Experimental test of a trace formula for two-dimensional dielectric resonators

Resonance spectra of two-dimensional dielectric microwave resonators of circular and square shapes have been measured. The deduced length spectra of periodic orbits were analyzed and a trace formula for dielectric resonators recently proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)] was tested. The observed deviations between the experimental length spectra and the predictions of the trace formula are attributed to a large number of missing resonances in the measured spectra. We show that by taking into account the systematics of observed and missing resonances the experimental length spectra are fully understood. In particular, a connection between the most long-lived resonances and certain periodic orbits is established experimentally.Comment: 14 pages, 12 figures, 1 tabl

Spectral theorem for the Lindblad equation for quadratic open fermionic systems

The spectral theorem is proven for the quantum dynamics of quadratic open systems of n fermions described by the Lindblad equation. Invariant eigenspaces of the many-body Liouvillean dynamics and their largest Jordan blocks are explicitly constructed for all eigenvalues. For eigenvalue zero we describe an algebraic procedure for constructing (possibly higher dimensional) spaces of (degenerate) non-equilibrium steady states.Comment: 19 pages, no figure

Finite Size Effects in Fluid Interfaces

It is shown that finite size effects in the free energy of a rough interface of the 3D Ising and three--state Potts models are well described by the capillary wave model at {\em two--loop} order. The agreement between theoretical predictions and Monte Carlo simulations strongly supports the idea of the universality of this description of order--order interfaces in 3D statistical systems above the roughening temperature.Comment: 3 pages, uuencoded .ps file, figures included. (Proceeding of Lattice '93

Asymptotic Entanglement and Lindblad Dynamics: a Perturbative Approach

We consider an open bipartite quantum system with dissipative Lindblad type dynamics. In order to study the entanglement of the stationary states, we develop a perturbative approach and apply it to the physically significant case when a purely dissipative perturbation is added to the unperturbed generator which by itself would produce reversible unitary dynamics.Comment: 15 page

On determination of statistical properties of spectra from parametric level dynamics

We analyze an approach aiming at determining statistical properties of spectra of time-periodic quantum chaotic system based on the parameter dynamics of their quasienergies. In particular we show that application of the methods of statistical physics, proposed previously in the literature, taking into account appropriate integrals of motion of the parametric dynamics is fully justified, even if the used integrals of motion do not determine the invariant manifold in a unique way. The indetermination of the manifold is removed by applying Dirac's theory of constrained Hamiltonian systems and imposing appropriate primary, first-class constraints and a gauge transformation generated by them in the standard way. The obtained results close the gap in the whole reasoning aiming at understanding statistical properties of spectra in terms of parametric dynamics.Comment: 9 pages without figure

Iowan Drift Problem, Northeastern Iowa

https://ir.uiowa.edu/igs_ri/1006/thumbnail.jp

Chaotic Scattering in the Regime of Weakly Overlapping Resonances

We measure the transmission and reflection amplitudes of microwaves in a resonator coupled to two antennas at room temperature in the regime of weakly overlapping resonances and in a frequency range of 3 to 16 GHz. Below 10.1 GHz the resonator simulates a chaotic quantum system. The distribution of the elements of the scattering matrix S is not Gaussian. The Fourier coefficients of S are used for a best fit of the autocorrelation function if S to a theoretical expression based on random--matrix theory. We find very good agreement below but not above 10.1 GHz

Experimental Test of a Two-dimensional Approximation for Dielectric Microcavities

Open dielectric resonators of different shapes are widely used for the manufacture of microlasers. A precise determination of their resonance frequencies and widths is crucial for their design. Most microlasers have a flat cylindrical geometry, and a two-dimensional approximation, the so-called method of the effective index of refraction, is commonly employed for numerical calculations. Our aim has been an experimental test of the precision and applicability of a model based on this approximation. We performed very thorough and accurate measurements of the resonance frequencies and widths of two passive circular dielectric microwave resonators and found significant deviations from the model predictions. From this we conclude that the model generally fails in the quantitative description of three-dimensional dielectric resonators.Comment: 10 pages, 13 figure