converge to classical dynamics.

Theoretical Physics

张晓燕 ZHANG Xiao-yan, 王继锁 WANG Ji-suo

By virtue of the thermo field dynamics and the coherent thermo state representation,the Wigner function of mesoscopic RLC circuit at finite temperature was obtained,and the quantum fluctuations of mesoscopic RLC circuit at finite temperature were studied.By means of the Weyl correspondence and Wigner theorem the marginal distribution of Wigner function in mesoscopic RLC circuit was discussed.The physical meaning of marginal distributions′ statistical average of the Wigner function was explained.The results show that the quantum fluctuations of both charge and current of mesoscopic RLC circuit at finite temperature increase with the rising of temperature and resistance value,and the mesoscopic RLC circuit has squeezed effects between charge and current,caused by the quantum mechanical zero-point fluctuations;the marginal distributions′ statistical averages of the Wigner function are the energy stored in capacity and in inductance of the mesoscopic RLC circuit,respectively.

William K. Wootters