相关论文: Quantum Poincar\'e Recurrences
We first compare the mathematical structure of quantum and classical mechanics when both are formulated in a C*-algebraic framework. By using finite von Neumann algebras, a quantum mechanical analogue of Liouville's theorem is then…
A high dimensional dynamical system is often studied by experimentalists through the measurement of a relatively low number of different quantities, called an observation. Following this idea and in the continuity of Boshernitzan's work,…
The understanding of the asymptotic decay of correlations and of the distribution of Poincar\'e recurrence times $P(t)$ has been a major challenge in the field of Hamiltonian chaos for more than two decades. In a recent Letter, Chirikov and…
Post-exponential decay of the probability density of a quantum particle leaving a trap can be reproduced accurately, except for interference oscillations at the transition to the post-exponential regime, by means of an ensemble of classical…
Statistics of Poincar\' e recurrence for a class of circle maps, including sub-critical, critical, and super-critical cases, are studied. It is shown how the topological differences in the various types of the dynamics are manifested in the…
Quantum (Poincar\'e) recurrence theorem are known for closed quantum (classical) systems. Can recurrence happen in open systems? We provide the recurrence theorem for open quantum systems via non-Hermitian (NH) description. We find that PT…
We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting…
We propose a definition for the P\'olya number of continuous-time quantum walks to characterize their recurrence properties. The definition involves a series of measurements on the system, each carried out on a different member from an…
We predict and numerically observe strong periodic orbit effects in the properties of open quantum systems with a chaotic classical limit. Antiscars lead to a large number of exponentially narrow resonances when the opening is located on a…
We study the asymptotic long-time behavior of open quantum maps and relate the decays to the eigenvalues of a coarse-grained superoperator. In specific ranges of coarse graining, and for chaotic maps, these decay rates are given by the…
One of the important questions in statistical mechanics is how irreversibility (time's arrow) occurs when Newton equations of motion are time reversal invariant. One objection to irreversibility is based on Poincar\'e's recursion theorem: a…
We analyze the recurrence probability (P\'olya number) for d-dimensional unbiased quantum walks. A sufficient condition for a quantum walk to be recurrent is derived. As a by-product we find a simple criterion for localisation of quantum…
Universal $T$-matrices, or Hopf algebra dual forms, for quantum groups are revisited, and their contraction theory is developed. As a first illustrative example, the (1+1) timelike $\kappa$-Poincar\'e $T$-matrix is explicitly worked out.…
Understanding stickiness and power-law behavior of Poincar\'e recurrence statistics is an open problem for higher-dimensional systems, in contrast to the well-understood case of systems with two degrees-of-freedom. We study such…
For chaotic classical systems, the distribution of return times to a small region of phase space is universal. We propose a simple tool to investigate multiple returns in quantum systems. Numerical evidence for the baker map and kicked top…
In this paper by using geometric techniques, we provide upper bounds for the Poincar\'e recurrence time of a quantum mixed state with discrete spectrum of energies. In the case of discrete but finite spectrum we obtain two type of upper…
Decoherence in quantum systems which are classically chaotic is studied. It is well-known that a classically chaotic system when quantized loses many prominent chaotic traits. We show that interaction of the quantum system with an…
We study the time dependence of the ionization probability of Rydberg atoms driven by a microwave field. The quantum survival probability follows the classical one up to the Heisenberg time and then decays inversely proportional to time,…
The quantum mechanical decay of two or more overlapped resonances in a common continuum is largely influenced by Fano interference, leading to important phenomena such as the existence of bound states in the continuum, fractional decay and…
The mechanism of the exponential transient statistics of Poincar\'e recurrences in the presence of chaos border with its critical structure is studied using two simple models: separatrix map and the kicked rotator ('microtron'). For the…