6,991 research outputs found
On a Linear Chaotic Quantum Harmonic Oscillator
We show that a linear quantum harmonic oscillator is chaotic in the sense of
Li-Yorke. We also prove that the weighted backward shift map, used as an
infinite dimensional linear chaos model, in a separable Hilbert space is
chaotic in the sense of Li-Yorke, in addition to being chaotic in the sense of
Devaney.Comment: LaTex file. Applied Mathematics Letters, to appea
Out-of-time-order correlators in quantum mechanics
The out-of-time-order correlator (OTOC) is considered as a measure of quantum
chaos. We formulate how to calculate the OTOC for quantum mechanics with a
general Hamiltonian. We demonstrate explicit calculations of OTOCs for a
harmonic oscillator, a particle in a one-dimensional box, a circle billiard and
stadium billiards. For the first two cases, OTOCs are periodic in time because
of their commensurable energy spectra. For the circle and stadium billiards,
they are not recursive but saturate to constant values which are linear in
temperature. Although the stadium billiard is a typical example of the
classical chaos, an expected exponential growth of the OTOC is not found. We
also discuss the classical limit of the OTOC. Analysis of a time evolution of a
wavepacket in a box shows that the OTOC can deviate from its classical value at
a time much earlier than the Ehrenfest time.Comment: 30 pages, 13 figure
Dynamical Stability and Quantum Chaos of Ions in a Linear Trap
The realization of a paradigm chaotic system, namely the harmonically driven
oscillator, in the quantum domain using cold trapped ions driven by lasers is
theoretically investigated. The simplest characteristics of regular and chaotic
dynamics are calculated. The possibilities of experimental realization are
discussed.Comment: 24 pages, 17 figures, submitted to Phys. Rev
Generating Finite Dimensional Integrable Nonlinear Dynamical Systems
In this article, we present a brief overview of some of the recent progress
made in identifying and generating finite dimensional integrable nonlinear
dynamical systems, exhibiting interesting oscillatory and other solution
properties, including quantum aspects. Particularly we concentrate on Lienard
type nonlinear oscillators and their generalizations and coupled versions.
Specific systems include Mathews-Lakshmanan oscillators, modified Emden
equations, isochronous oscillators and generalizations. Nonstandard Lagrangian
and Hamiltonian formulations of some of these systems are also briefly touched
upon. Nonlocal transformations and linearization aspects are also discussed.Comment: To appear in Eur. Phys. J - ST 222, 665 (2013
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