Given a quantum Hamiltonian of point particles and angular momenta, we give a procedure to define a corresponding semiclassical dynamics with essentially classical content, around which the quantum ...dynamics can be expanded. The modulus of the quantum overlap of coherent states, evolved with the semiclassical Hamiltonian, naturally introduces a classical distance between classical phase points. Using this fact we analytically show that the time rate of change (trc) of two neighboring classical trajectories is directly proportional to the trc of quantum correlations. Coherence loss and nonlocality effects appear as corrections to semiclassical dynamics and we show that they can be perturbatively given in terms of classical trajectories and generalized actions. We apply the results to the nonintegrable (classically chaotic) version of the
N-atom Jaynes–Cummings model.
A system of two quartic oscillators coupled by a quartic perturbation is numerically studied for quantum mechanical eigenvalues and classical periodic orbits. The coupling strength serves as a ...control parameter to simulate the transition from integrable to chaotic regimes. In order to obtain higher-energy eigenvalues of a huge dimensional matrix, the Lanczos method and the equi-energy method are investigated for a practical use.
Numerical evidence is presented on fluctuations of reduced density matrix elements of subsystems of a chaotic quantum system. In contrast to regular systems these fluctuations are broadband in ...nature. We consider finite spin systems as also the kicked quantum top. The broadening increases with loss in correlation among the Hamiltonian matrix elements.
We study the quantum trajectory of an individual particle in the presence of chaos by virtue of the de Broglie–Bohmian causal formulation of quantum mechanics. It is shown that the single quantum ...trajectory can be obtained by numerically solving an auxiliary differential equation. The present results show that, corresponding to the chaotic motion of the individual particle in the classical limit, a stochastic quantum trajectory can be obtained. Moreover, it is found that pure quantum phenomena such as chaos-assisted tunnelling can also be directly exhibited by means of the method developed here. A driven anharmonic oscillator model is taken as an example to illustrate the main results described above.
Chaotic electron transport has been explored in a variety of semiconductor structures in which the transition to chaos occurs by the gradual and progressive destruction of stable orbits in response ...to an increasing perturbation. There is also a much rarer type of chaos, known as non-KAM dynamics, which switches on and off abruptly when the temporal frequency of the perturbation reaches certain critical values. This type of chaotic motion is of great interest due to diverse applications in the theory of plasma physics, tokamak fusion, turbulent fluid dynamics, ion traps, and quasicrystals, but has not yet been realized in experiment. Here, we show that electrons in a superlattice miniband with a tilted magnetic field provide an experimentally-accessible non-KAM system and, moreover, that this unusual type of chaotic dynamics can produce strong resonant enhancement of the electron drift velocity. The onset of chaos is characterized by the formation of intricate “stochastic web” patterns in the electron phase space. These webs delocalize the electron orbits, thereby generating strong resonant peaks in our calculated drift velocity versus electric field characteristics.
We investigate the numerical computation of Maaß cusp forms for the modular group corresponding to large eigenvalues. We present Fourier coefficients of two cusp forms whose eigenvalues exceed ...r=40000. These eigenvalues are the largest that have so far been found in the case of the modular group. They are larger than the 130millionth eigenvalue.
Signature of quantum chaos in SQUIDs Kato, Takeo; Tanimoto, Ken-Ichi; Nakamura, Katsuhiro
Physics letters. A,
03/2004, Volume:
322, Issue:
5
Journal Article
Peer reviewed
Open access
Spectral statistics in band structures is studied in a realistic model describing superconducting quantum interference devices (SQUIDs). By controlling an external magnetic flux, the level statistics ...may show a crossover from the GUE to the GOE. Effects of secondary discrete symmetries seen in specific regions of the first Brillouin zone are also discussed.
Results of an extensive study of a real quantum chaotic many-body system - the Ce atom - are presented. We discuss the origins of the quantum chaotic behaviour of the system, analyse statistical and ...dynamical properties of the multi-particle chaotic eigenstates and consider matrix elements or transition amplitudes between them. We show that based on the universal properties of the chaotic eigenstates a
statistical theory of finite few-particle systems with strong interaction can be developed. We also discuss such important physical effects as enhancement of weak perturbations in many-body quantum chaotic systems, distribution of single-particle occupation numbers and its deviations from the standard Fermi-Dirac shape, and ways of introducing statistical temperature-based description in such systems.
PDF
