Biomedical subjects
Publications and source records attributed to Tsampikos Kottos.
We propose a random matrix modeling for the parametric evolution of eigenstates. The model is inspired by a large class of quantized chaotic systems. Its unique feature is having parametric invariance while still possessing the nonperturbative breakdown that had been discussed by Wigner 50 years ago. Of particular interest is the emergence of an additional crossover to multifractality.
Considering a quantized chaotic system, we analyze the evolution of its eigenstates as a result of varying a control parameter. As the induced perturbation becomes larger, there is a crossover from a perturbative to a non-perturbative regime, which is reflected in the structural changes of the local density of states. The full scenario is explored for a physical system: an Aharonov-Bohm cylindrical billiard. As we vary the magnetic flux, we discover an intermediate twilight regime where perturbative and semiclassical features coexist. This is in contrast with the simple crossover from a Lorentzian to a semicircle line shape which is found in random-matrix models.
The amount of charge that is pushed by a moving scatterer is dQ= -GdX , where dX is the displacement of the scatterer. The question is: what is G ?. Does it depend on the transmission g(0) of the scatterer? Does the answer depend on whether the system is open (with leads attached to reservoirs) or closed? In the latter case what are the implications of having "quantum chaos" and/or coupling to the environment? The answers to these questions illuminate some fundamental aspects of the theory of quantum pumping. For the analysis we take a network (graph) as a model system, and use the Kubo formula approach.
We study the current relaxation of a wave packet in a nonlinear random sample coupled to the continuum and show that the survival probability decays as P(t) approximately 1/t(alpha). For intermediate times t >t(*) and chi>chi(cr) we find a universal decay with alpha=2/3 which is a signature of the nonlinearity-induced delocalization. Experimental evidence should be observable in coupled nonlinear optical waveguides.
We discuss the possibility of having "quantum dissipation" due to the interaction with chaotic degrees of freedom. We define the conditions that should be satisfied in order to have a dissipative effect similar to the one due to an interaction with a (many body) bath. We also compare with the case where the environment is modeled by a random matrix model. In the case of interaction with "chaos" we observe a regime where the relaxation process is nonuniversal and reflects the underlaying semiclassical dynamics. As an example we consider a two level system (spin) that interacts with a two-dimensional anharmonic oscillator.
We study the possibility to undo the quantum mechanical evolution in a time reversal experiment. The naive expectation, as reflected in the common terminology ("Loschmidt echo"), is that maximum compensation results if the reversed dynamics extends to the same time as the forward evolution. We challenge this belief and demonstrate that the time t(r) for maximum return probability is in general shorter. We find that t(r) depends on lambda=epsilon(evol)/epsilon(prep), being the ratio of the error in setting the parameters (fields) for the time-reversed evolution to the perturbation which is involved in the preparation process. Our results should be observable in spin-echo experiments where the dynamical irreversibility of quantum phases is measured.
We study the proximity effect of a superconductor to a normal system with a fractal spectrum. We find that there is no gap in the excitation spectrum, even in the case where the underlying classical dynamics of the normal system is chaotic. An analytical expression for the distribution of the smallest excitation eigenvalue E1 of the hybrid structure is obtained. On small scales it decays algebraically as P(E1) approximately E1(-D0), where D0 is the fractal dimension of the spectrum of the normal system. Our theoretical predictions are verified by numerical calculations performed for various models.
We consider a two-dimensional (2D) generalization of the standard kicked rotor and show that it is an excellent model for the study of universal features of 2D quantum systems with underlying diffusive classical dynamics. First we analyze the distribution of wave-function intensities and compare them with the predictions derived in the framework of diffusive disordered samples. Next, we turn the closed system into an open one by constructing a scattering matrix. The distribution of the resonance widths P(Gamma) and Wigner delay times P(tau(W)) are investigated. The forms of these distributions are obtained for different symmetry classes and the traces of classical diffusive dynamics are identified. Our theoretical arguments are supported by extensive numerical calculations.
We show that enhanced wave function localization due to the presence of short unstable orbits and strong scarring can rely on completely different mechanisms. Specifically we find that in quantum networks the shortest and most stable orbits do not support visible scars, although they are responsible for enhanced localization in the majority of the eigenstates. Scarring orbits are selected by a criterion which does not involve the classical stability. We obtain predictions for the energies of visible scars and the distributions of scarring strengths and inverse participation numbers.
We study the distributions of the normalized resonance widths P(Gamma;) and delay times P(tau;) for 3D disordered tight-binding systems at the metal-insulator transition (MIT) by attaching leads to the boundary sites. Both distributions are scale invariant, independent of the microscopic details of the random potential and the number of channels. Theoretical considerations suggest the existence of a scaling theory for P(Gamma;) in finite samples, and numerical calculations confirm this hypothesis. Based on this, we give a new criterion for the determination and analysis of the MIT.
We investigate the statistics of eigenfunction intensities P(/psi/(2)) in dynamical systems with classical chaotic diffusion. Our results contradict some recent theoretical considerations that challenge the applicability of field theoretical predictions, derived in a different framework for diffusive disordered samples. For two-dimensional systems, the tails of P(/psi/(2)) contradict the results of the optimal fluctuation method, but agree very well with the predictions of the nonlinear sigma model.