Microscopic analysis of the microscopic reversibility in quantum systems

We investigate the robustness of the microscopic reversibility in open quantum systems which is discussed by Monnai [arXiv:1106.1982 (2011)]. We derive an exact relation between the forward transition probability and the reversed transition probability in the case of a general measurement basis. We show that the microscopic reversibility acquires some corrections in general and discuss the physical meaning of the corrections. Under certain processes, some of the correction terms vanish and we numerically confirmed that the remaining correction term becomes negligible; the microscopic reversibility almost holds even when the local system cannot be regarded as macroscopic.Comment: 12 pages, 10 figure

Complexity of Quantum States and Reversibility of Quantum Motion

We present a quantitative analysis of the reversibility properties of classically chaotic quantum motion. We analyze the connection between reversibility and the rate at which a quantum state acquires a more and more complicated structure in its time evolution. This complexity is characterized by the number ${\cal M}(t)$ of harmonics of the (initially isotropic, i.e. ${\cal M}(0)=0$) Wigner function, which are generated during quantum evolution for the time $t$. We show that, in contrast to the classical exponential increase, this number can grow not faster than linearly and then relate this fact with the degree of reversibility of the quantum motion. To explore the reversibility we reverse the quantum evolution at some moment $T$ immediately after applying at this moment an instant perturbation governed by a strength parameter $\xi$. It follows that there exists a critical perturbation strength, $\xi_c\approx \sqrt{2}/{\cal M}(T)$, below which the initial state is well recovered, whereas reversibility disappears when $\xi\gtrsim \xi_c(T)$. In the classical limit the number of harmonics proliferates exponentially with time and the motion becomes practically irreversible. The above results are illustrated in the example of the kicked quartic oscillator model.Comment: 15 pages, 13 figures; the list of references is update

Reversibility of laser filamentation

We investigate the reversibility of laser filamentation, a self-sustained, non-linear propagation regime including dissipation and time-retarded effects. We show that even losses related to ionization marginally affect the possibility of reverse propagating ultrashort pulses back to the initial conditions, although they make it prone to finite-distance blow-up susceptible to prevent backward propagation.Comment: 12 pages, 3 figure

Reversibility Violation in the Hybrid Monte Carlo Algorithm

We investigate reversibility violations in the Hybrid Monte Carlo algorithm. Those violations are inevitable when computers with finite numerical precision are being used. In SU(2) gauge theory, we study the dependence of observables on the size of the reversibility violations. While we cannot find any statistically significant deviation in observables related to the simulated physical model, algorithmic specific observables signal an upper bound for reversibility violations below which simulations appear unproblematic. This empirically derived condition is independent of problem size and parameter values, at least in the range of parameters studied here.Comment: 17 pages, 5 figures, typos corrected, comment added, matches published versio