arXiv subjects

L. E. Reichl

Publications and source records attributed to L. E. Reichl.

At least 19 recordsLinked to original sources

arXiv2019

Bound states in the Brillouin zone continuum

Systems with space-periodic Hamiltonians have unique scattering properties. The discrete translational symmetry associated with periodicity of the Hamiltonian creates scattering channels that govern the scattering process. We consider a two-dimensional scattering system in which one dimension is a periodic lattice and the other is localized in space. The scattering and decay processes can then be described in terms of channels indexed by the Bloch momentum. We find the 1D periodic lattice can sustain two types of bound states in the positive energy continuum (BICs): one protected by reflection symmetry, the other protected by discrete translational symmetry. The lattice also sustains long-lived quasibound states. We expect that our results can be generalized to the behavior of states in the continuum of 2D periodic lattices.

quant-ph↗

arXiv2015

Chaos in the Honeycomb Optical Lattice Unit Cell

Natural and artificial honeycomb lattices are of great interest because the band structure of these lattices, if properly constructed, contains a Dirac point. Such lattices occur naturally in the form of graphene and carbon nanotubes. They have been created in the lab in the form of semiconductor 2DEGs, optical lattices, and photonic crystals. We show that, over a wide energy range, gases (of electrons, atoms, or photons) that propagate through these lattices are Lorentz gases and the corresponding classical dynamics is chaotic. Thus, honeycomb lattices are also of interest for understanding eigenstate thermalization and the conductor-insulator transition due to dynamic Anderson localization.

cond-mat.mes-hall↗

arXiv2012

Transport coefficients from the Boson Uehling-Uhlenbeck Equation

We derive microscopic expressions for the bulk viscosity, shear viscosity and thermal conductivity of a quantum degenerate Bose gas above $T_C$, the critical temperature for Bose-Einstein condensation. The gas interacts via a contact potential and is described by the Uehling-Uhlenbeck equation. To derive the transport coefficients, we use Rayleigh-Schrodinger perturbation theory rather than the Chapman-Enskog approach. This approach illuminates the link between transport coefficients and eigenvalues of the collision operator. We find that a method of summing the second order contributions using the fact that the relaxation rates have a known limit improves the accuracy of the computations. We numerically compute the shear viscosity and thermal conductivity for any boson gas that interacts via a contact potential. We find that the bulk viscosity remains identically zero as it is for the classical case.

cond-mat.quant-gas↗

arXiv2012

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, $\mathcal{G}^{12}$, $\mathcal{G}^{22}$, and $\mathcal{G}^{31}$. All three collision integrals conserve momentum and energy during bogolon collisions, but only $ \mathcal{G}^{22}$ conserves bogolon number. Previous works have considered the contribution of only two collision integrals, $ \mathcal{G}^{22}$ and $ \mathcal{G}^{12}$. In this work, we show that the third collision integral $ \mathcal{G}^{31}$ 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.

cond-mat.quant-gas↗

arXiv2012

Collision Integrals in the Kinetic Equations of dilute Bose-Einstein Condensates

We derive the mean field kinetic equation for the momentum distribution of Bogoliubov excitations (bogolons) in a spatially uniform Bose-Einstein condensate (BEC), with a focus on the collision integrals. We use the method of Peletminksii and Yatsenko rather than the standard non-equilibrium Green's function formalism. This method produces three collision integrals ${\cal G}^{12}$, ${\cal G}^{22}$ and ${\cal G}^{31}$. Only ${\cal G}^{12}$ and ${\cal G}^{22}$ have been considered by previous authors. The third collision integral ${\cal G}^{31}$ contains the effects of processes where one bogolon becomes three and vice versa. These processes are allowed because the total number of bogolons is not conserved. Since ${\cal G}^{31}$ is of the same order in the interaction strength as ${\cal G}^{22}$, we predict that it will significantly influence the dynamics of the bogolon gas, especially the relaxation of the total number of bogolons to its equilibrium value.

cond-mat.quant-gas↗

arXiv2009

Resonance width oscillation in the bi-ripple ballistic electron waveguide

Interference of quasi bound states is studied in a ballistic electron ripple waveguide with two ripple cavities whose distance apart can be varied. This system is the waveguide analog of Dicke's model for two interacting atoms in a radiation field. Dicke's model has resonances whose widths change in an oscillatory manner as the distance between the atoms is varied. Resonances that form in a bi-ripple waveguide behave in a manner that has some similarity to Dicke's system, but also important differences. We numerically investigate the behavior of resonance widths in the waveguide as the distance between the two ripple cavities changes and we find that the resonance widths oscillate with variation of distance, but the coupling does not decrease as it does in Dicke's system. We discuss differences between our waveguide system and other systems showing the analogous of Dicke effect. We also study S-matrix pole trajectories and find that they rotate in counterclockwise direction on a circle in the complex energy plane.

cond-mat.mes-hall↗

arXiv2004

Chaos assisted adiabatic passage

We study the exact dynamics underlying stimulated Raman adiabatic passage (STIRAP) for a particle in a multi-level anharmonic system (the infinite square-well) driven by two sequential laser pulses, each with constant carrier frequency. In phase space regions where the laser pulses create chaos, the particle can be transferred coherently into energy states different from those predicted by traditional STIRAP. It appears that a transition to chaos can provide a new tool to control the outcome of STIRAP.

quant-ph↗

arXiv2003

Classical Scattering for a driven inverted Gaussian potential in terms of the chaotic invariant set

