scholarly journals Quantum chaos for two-dimensional Sinai billiard

2014 ◽  
Vol 63 (14) ◽  
pp. 140507
Author(s):  
Qin Chen-Chen ◽  
Yang Shuang-Bo
Keyword(s):  
Quantum Chaos ◽  
Two Dimensional ◽  
Sinai Billiard

QUANTUM CHAOS FOR THE VIBRATING RECTANGULAR BILLIARD

2001 ◽  
Vol 11 (09) ◽  
pp. 2317-2337 ◽  
Author(s):  
MASON A. PORTER ◽  
RICHARD L. LIBOFF
Keyword(s):  
Quantum Well ◽  
Quantum Number ◽  
Quantum Chaos ◽  
Evolution Equations ◽  
Necessary Conditions ◽  
Chaotic Behavior ◽  
Present System ◽  
Two Dimensional ◽  
Quantum Numbers ◽  
Superposition States

We consider oscillations of the length and width in rectangular quantum billiards, a two "degree-of-vibration" configuration. We consider several superpositon states and discuss the effects of symmetry (in terms of the relative values of the quantum numbers of the superposed states) on the resulting evolution equations and derive necessary conditions for quantum chaos for both separable and inseparable potentials. We extend this analysis to n-dimensional rectangular parallelepipeds with two degrees-of-vibration. We produce several sets of Poincaré maps corresponding to different projections and potentials in the two-dimensional case. Several of these display chaotic behavior. We distinguish between four types of behavior in the present system corresponding to the separability of the potential and the symmetry of the superposition states. In particular, we contrast harmonic and anharmonic potentials. We note that vibrating rectangular quantum billiards may be used as a model for quantum-well nanostructures of the stated geometry, and we observe chaotic behavior without passing to the semiclassical (ℏ → 0) or high quantum-number limits.

scholarly journals Two-dimensional Scattering by a Potential without a Classical Analogue

1999 ◽  
Vol 52 (5) ◽  
pp. 859 ◽  
Author(s):  
I. V. Ponomarev
Keyword(s):  
Quantum Chaos ◽  
Matrix Theory ◽  
Delta Function ◽  
Two Dimensional ◽  
Dirac Delta ◽  
S Matrix ◽  
Classical Analogue ◽  
Scattering Potential ◽  
The One ◽  
The Given

A two-dimensional scattering potential represents the quantum extension of a diffractive lattice: a Dirac delta function with a modulated permeability along the y-axis. This model does not have an explicit classical analogue and quantum effects such as tunneling and diffraction play an important role. An analytical solution for the one-harmonic case is found. For the general case of an arbitrary number of harmonics a simple criterion is derived for the range of parameters where quantum chaos is permitted (but does not necessarily occur). The statistical properties of the S-matrix for the given model have been investigated. The deviations from the usual predictions for irregular scattering in the random matrix theory (RMT) framework have been found and are discussed.

scholarly journals Quantum chaos inside space-temporal Sinai billiards

2016 ◽  
Vol 13 (06) ◽  
pp. 1650082 ◽  
Author(s):  
Andrea Addazi
Keyword(s):  
Quantum Chaos ◽  
Time Delays ◽  
Relativistic Quantum ◽  
Relativistic Quantum Field Theory ◽  
Naked Singularities ◽  
Sinai Billiards ◽  
Sinai Billiard ◽  
General Aspects ◽  
Scattering Time ◽  
Semiclassical Regime

We discuss general aspects of non-relativistic quantum chaos theory of scattering of a quantum particle on a system of a large number of naked singularities. We define such a system space-temporal Sinai billiard. We discuss the problem in semiclassical approach. We show that in semiclassical regime the formation of trapped periodic semiclassical orbits inside the system is unavoidable. This leads to general expression of survival probabilities and scattering time delays, expanded to the chaotic Pollicott–Ruelle resonances. Finally, we comment on possible generalizations of these aspects to relativistic quantum field theory.

scholarly journals On the Entropy of a One-Dimensional Gas with and without Mixing Using Sinai Billiard

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1188
Author(s):  
Alexander Sobol ◽  
Peter Güntert ◽  
Roland Riek
Keyword(s):  
Probability Distributions ◽  
Dimensional System ◽  
Strongly Correlated ◽  
Two Dimensional ◽  
One Dimensional ◽  
Point Particles ◽  
Sinai Billiard ◽  
Finite Space ◽  
The One ◽  
Special Case

A one-dimensional gas comprising N point particles undergoing elastic collisions within a finite space described by a Sinai billiard generating identical dynamical trajectories are calculated and analyzed with regard to strict extensivity of the entropy definitions of Boltzmann–Gibbs. Due to the collisions, trajectories of gas particles are strongly correlated and exhibit both chaotic and periodic properties. Probability distributions for the position of each particle in the one-dimensional gas can be obtained analytically, elucidating that the entropy in this special case is extensive at any given number N. Furthermore, the entropy obtained can be interpreted as a measure of the extent of interactions between molecules. The results obtained for the non-mixable one-dimensional system are generalized to mixable one- and two-dimensional systems, the latter by a simple example only providing similar findings.

scholarly journals REGULARIZATION OF TUNNELING RATES WITH QUANTUM CHAOS

2012 ◽  
Vol 22 (10) ◽  
pp. 1250247 ◽  
Author(s):  
LOUIS M. PECORA ◽  
HOSHIK LEE ◽  
DONG-HO WU
Keyword(s):  
Quantum Chaos ◽  
Chaotic Behavior ◽  
Energy Splitting ◽  
Energy Relation ◽  
Antisymmetric State ◽  
Sinai Billiard ◽  
Classical Behavior ◽  
To Come ◽  
Double Wells ◽  
Tunneling Rates

We study tunneling in various shaped, closed, two-dimensional, flat-potential, double wells by calculating the energy splitting between symmetric and antisymmetric state pairs. For shapes that have regular or nearly regular classical behavior (e.g. rectangular or circular) the tunneling rates vary greatly over wide ranges often by several orders of magnitude. However, for well shapes that admit more classically chaotic behavior (e.g. the stadium, the Sinai billiard) the range of tunneling rates narrows, often by orders of magnitude. This dramatic narrowing appears to come from destabilization of periodic orbits in the regular wells that produce the largest and smallest tunneling rates and causes the splitting versus energy relation to take on a possibly universal shape. It is in this sense that we say the quantum chaos regularizes the tunneling rates.

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

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