The geometric phases of the cyclic states of a generalized harmonic oscillator with nonadiabatic time-periodic parameters are discussed in the framework of squeezed state. It is shown that the cyclic and quasicyclic s...
The geometric phases of the cyclic states of a generalized harmonic oscillator with nonadiabatic time-periodic parameters are discussed in the framework of squeezed state. It is shown that the cyclic and quasicyclic squeezed states correspond to the periodic and quasiperiodic solutions of an effective Hamiltonian defined on an extended phase space, respectively. The geometric phase of the cyclic squeezed state is found to be a phase-space area swept out by a periodic orbit. Furthermore, a class of cyclic states is expressed as a superposition of an infinite number of squeezed states. Their geometric phases are found to be independent of ħ, and equal to −(n+1/2) times the classical nonadiabatic Hannay angle.
The dynamics of a thin Huygens front propagating through a turbulent medium is considered. A rigorous asymptotic expression for the effective velocity vF proportional to the front area is derived. The small-scale fluc...
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The dynamics of a thin Huygens front propagating through a turbulent medium is considered. A rigorous asymptotic expression for the effective velocity vF proportional to the front area is derived. The small-scale fluctuations of the front position are shown to be strongly intermittent. This intermittency plays a crucial role in establishing a steady state magnitude of the front velocity. The results are compared with experimental data.
We study kicked quantum systems by using the squeezed state approach. Taking the kicked quantum harmonic oscillator as an example, we demonstrate that chaos in an underlying classical system can be enhanced as well as...
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We study kicked quantum systems by using the squeezed state approach. Taking the kicked quantum harmonic oscillator as an example, we demonstrate that chaos in an underlying classical system can be enhanced as well as suppressed by quantum fluctuations. Three different energy diffusions are observed in the kicked quantum harmonic oscillator, namely, localization, linear diffusion, and quadratic diffusion.
We have developed a simplified relativistic configuration-interaction method to calculate the dielectronic recombination (DR) cross sections and rate coefficients. In this method, the infinite resonant doubly excited ...
We have developed a simplified relativistic configuration-interaction method to calculate the dielectronic recombination (DR) cross sections and rate coefficients. In this method, the infinite resonant doubly excited states can be treated conveniently in the framework of quantum defect theory. Here we report a systematic study of DR rate coefficients of hydrogenlike isoelectronic sequence with atomic number 2<~Z<~79. The behavior of the DR rate coefficients along the isoelectronic sequence is studied. The results are compared with the Burgess formula and other theoretical works. Because of its relativistic treatment, our method can be applicable for arbitrary Z ions and the validity of the widely used Burgess formula can be examined, e.g., for the ion with Z>~36, the results calculated from Burgess formula would be larger by a factor of 2.
Based on multichannel quantum-defect theory, a method to calculate and compile radiative transition processes for atoms (including highly ionized high-Z atoms) is proposed. Through defining the renormalized transition...
Based on multichannel quantum-defect theory, a method to calculate and compile radiative transition processes for atoms (including highly ionized high-Z atoms) is proposed. Through defining the renormalized transition matrix elements from initial eigenchannels to final eigenchannels, the transition processes between infinitely many initial states and infinitely many final states can be treated conveniently. As illustrative examples, we study the alkali-metal atoms in detail.
The performance of maximum-likelihood (ML) and maximum a posteriori (MAP) estimates in non-linear problems at low data SNR is not well predicted by the Cramér-Rao or other lower bounds on variance. In order to be...
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The performance of maximum-likelihood (ML) and maximum a posteriori (MAP) estimates in non-linear problems at low data SNR is not well predicted by the Cramér-Rao or other lower bounds on variance. In order to better characterize the distribution of ML and MAP estimates under these conditions, we derive a point approximation to density values of the conditional distribution of such estimates. In an example problem, this approximate distribution captures the essential features of the distribution of ML estimates in the presence of Gaussian-distributed noise.
We investigate the relationship between bulk and local relaxation in the Ising spin glass (in two and three dimensions) for temperatures above but approaching the glass transition temperature, using Monte Carlo comput...
We investigate the relationship between bulk and local relaxation in the Ising spin glass (in two and three dimensions) for temperatures above but approaching the glass transition temperature, using Monte Carlo computer simulations. We find that the stretched exponential form of the bulk spin autocorrelation function results from a spatial average over a broad range of behavior, from strongly nonexponential to nearly exponential, for the local autocorrelation functions. The spatial correlation of single-site relaxation times obtained from these functions provides a length scale for dynamical heterogeneity that grows with decreasing temperature.
Some modified AGE methods for the convection–diffusion equation are developed in this paper. Firstly, there is a treatment on the convection term in the equation which is different from that in the AGE method by Evan...
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