Related papers: Chaos in M(atrix) Theory
Classical dynamics in SU(2) Matrix theory is investigated. A classical chaos-order transition is found. For the angular momentum small enough (even for small coupling constant) the system exhibits a chaotic behavior, for angular momentum…
Consider a classically chaotic system which is described by a Hamiltonian H_0. At t=0 the Hamiltonian undergoes a sudden-change H_0 -> H. We consider the quantum-mechanical spreading of the evolving energy distribution, and argue that it…
Trajectories in the space of the unitarily inequivalent representations of the canonical commutation relations are shown to be classical trajectories. Under convenient conditions, they may exhibit properties typical of chaotic behavior in…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
I describe the footprints of the classical chaos of the Yang-Mills fields in the quantum description. I also review the behavior of the BKL chaotic approach to the classical singularity on the basis of the Loop Quantum Gravity.
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
Phase space representations of the dynamics of the quantal and classical cat map are used to explore quantum--classical correspondence in a K-system: as $\hbar \to 0$, the classical chaotic behavior is shown to emerge smoothly and exactly.…
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…
We extract the information of a quantum motion and decode it into a certain orbit via a single measurable quantity. Such that a quantum chaotic system can be reconstructed as a chaotic attractor. Two configurations for reconstructing this…
The maximally chaotic dynamical systems (DS) are the systems which have nonzero Kolmogorov entropy. The Anosov C-condition defines a reach class of hyperbolic dynamical systems that have exponential instability of the phase trajectories and…
Spatio-temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio-temporally periodic solutions. The periodic orbit theory yields the global averages characterizing the chaotic…
The effective dynamics of a slow classical system coupled to a fast chaotic environment is described by means of a Master equation. We show how this approach permits a very simple derivation of geometric magnetism.
We investigate the dynamics of classical and quantum N-component phi^4 oscillators in the presence of an external field. In the large N limit the effective dynamics is described by two-degree-of-freedom classical Hamiltonian systems. In the…
We have identified ultra-cold atoms in magneto-optical double-well potentials as a very clean setting in which to study the quantum and classical dynamics of a nonlinear system with multiple degrees of freedom. In this system, entanglement…
The interaction of an atom with an electromagnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electromagnetic fields helps to design the quantum analog of…
The classical invariants of a Hamiltonian system are expected to be derivable from the respective quantum spectrum. In fact, semiclassical expressions relate periodic orbits with eigenfunctions and eigenenergies of classical chaotic…
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…
Chaos is an important characterization of classical dynamical systems. How is chaos linked to the long-time dynamics of collective modes across phases and phase transitions? We address this by studying chaos across Ising and…
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…
In quantum many-body theory no generic microscopic principle at the origin of complex dynamics is known. Quite opposed, in classical mechanics the theory of non-linear dynamics provides a detailed framework for the distinction between…