Biomedical subjects

Steven Tomsovic

Publications and source records attributed to Steven Tomsovic.

8 recordsLinked to original sources

PubMed2003

Exploring classical phase space structures of nearly integrable and mixed quantum systems via parametric variation.

The correlation between overlap intensities and level velocities has been introduced as a sensitive measure capable of revealing phase space localization. Previously applied to chaotic quantum systems, here we extend the theory to near-integrable and mixed quantum systems. This measure is useful in the latter cases because it has the ability to highlight certain phase space structures depending upon the perturbation used to parametrically vary the Hamiltonian. A detailed semiclassical theory is presented relating the correlation coefficient to the phase space weighted derivatives of the classical action. In the process, we confront the question of whether the Hannay-Ozorio de Almeida sum rules are simply extendable to mixed phase space systems. In addition, the variant Planck's over 2pi scalings of the correlation coefficient and relevant quantities are derived for nearly integrable systems. Excellent agreement is found between the theory and the results for integrable billiards as well as for the standard map.

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PubMed2003

Comment on "Ehrenfest times for classically chaotic systems".

In a recent Rapid Communication [P. G. Silvestrov and C. W. J. Beenakker, Phys. Rev. E 65, 035208(R) (2002)], the authors, Silvestrov and Beenakker, introduce a way to lengthen the Ehrenfest time tau for fully chaotic systems. We disagree with several statements made in their paper, and address the following points essential to their conclusions: (1) it is not true that all semiclassical approximations for chaotic systems fail at a so-called "log time" tau proportional, variant -ln( variant Planck's over 2pi ), differing only by a numerical coefficient; and (2) the limitation of the semiclassical approximation as expressed in the authors' Eq. (8) is not limited by their argument leading to Eq. (12).

Comment↗

PubMed2003

Breaking time reversal in a simple smooth chaotic system.

Within random matrix theory, the statistics of the eigensolutions depend fundamentally on the presence (or absence) of time reversal symmetry. Accepting the Bohigas-Giannoni-Schmit conjecture, this statement extends to quantum systems with chaotic classical analogs. For practical reasons, much of the supporting numerical studies of symmetry breaking have been done with billiards or maps, and little with simple, smooth systems. There are two main difficulties in attempting to break time reversal invariance in a continuous time system with a smooth potential. The first is avoiding false time reversal breaking. The second is locating a parameter regime in which the symmetry breaking is strong enough to transform the fluctuation properties fully to the broken symmetry case, and yet remain weak enough so as not to regularize the dynamics sufficiently that the system is no longer chaotic. We give an example of a system of two coupled quartic oscillators whose energy level statistics closely match with those of the Gaussian unitary ensemble, and which possesses only a minor proportion of regular motion in its phase space.

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PubMed2003

Quantum-dot ground-state energies and spin polarizations: soft versus hard chaos.

We consider how the nature of the dynamics affects ground state properties of ballistic quantum dots. We find that "mesoscopic Stoner fluctuations" that arise from the residual screened Coulomb interaction are very sensitive to the degree of chaos. It leads to ground state energies and spin polarizations whose fluctuations strongly increase as a system becomes less chaotic. The crucial features are illustrated with a model that depends on a parameter that tunes the dynamics from nearly integrable to mostly chaotic.

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PubMed2003

Ray dynamics in long-range deep ocean sound propagation.

Recent results relating to ray dynamics in ocean acoustics are reviewed. Attention is focused on long-range propagation in deep ocean environments. For this class of problems, the ray equations may be simplified by making use of a one-way formulation in which the range variable appears as the independent (timelike) variable. Topics discussed include integrable and nonintegrable ray systems, action-angle variables, nonlinear resonances and the KAM theorem, ray chaos, Lyapunov exponents, predictability, nondegeneracy violation, ray intensity statistics, semiclassical breakdown, wave chaos, and the connection between ray chaos and mode coupling. The Hamiltonian structure of the ray equations plays an important role in all of these topics.

Acoustics↗

PubMed2003

Ray dynamics in a long-range acoustic propagation experiment.

A ray-based wave-field description is employed in the interpretation of broadband basin-scale acoustic propagation measurements obtained during the Acoustic Thermometry of Ocean Climate program's 1994 Acoustic Engineering Test. Acoustic observables of interest are wavefront time spread, probability density function (PDF) of intensity, vertical extension of acoustic energy in the reception finale, and the transition region between temporally resolved and unresolved wavefronts. Ray-based numerical simulation results that include both mesoscale and internal-wave-induced sound-speed perturbations are shown to be consistent with measurements of all the aforementioned observables, even though the underlying ray trajectories are predominantly chaotic, that is, exponentially sensitive to initial and environmental conditions. Much of the analysis exploits results that relate to the subject of ray chaos; these results follow from the Hamiltonian structure of the ray equations. Further, it is shown that the collection of the many eigenrays that form one of the resolved arrivals is nonlocal, both spatially and as a function of launch angle, which places severe restrictions on theories that are based on a perturbation expansion about a background ray.

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PubMed2002

Sensitivity of wave field evolution and manifold stability in chaotic systems.

The sensitivity of a wave field's evolution to small perturbations is of fundamental interest. For chaotic systems, there are two distinct regimes of either exponential or Gaussian overlap decay in time. We develop a semiclassical approach for understanding both regimes and give a simple expression for the crossover time between the regimes. The wave field's evolution is considerably more stable than the exponential instability of chaotic trajectories seems to suggest. The resolution of this paradox lies in the collective behavior of the appropriate set of trajectories. Results are given for the standard map.

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PubMed1992

Time domain approach to semiclassical dynamics: Breaking the log time barrier.

The presence of chaos in the classical dynamics is not necessarily the destructive element it was thought to be for semiclassical approximations in the time domain. The method of calculating the semiclassical propagation of initial states and correlation functions for nonlinear and chaotic dynamics is shown, and the excellent accuracy is noted for rather long times. The breakdown timescale is much longer than the infamous "log time" for the cases investigated here.

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