Related papers: Quantum Chaos, Degeneracies and Exceptional Points

We utilize degenerate perturbation theory to investigate continuous-time quantum search on second-order truncated simplex lattices. In this work, we show that the construction of the Hamiltonian must consider the structure of the lattice.…

A broad family of phase transitions in the closed as well as open quantum systems is known to be mediated by a non-Hermitian degeneracy (a.k.a. exceptional point, EP) of the Hamiltonian. In the EP limit, in general, the merger of an…

Quantum chaos is presented as a paradigm of information processing by dynamical systems at the bottom of the range of phase-space scales. Starting with a brief review of classical chaos as entropy flow from micro- to macro-scales, I argue…

This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the…

Decoherence of a quantum system (which then starts to display classical features) results from the interaction of the system with the environment, and is well described in the framework of the theory of continuous quantum measurements…

I study the scaling behavior in the physical parameters of dynamical entropies, classical and quantum, in a specifically devised model of collision-induced decoherence in a chaotic system. The treatment is fully canonical and no…

Black hole perturbation theory beyond second order is not well understood because typically one defines the meaning of gauge invariance order by order which is ambiguous. In this series of works we therefore developed a new approach which…

Chaos in both dissipative systems and conservative systems is investigated on the approach of renormalization group. It is found that the chaos is regarded as the critical phenomenon of equilibrium statistics in phase space. The two…

An extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter…

Quantum chaos, a phenomenon that began to be studied in the last century, still does not have a rigorous understanding. By virtue of the correspondence principle, the properties of the system that lead to chaotic dynamics at the classical…

Our account of the problem of the classical limit of quantum mechanics involves two elements. The first one is self-induced decoherence, conceived as a process that depends on the own dynamics of a closed quantum system governed by a…

First order quantum phase transition (QPT) between spherical and axially deformed nuclei shows coexisting, but well-separated regions of regular and chaotic dynamics. We employ a Hamiltonian of the Arima-Iachello Interacting Boson Model…

Quantum phase transition is interpreted as an evolution, at the end of which a parameter-dependent Hamiltonian $H(g)$ loses its observability. In the language of mathematics, such a quantum catastrophe occurs at an exceptional point of…

Quantum decoherence refers to the phenomenon when the interaction of a quantum system with its environment results in the degradation of quantum coherence. Decoherence is considered to be the most popular mechanism responsible for the…

We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…

It is believed that classical behavior emerges in a quantum system due to decoherence. It has also been proposed that gravity can be a source of this decoherence. We examine this in detail by studying a number of quantum systems, including…

An adiabatic change of a bound state along a closed circuit in the parameter space can induces holonomies not only in the phase of the state, but also in the associated eigenspace and eigenvalue. The former is the well-known Berry phase…

Classical chaotic dynamics is characterized by the exponential sensitivity to initial conditions. Quantum mechanics, however, does not show this feature. We consider instead the sensitivity of quantum evolution to perturbations in the…

We study the competing order and chaos in a first-order quantum phase transition with a high barrier. The boson model Hamiltonian employed, interpolates between its U(5) (spherical) and SU(3) (deformed) limits. A classical analysis reveals…

The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…