Related papers: An Introduction to Quantum Chaos
Chaos transition, as an important topic, has become an active research subject in non-linear science. By considering a Dicke Hamiltonian coupled to a bath of harmonic oscillator, we have been able to introduce a logistic map with quantum…
The emergence of chaotic phenomena in a quantum system has long been an elusive subject. Experimental progresses in this subject have become urgently needed in recent years, when considerable theoretical studies have unveiled the vital…
We establish the emergence of chaotic motion in optomechanical systems. Chaos appears at negative detuning for experimentally accessible values of the pump power and other system parameters. We describe the sequence of period doubling…
The interplay between classical chaos and quantum tunneling is examined in driven nonlinear systems, with emphasis on how semi classical phase space structures influence purely quantum transport phenomena. We show that, in the presence of…
We address the problem of quantum chaos: Is there a rigorous, physically meaningful definition of chaos in quantum physics? Can the tools of classical chaos theory, like Lyapunov exponents, Poincar\'e sections etc. be carried over to…
In recent years, analysis and control of quantum chaos are increasingly important, but the lack of the concept of trajectory makes it impossible to analyze quantum chaos by the methods used in classical chaos. This research aims to connect…
The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation --…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
Dissipative quantum chaos is an emerging theory that is expected to extend the ideas, concepts, and methodology of conventional Hamiltonian quantum chaos from coherent evolution to open quantum dynamics. The new theory should provide a set…
We introduce an analytical solution to the one of the most familiar problems from the elementary quantum mechanics textbooks. The following discussion provides simple illustrations to a number of general concepts of quantum chaology, along…
We explore the border between regular and chaotic quantum dynamics, characterized by a power law decrease in the overlap between a state evolved under chaotic dynamics and the same state evolved under a slightly perturbed dynamics. This…
Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
The subject area referred to as "wave chaos", "quantum chaos" or "quantum chaology" has been investigated mostly by the theoretical physics community in the last 30 years. The questions it raises have more recently also attracted the…
This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
We propose a formalism which makes the chaos to be quantized. Quantum mechanical equation is derived for describing the chaos for a particle moving in an electromagnetic field.
The quantum and classical dynamics of particles kicked by a gaussian attractive potential are studied. Classically, it is an open mixed system (the motion in some parts of the phase space is chaotic, and in some parts it is regular). The…
Some intriging connections between the properties of nonlinear noise driven systems and the nonlinear dynamics of a particular set of Hamilton's equation are discussed. A large class of Fokker-Planck Equations, like the Schr\"odinger…
This article is the written version of a talk delivered at the Bexbach Colloquium of Science 2000 and starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…