We study the classical electron scattering from a driven inverted Gaussian potential, an open system, in terms of its chaotic invariant set. This chaotic invariant set is described by a ternary horseshoe construction on an appropriate Poincare surface of section. We find the development parameters that describe the hyperbolic component of the chaotic invariant set. In addition, we show that the hierarchical structure of the fractal set of singularities of the scattering functions is the same as the structure of the chaotic invariant set. Finally, we construct a symbolic encoding of the hierarchical structure of the set of singularities of the scattering functions and use concepts from the thermodynamical formalism to obtain one of the measures of chaos of the fractal set of singularities, the topological entropy.

physics.class-ph↗

arXiv2003

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 wavefunctions,eigenphases, and time delays is discussed.

nlin.CD↗

arXiv2002

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 which match those observed in both experiments. The dynamical origin of the dominant Floquet states is identified.

quant-ph↗

arXiv2001

Floquet Scattering and Classical-Quantum correspondence in strong time periodic fields

We study the scattering of an electron from a one dimensional inverted Gaussian atomic potential in the presence of strong time periodic electric fields. Using Floquet theory, we construct the Floquet Scattering matrix in the Kramers-Henneberger frame. We compute the transmission coefficients as a function of electron incident energy and find that they display asymmetric Fano resonances due to the electron interaction with the driving field. We find that the Fano resonances are associated with zero-pole pairs of the Floquet Scattering matrix in the complex energy plane. Another way we "probe" the complex spectrum of the system is by computing the Wigner-Smith delay times. Finally we find that the eigenphases of the Floquet Scattering matrix undergo a number of "avoided crossings" as a function of electron Floquet energy that increases with increasing strength of the driving field. These "avoided crossings" appear to be quantum manifestations of the destruction of the constants of motion and the onset of chaos in classical phase space.

physics.atom-ph↗

arXiv2001

Transmission Properties of the oscillating delta-function potential

We derive an exact expression for the transmission amplitude of a particle moving through a harmonically driven delta-function potential by using the method of continued-fractions within the framework of Floquet theory. We prove that the transmission through this potential as a function of the incident energy presents at most two real zeros, that its poles occur at energies $n\hbarω+\varepsilon^*$ ($0<Re(\varepsilon^*)<\hbarω$), and that the poles and zeros in the transmission amplitude come in pairs with the distance between the zeros and the poles (and their residue) decreasing with increasing energy of the incident particle. We also show the existence of non-resonant "bands" in the transmission amplitude as a function of the strength of the potential and the driving frequency.

cond-mat.mes-hall↗

arXiv2001

Scattering from Spatially Localized Chaotic and Disordered Systems

A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically chaotic dynamics. Recently, it has been used to make random matrix theory predictions concerning the statistical properties of scattering resonances in mesoscopic electron waveguides and electromagnetic waveguides. We provide a simple derivation of this scattering theory and we compare its predictions to those obtained from an exactly solvable scattering model; and we use it to study the scattering of a particle wave from a random potential. This method may prove useful in distinguishing the effects of chaos from the effects of disorder in real scattering processes.

nlin.CD↗

arXiv2000

The Effect of Evanescent Modes and Chaos on Deterministic Scattering in Electron Waveguides

Statistical properties of Wigner delay times and the effect of evanescent modes on the deterministic scattering of an electron matter wave from a classically chaotic 2-d electron waveguide are studied for the case of 2, 6, and 16 propagating modes. Deterministic reaction matrix theory for this system is generalized to include the effect of evanescent modes on the scattering process. Inclusion of evanescent modes can change the positions of resonance poles in the complex energy plane and can delay electron scattering, particularly at energies where new channels open. The statistical properties of the Wigner delay times for the deterministic scattering process are compared to the predictions of random reaction matrix theory.

nlin.CD↗

arXiv2000

Scattering properties of a cut-circle billiard waveguide with two conical leads

We examine a two-dimensional electron waveguide with a cut-circle cavity and conical leads. By considering Wigner delay times and the Landauer-Büttiker conductance for this system, we probe the effects of the closed billiard energy spectrum on scattering properties in the limit of weakly coupled leads. We investigate how lead placement and cavity shape affect these conductance and time delay spectra of the waveguide.

cond-mat↗

arXiv2000

Phase-space picture of resonance creation and avoided crossings

Complex coordinate scaling (CCS) is used to calculate resonance eigenvalues and eigenstates for a system consisting of an inverted Gaussian potential and a monochromatic driving field. Floquet eigenvalues and Husimi distributions of resonance eigenfunctions are calculated using two different versions of CCS. The number of resonance states in this system increases as the strength of the driving field is increased, indicating that this system might have increased stability against ionization when the field strength is very high. We find that the newly created resonance states are scarred on unstable periodic orbits of the classical motion. The behavior of these periodic orbits as the field strength is increased may explain why there are more resonance states at high field strengths than at low field strengths. Close examination of an avoided crossing between resonance states shows that this type of avoided crossing does not delocalize the resonance states, although it may lead to interesting effects at certain field strengths.

quant-ph↗

arXiv2000

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 inter-channel coupling. It was shown that such systems depend sensitively on the number of transverse modes included. Based on a poor man's 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.

cond-mat.mes-hall↗

arXiv1999

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 quasi-bound states both by using a direct solution of the Schroedinger equation and by studying the Green's function of the system. Using the Green's function we calculate the survival probability as well as the power absorption and show the influence of the quasi-bound states on these two quantities.

cond-mat.mes-hall↗