arXiv subjects

T. Guhr

Publications and source records attributed to T. Guhr.

21 records · Page 2Linked to original sources

arXiv1997

Correlation-Hole Method for Spectra of Superconducting Microwave Billiards

The spectral fluctuation properties of various two- and three-dimensional superconducting billiard systems are investigated by employing the correlation-hole method. It rests on the sensitivity of the spectral Fourier transform to long range correlations and is thus an alternative technique to study chaotic dynamics. First, we apply the method to the eigenfrequencies which are extracted from the measured resonances. Second, we analyze the unfolded raw spectra, including the shape of the resonances. The merit of the method lies in a clear separation of the statistics due to the positions and due to the shape of the resonances. However, we show that statistical fluctuations of the intensities of the resonances have a strong impact on the observable. Therefore, the visibility of the correlation hole is studied as a function of the number of independent statistical variables entering into the intensities. The visibility improves if independent spectra are superimposed.

chao-dyn↗

arXiv1997

The chiral phase transition, random matrix models, and lattice data

We present two pieces of evidence in support of the conjecture that the microscopic spectral density of the Dirac operator is a universal quantity. First, we compare lattice data to predictions from random matrix theory. Second, we show that the functional form of the microscopic spectral correlations remains unchanged in random matrix models which take account of finite temperature. Furthermore, we present a random matrix model for the chiral phase transition in which all Matsubara frequencies are included.

hep-ph↗

arXiv1995

Transitions toward Quantum Chaos: with Supersymmetry from Poisson to Gauss

The transition from arbitrary to chaotic fluctuation properties in quantum systems is studied in a random matrix model. It is assumed that the Hamiltonian can be written as the sum of an arbitrary and a chaos producing part. The Gaussian ensembles are used to model the chaotic part. A closed integral representation for all correlations in the case of broken time reversal invariance is derived by employing supersymmetry and the graded eigenvalue method. In particular, the two level correlation function is expressed as a double integral. For a correlation index, exact diffusion equations are derived for all three universality classes which describe the transition to the chaotic regime from arbitrary initial conditions. As an application, the transition from Poisson regularity to chaos is discussed. The two level correlation function becomes a double integral for all values of the transition parameter.

cond-mat↗