Disordered Systems

Bodo Huckestein, Alexander Altland

Disorder in electronic systems suppresses diffusion and can lead to localization. The origin of this behavior is enhanced backscattering due to quantum interference. In addition, disorder leads to a broadening of the density of states (DoS). However, the localization properties of a disordered system are usually not discernible from a study of the DoS. It is necessary to calculate two-particle properties or consider the influence of boundary conditions on energy eigenvalues as in the study of Thouless numbers to obtain information about localization. Another feature of disordered systems is the independence of their localization properties from details of the disorder in the system. For example, the range of the disorder affects non-universal quantities like the mean-free path but does not influence whether or not the system shows localization at all. Recently, new symmetry classes came into focus that do not conform to the standard expectations about disordered systems outlined above. As we will show in this contribution, details of disorder do matter for these systems and localization properties leave their mark on the DoS. In particular, we look at a system that presents an idealization of a disordered d-wave superconductor. In our study we neglect effects of self-consistency and concentrate on the d-wave symmetry and influence of different kinds of disorder. We consider the lattice quasi-particle Hamiltonian

Russell K. Hobbie, Bradley John Roth

Tigran V. Shahbazyan, Mikhail E. Raikh, Zeev Valy Vardeny

The effect of disorder on the collective emission from a system of classical oscillators is studied theoretically. Three types of disorder are considered: random orientation of dipole moments, finite spread in frequencies of the individual oscillators (diagonal disorder), and dipole- dipole interaction (off-diagonal disorder). We found that for sufficiently high concentration of oscillators the diagonal disorder does not completely destroy the collective character of the emission. We show that the eigenmodes of a cooperative system with disorder comprise a large number of oscillators and, due to cooperative character of the emission, their lifetime is much longer than the lifetime of an individual oscillator. Consequently, the cooperative emission spectrum of the system is not simply broadened by the disorder, but represents a superposition of relatively narrow peaks.

K. Tamvakis

Matthew C. Beeler

Ultracold bose gase systems can perform quantum simulations of high temperature superconductors in certain parameter regimes. Specifically, 2D bose gases at low temperatures exhibit a superfluid to thermal gas phase transition analogous to the superconductor to insulator transition in certain superconductors. The unbinding of thermally activated vortex pairs drives this phase transition, and disorder is expected to affect vortex motion in this system. In addition, disorder itself can drive phase transitions in superconductors. We have designed and built a system which produces two 2D ultracold Bose gas systems separated by a few microns. In addition, we have also produced a disordered speckled laser intensity pattern with a grain size of ~1 μm, small enough to provide a disordered potential for the two systems. We have observed the superfluid phase transition with and without the presence of disorder. The coherence of the system, which is related to superfluidity, is strongly reduced by the presence of disorder, even at small disorder strength, but the effect of the disorder on observed vortices in the system is less clear.