Biomedical subjects

Antonio M García-García

Publications and source records attributed to Antonio M García-García.

5 recordsLinked to original sources

PubMed2006

Semi-Poisson statistics in quantum chaos.

We investigate the quantum properties of a nonrandom Hamiltonian with a steplike singularity. It is shown that the eigenfunctions are multifractals and, in a certain range of parameters, the level statistics is described exactly by semi-Poisson statistics (SP) typical of pseudointegrable systems. It is also shown that our results are universal, namely, they depend exclusively on the presence of the steplike singularity and are not modified by smooth perturbations of the potential or the addition of a magnetic flux. Although the quantum properties of our system are similar to those of a disordered conductor at the Anderson transition, we report important quantitative differences in both the level statistics and the multifractal dimensions controlling the transition. Finally, the study of quantum transport properties suggests that the classical singularity induces quantum anomalous diffusion. We discuss how these findings may be experimentally corroborated by using ultracold atoms techniques.

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PubMed2006

Power spectrum characterization of the Anderson transition.

We examine the power spectrum of the energy level fluctuations of a family of critical power-law random banded matrices whose spectral properties are similar to those of a disordered conductor at the Anderson transition. It is shown analytically and numerically that at the Anderson transition the power spectrum presents 1/f2 noise for small frequencies but 1/f noise for larger frequencies. The analysis of the region between these two power-law limits gives an accurate estimation of the Thouless energy of the system. Finally we discuss in what circumstances these findings may be relevant in the case of nonrandom Hamiltonians.

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PubMed2005

Classical singularities and semi-Poisson statistics in disordered systems.

We investigate a one-dimensional disordered Hamiltonian with a nonanalytical dispersion relation whose level statistics is exactly described by semi-Poisson statistics. It is shown that this result is robust, namely, it does not depend on the microscopic details of the Hamiltonian but only on the type of nonanalytical potential. We also argue that a deterministic kicked rotator with a steplike potential has the same spectral properties. Semi-Poisson statistics, typical of pseudointegrable billiards, have been frequently claimed to describe critical statistics, namely, the level statistics of a disordered system at the Anderson transition. However, we provide convincing evidence they are indeed different: each of them has its origin in a different type of classical singularity.

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PubMed2004

QCD vacuum as a disordered medium: a simplified model for the QCD dirac operator.

We model the QCD Dirac operator as a power-law random banded matrix (RBM) with the appropriate chiral symmetry. Our motivation is the form of the Dirac operator in a basis of instantonic zero modes with a corresponding gauge background of instantons. We compare the spectral correlations of this model to those of an instanton liquid model (ILM) and find agreement well beyond the Thouless energy. In the bulk of the spectrum the dimensionless Thouless energy of the RBM scales with the square root of system size in agreement with the ILM and chiral perturbation theory. Near the origin the scaling in the RBM remains the same as in the bulk which agrees with chiral perturbation theory but not with the ILM. Finally we discuss how this RBM should be modified in order to describe the spectral correlations of the QCD Dirac operator at the finite temperature chiral restoration transition.

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PubMed2004

Classical intermittency and the quantum Anderson transition.

We investigate the properties of quantum systems whose classical counterpart presents intermittency. It is shown, by using recent semiclassical techniques, that the quantum spectral correlations of such systems are expressed in terms of the eigenvalues of an anomalous diffusion operator. For certain values of the parameters leading to ballistic diffusion and 1/f noise the spectral properties of our model show similarities with those of a disordered system at the Anderson transition. In Hamiltonian systems, intermittency is closely related to the presence of cantori in the classical phase space. We suggest, based on this relation, that our findings may be relevant for the description of the spectral correlations of Hamiltonians with a classical phase space homogeneously filled by cantori. Finally we discuss the extension of our results to higher dimensions and their relation to Anderson models with long-range hopping.

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