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.

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.

QUANTUM CHAOS IN NON-SYMMETRIC POTENTIAL WELL IN A TILTED MAGNETIC FIELD

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2752-2756 ◽  
Author(s):  
GUOYONG YUAN ◽  
SHIPING YANG ◽  
HONGLING FAN ◽  
HONG CHANG
Keyword(s):  
Magnetic Field ◽  
Quantum Chaos ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Potential Well ◽  
Symmetric Potential ◽  
Tunnelling Effect ◽  
Non Linear ◽  
Spectral Statistics ◽  
Tilted Magnetic Field

In this paper, the dynamical behavior of a non-symmetric double potential well in a tilted magnetic field is studied. The classical Poincare section is given to exhibit the chaotic behavior of the system, and non-linear resonant lead to chaos. The paper has also given the energy spectral statistics which satisfies Brody's distribution, tunnelling effect develops quantum chaos and also holds back the development of chaos.

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

scholarly journals A sharp transition in quantum chaos and thermodynamics of mass deformed SYK model

2021 ◽  
Author(s):  
Tomoki Nosaka
Keyword(s):  
Field Theory ◽  
Phase Transition ◽  
Black Hole ◽  
Transition Temperature ◽  
Quantum Chaos ◽  
Chaotic Behavior ◽  
Sharp Transition ◽  
Bilocal Field ◽  
Hole Geometry ◽  
Field Formalism

We review our recent work [1] where we studied the chaotic property of the two coupled Sachdev-Ye-Kitaev systems exhibiting a Hawking-Page like phase transition. By computing the out-of-time-ordered correlator in the large NN limit by using the bilocal field formalism, we found that the chaos exponent of this model shows a discontinuous fall-off at the phase transition temperature. Hence in this model the Hawking-Page like transition is correlated with a transition in chaoticity, as expected from the relation between a black hole geometry and the chaotic behavior in the dual field theory.

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 Partial dynamical symmetry versus quasi dynamical symmetry examination within a quantum chaos analyses of spectral data for even–even nuclei

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
H. Sabri ◽  
S. K. Mousavi Mobarakeh ◽  
A. J. Majarshin ◽  
Yan-An Luo ◽  
Feng Pan
Keyword(s):  
Quantum Chaos ◽  
Nearest Neighbor ◽  
Matrix Theory ◽  
Chaotic Behavior ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Mass Region ◽  
Band Head ◽  
Symmetry Limit ◽  
Rotational Bands

AbstractStatistical analyses of the spectral distributions of rotational bands in 51 deformed prolate even–even nuclei in the 152 ≤ A ≤ 250 mass region $$R_{{4_{1}^{ + } /2_{1}^{ + } }} \ge 3.00$$ R 4 1 + / 2 1 + ≥ 3.00 are examined in terms of nearest neighbor spacing distributions. Specifically, the focus is on data for 0+, 2+, and 4+ energy levels of the ground, gamma, and beta bands. The chaotic behavior of the gamma band, especially the position of the $$2_{\gamma }^{ + }$$ 2 γ + band-head compared to other levels and bands, is clear. The levels are analyzed within the framework of two models, namely, a SU(3)-partial dynamical symmetry Hamiltonian and a SU(3) two-coupled quasi-dynamical symmetry Hamiltonian, with results that are further analyzed using random matrix theory. The partial and quasi dynamics both yield outcomes that are in reasonable agreement with the known experimental results. However, due to the degeneracy of the beta and gamma bands within the simplest SU(3) picture, the theory cannot be used to describe the fluctuation properties of excited bands. By changing relative weights of the different terms in the partial and quasi dynamical Hamiltonians, results are obtained that show more GOE-like statistics in the partial dynamical formalism as the strength of the pairing term is increased. Also, in the quasi-dynamical symmetry limit, more correlations are found because of the stronger couplings.

CHAOS AND QUANTUM FLUCTUATIONS IN A QUARTIC HAMILTONIAN SYSTEM

1993 ◽  
Vol 07 (22) ◽  
pp. 1421-1427
Author(s):  
M. P. JOY ◽  
M. SABIR
Keyword(s):  
Hamiltonian System ◽  
Effective Potential ◽  
Quantum Chaos ◽  
Quantum Fluctuations ◽  
Potential Method ◽  
Oscillator System ◽  
Quantum Behavior ◽  
Classical Behavior ◽  
Gaussian Effective Potential

Quantum chaos in a quartic oscillator system given by [Formula: see text] is studied using Gaussian Effective Potential method. It is shown that though quantum fluctuations reduce chaos, there is a correspondence between classical behavior and quantum behavior with regard to integrability and chaos.

scholarly journals Chaotic behavior of the lattice Yang-Mills on CUDA

2015 ◽  
Vol 7 (2) ◽  
pp. 216-238
Author(s):  
Richárd Forster ◽  
Ágnes Fülöp
Keyword(s):  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Monodromy Matrix ◽  
Gluon Plasma ◽  
Theoretical Background ◽  
Energy Relation ◽  
Abelian Gauge ◽  
Computing Power ◽  
Yang Mills ◽  
3 Dimensional

Abstract The Yang-Mills fields plays important role in the strong interaction, which describes the quark gluon plasma. The non-Abelian gauge theory provides the theoretical background understanding of this topic. The real time evolution of the classical fields is derived by the Hamiltonian for SU(2) gauge field tensor. The microcanonical equations of motion is solved on 3 dimensional lattice and chaotic dynamics was searched by the monodromy matrix. The entropy-energy relation was presented by Kolmogorov-Sinai entropy. We used block Hessenberg reduction to compute the eigenvalues of the current matrix. While the purely CPU based algorithm can handle effectively only a small amount of values, the GPUs provide enough performance to give more computing power to solve the problem.

scholarly journals Quantum Chaos is Quantum

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 453
Author(s):  
Lorenzo Leone ◽  
Salvatore F. E. Oliviero ◽  
You Zhou ◽  
Alioscia Hamma
Keyword(s):  
Quantum Chaos ◽  
Chaotic Behavior ◽  
Quantum Circuit ◽  
Classical Computer ◽  
Necessary And Sufficient

It is well known that a quantum circuit on N qubits composed of Clifford gates with the addition of k non Clifford gates can be simulated on a classical computer by an algorithm scaling as poly(N)exp⁡(k)\cite{bravyi2016improved}. We show that, for a quantum circuit to simulate quantum chaotic behavior, it is both necessary and sufficient that k=Θ(N). This result implies the impossibility of simulating quantum chaos on a classical computer.

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