相关论文: Classical singularities and Semi-Poisson statistic…

A semi-classical non-Hamiltonian model of a spontaneous collapse of unstable quantum system is given. The time evolution of the system becomes non-Hamiltonian at random instants of transition of pure states to reduced ones, given by a…

Integrability is a cornerstone of classical mechanics, where it has a precise meaning. Extending this notion to quantum systems, however, remains subtle and unresolved. In particular, deciding whether a quantum Hamiltonian - viewed simply…

The classical trajectories of the family of complex PT-symmetric Hamiltonians $H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) form closed orbits. All such complex orbits that have been studied in the past are PT symmetric (left-right symmetric).…

The impression gained from the literature published to date is that the spectrum of the stadium billiard can be adequately described, semiclassically, by the Gutzwiller periodic orbit trace formula together with a modified treatment of the…

A non-Hermitian operator that is related to its adjoint through a similarity transformation is defined as a pseudo-Hermitian operator. We study the level-statistics of a pseudo-Hermitian Dicke Hamiltonian that undergoes Quantum Phase…

Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…

The surprisingly long-lasting oscillations observed in the dynamics of highly excited states of chains of Rydberg atoms defy the expectation that interacting systems should thermalize fast. The phenomenon is reminiscent of wavepackets in…

This paper reviews the physics of quantum disorder in relation with a series of experiments using laser-cooled atoms exposed to "kicks" of a standing wave, realizing a paradigmatic model of quantum chaos, the kicked rotor. This dynamical…

Quantum walks are at present an active field of study in mathematics, with important applications in quantum information and statistical physics. In this paper, we determine the influence of basic chaotic features on the walker behavior.…

The nearest-neighbor level-spacing distributions are a fundamental quantity of disordered systems and universal. It is well-known that extended and localized states of random Hermitian systems follow the Wigner-Dyson and the Poison…

Understanding how physical systems are influenced by disorder is a fundamental challenge in quantum science. Addressing its effects often involves numerical averaging over a large number of samples, and it is not always easy to gain an…

The one parameter scaling theory is a powerful tool to investigate Anderson localization effects in disordered systems. In this paper we show this theory can be adapted to the context of quantum chaos provided that the classical phase space…

Classical chaos arises from the inherent non-linearity of dynamical systems. However, quantum maps are linear; therefore, the definition of chaos is not straightforward. To address this, we study a quantum system that exhibits chaotic…

We report on recent results on the spectral statistics of the discrete Anderson model in the localized phase. Our results show, in particular, that, for the discrete Anderson Hamiltonian with smoothly distributed random potential at…

In a fully 3-D system such as a stellarator, the toroidal mode number $n$ ceases to be a good quantum number--all $n$s within a given mode family being coupled. It is found that the discrete spectrum of unstable ideal MHD…

An initial coherent state is propagated exactly by a kicked quantum Hamiltonian and its associated classical stroboscopic map. The classical trajectories within the initial state are regular for low kicking strengths, then bifurcate and…

Diffractive systems are quantum-mechanical models with point-like singularities where usual semiclassical approximation breaks down. An overview of recent investigations of such systems is presented. The following examples are considered in…

We propose a plasma model for spectral statistics displaying level repulsion without long-range spectral rigidity, i.e. statistics intermediate between random matrix and Poisson statistics similar to the ones found numerically at the…

We investigate the spontaneous parity-time (PT )-symmetry breaking and spectral properties of a PT symmetric quantum kicked rotor under resonance conditions. At resonance, the QKR reduces to a finite-dimensional system. In the localized…

We derive analytic expressions for the wavefunctions and energy levels in the semiclassical approximation for perturbed integrable systems. We find that some eigenstates of such systems are substantially different from any of the…