L. E. Reichl

Scaling behavior in a quantum wire with scatterers

We study the conductance properties of a straight two-dimensional quantum wire with impurities modeled by s-like scatterers. Their presence can lead to strong interchannel coupling. It was shown that such systems depend sensitively on the number of transverse modes included. Based on a poor mans scaling technique we include the effect of higher modes in a renormalized coupling constant. We therefore show that the low-energy behavior of the wire is dominated by only a few modes, which hence is a way to reduce the necessary computing power. The technique is successfully applied to the case of one and two s-like scatterers.

Direct scattering processes and signatures of chaos in quantum waveguides

The effect of direct processes on the statistical properties of deterministic scattering processes in a chaotic waveguide is examined. The single-channel Poisson kernel describes well the distribution of S-matrix eigenphases when evaluated over an energy interval. When direct processes are transformed away, the scattering processes exhibit universal random matrix behavior. The effect of chaos on scattering wave functions, eigenphases, and time delays is discussed.

Changes in Floquet-state structure at avoided crossings: Delocalization and harmonic generation

Avoided crossings are common in the quasienergy spectra of strongly driven nonlinear quantum wells. In this paper we examine the sinusoidally driven particle in a square potential well to show that avoided crossings can alter the structure of Floquet states in this system. Two types of avoided crossings are identified: one type leads only to temporary changes (as a function of driving field strength) in Floquet state structure while the second type can lead to permanent delocalization of the Floquet states. Radiation spectra from these latter states show a significant increase in high harmonic generation as the system passes through the avoided crossing. {copyright} {ital 1999} {ital The American Physical Society}

Resonances in a two-dimensional electron waveguide with a single {delta}-function scatterer

We study the conductance properties of a straight two-dimensional electron waveguide with an s-like scatterer modeled by a single {delta}-function potential with a finite number of modes. Even such a simple system exhibits interesting resonance phenomena. These resonances are explained in terms of quasibound states both by using a direct solution of the Schroedinger equation and by studying the Greens function of the system. Using the Greens function we calculate the survival probability as well as the power absorption, and show the influence of the quasibound states on these two quantities. (c) 2000 The American Physical Society.

Conductance and statistical properties of chaotic and integrable electron waveguides

We show that the S-matrix for electrons propagating in a waveguide has different statistical properties depending on whether the waveguide cavity shape gives rise to chaotic or integrable behavior classically. We obtain distributions of energy level spacings for integrable and chaotic billiards shaped like the waveguide cavity. We also obtain distributions for Wigner delay times and resonance widths for the waveguide, for integrable and chaotic cavity geometries. Our results, obtained by direct numerical calculation of the electron wave function, are consistent with the predictions of random matrix theory.

Relaxation Rates and Collision Integrals for Bose-Einstein Condensates

Near equilibrium, the rate of relaxation to equilibrium and the transport properties of excitations (bogolons) in a dilute Bose-Einstein condensate (BEC) are determined by three collision integrals, , , and . All three collision integrals conserve momentum and energy during bogolon collisions, but only conserves bogolon number. Previous works have considered the contribution of only two collision integrals, and . In this work, we show that the third collision integral makes a significant contribution to the bogolon number relaxation rate and needs to be retained when computing relaxation properties of the BEC. We provide values of relaxation rates in a form that can be applied to a variety of dilute Bose-Einstein condensates.

Electron Conductance and Lifetimes in a Ballistic Electron Waveguide

Ballistic electron waveguides are open quantum systems that can be formed at very low temperatures at a GaAs/AlGaAs interface. Dissipation due to electron–phonon and electron–electron interactions in these systems is negligible. Although the electrons only interact with the walls of the waveguide, they can have a complicated spectrum including both positive energy bound states and quasibound states which appear as complex energy poles of the scattering S-matrix or energy Greens function. The quasibound states can give rise to zeros in the waveguide conductance as the energy of the electrons is varied. The width of the conduction zeros is determined by the lifetimes of the quasibound states. The “complex energy spectrum” associated with the quasibound states also governs the survival probability of electrons placed in the waveguide cavities.

Floquet analysis of atom-optics tunneling experiments

Dynamical tunneling has been observed in atom-optics experiments by two groups. We show that the experimental results are extremely well described by time-periodic Hamiltonians with momentum quantized in units of the atomic recoil. The observed tunneling has a well-defined period when only two Floquet states dominate the dynamics. Beat frequencies are observed when three Floquet states dominate. We find frequencies that match those observed in both experiments. The dynamical origin of the dominant Floquet states is identified.

Dynamics of radiation induced isomerization for HCN–CNH

We have analyzed the dynamics underlying the use of sequential radiation pulses to control the isomerization between the HCN and the CNH molecules. The appearance of avoided crossings among Floquet eigenphases as the molecule interacts with the radiation pulses is the key to understanding the isomerization dynamics, both in the adiabatic and nonadiabatic regimes. We find that small detunings of the incident pulses can have a significant effect on the outcome of the isomerization process for the model we consider.

Coulomb entangler and entanglement-testing network for waveguide qubits

We present a small network for the testing of the entanglement of two ballistic electron waveguide qubits. The network produces different output conditional on the presence or absence of entanglement. The structure of the network allows for the determination of successful entanglement operations through the measurement of the output of a single qubit. We also present a simple model of a dynamic Coulomb-like interaction and use it to describe some characteristics of a proposed scheme for the entanglement of qubits in ballistic electron waveguides.