Phase-space treatment of the driven quantum harmonic oscillator

Xianghong Hu, Shuning Sun, Yujun Zheng

In this paper, we present the theoretical framework of quantum speed limits (QSLs) in terms of trajectory ensembles in phase space. This indicates that the QSL can be thought of as the summation of the connecting harmonic oscillators: the connections between the points of the system in phase space and the trajectory ensemble. Two typical models, the time-dependent harmonic oscillator and the undriven harmonic oscillator coupled to a thermal bath, are investigated by employing the theoretical framework. Our results from this perspective are in agreement with previous treatments.

Ursula Carow-Watamura, Satoshi Watamura

Leila Khiari, Tahar Boudjedaa, Abdenacer Makhlouf +1 more

The purpose of this paper is the description of Berry’s phase, in the Euclidean Path Integral formalism, for 2D quadratic system: two time dependent coupled harmonic oscillators. This treatment is achieved by using the adiabatic approximation in the commutative and noncommutative phase space

R. Shepard Scott

Sebastian Deffner

A fluctuation theorem for the nonequilibrium entropy production in quantum phase space is derived, which enables the consistent thermodynamic description of arbitrary quantum systems, open and closed. The new treatment naturally generalizes classical results to the quantum domain. As an illustration the harmonic oscillator dragged through a thermal bath is solved numerically. Finally, the significance of the new approach is discussed in detail, and the phase space treatment is opposed to the two-time energy measurement approach.

Michele Cini