Quantum evolution as a nonlinear Markov process

Jun-Qing Cheng, Guoqing Zhang, Jing‐Bo Xu

We investigate the quantum evolution speed of a qubit in two kinds of finite-temperature environments. For the first bosonic bath with an ohmic-like spectrum, the high temperature leads to not only the speed-up but also speed-down processes in the weak-coupling regime, which is different from the strong-coupling case, in which only the speed-up process is exhibited. Furthermore, we realize the controllable and stationary quantum evolution speed by applying the bang-bang pulse. For the second nonlinear bath, we study the quantum evolution speed by resorting to the hierarchical equations of a motion method beyond the Born–Markov approximation. It is shown that the quantum evolution speed can be decelerated by the rise of temperature in the strong-coupling regime, which is an anomalous phenomenon and contrary to the common recognition that quantum evolution speed always increases with the temperature.

Dariusz Chruściński, Andrzej Kossakowski

Dariusz Chruściński, Andrzej Kossakowski

Carlos M. Mora, Rolando Rebolledo

The paper is devoted to the study of nonlinear stochastic Schrödinger equations driven by standard cylindrical Brownian motions (NSSEs) arising from the unraveling of quantum master equations. Under the Born--Markov approximations, this class of stochastic evolutions equations on Hilbert spaces provides characterizations of both continuous quantum measurement processes and the evolution of quantum systems. First, we deal with the existence and uniqueness of regular solutions to NSSEs. Second, we provide two general criteria for the existence of regular invariant measures for NSSEs. We apply our results to a forced and damped quantum oscillator.

Carlos M. Mora, Rolando Rebolledo

The paper is devoted to the study of nonlinear stochastic Schrödinger equations driven by standard cylindrical Brownian motions (NSSEs) arising from the unraveling of quantum master equations. Under the Born–Markov approximations, this class of stochastic evolutions equations on Hilbert spaces provides characterizations of both continuous quantum measurement processes and the evolution of quantum systems. First, we deal with the existence and uniqueness of regular solutions to NSSEs. Second, we provide two general criteria for the existence of regular invariant measures for NSSEs. We apply our results to a forced and damped quantum oscillator.

G. O. S. Ekhaguere