Particle-hole thermalization in a composite superconducting and normal-conducting nanowire.

The mechanisms by which isolated condensed matter systems thermalize is a topic of growing interest. Thermalization is known to be linked to the emergence of chaos in the dynamics of a system. We show that a solid state scattering system, containing superconducting elements, can thermalize scattered states without affecting the degree of entanglement of the scattered states. We consider a composite NSNSNSNSN nanowire composed of Bi_{2}Sr_{2}CaCu_{2}O_{8+x} superconducting segments (S) and normal conducting segments (N). We consider parameter regimes where all current flow is due to tunneling currents that are facilitated by quasibound state resonances inside the SNSNSNS structure. At certain energies, scattered pure states approach ergodicity, even though they remain pure.

Intrinsic thermalization of the honeycomb optical lattice.

Ultracold atoms confined to optical lattices provide a platform for simulation of phenomena not readily accessible in condensed matter and chemical systems. One area of growing interest is the mechanism by which isolated condensed matter systems can thermalize. The mechanism for thermalization of quantum systems has been directly linked to a transition to chaos in their classical counterpart. Here we show that the broken spatial symmetries of the honeycomb optical lattice leads to a transition to chaos in the single-particle dynamics which, in turn, causes mixing of the energy bands of the quantum honeycomb lattice. For systems with single-particle chaos, "soft" interactions between atoms can cause the system to thermalize (achieve a Fermi-Dirac distribution for fermions or a Bose-Einstein distribution for bosons).

Quasibound states in a triple Gaussian potential.

We derive the transmission probabilities and delay times, and identify quasibound state structures in an open quantum system consisting of three Gaussian potential energy peaks, a system whose classical scattering dynamics we show to be chaotic. Such open quantum systems can serve as models for nanoscale quantum devices and their wave dynamics are similar to electromagnetic wave dynamics in optical microcavities. We use a quantum web to determine energy regimes for which the system exhibits the quantum manifestations of chaos, and we show that the classical scattering dynamics contains a significant amount of chaos. We also derive an exact expression for the non-Hermitian Hamiltonian whose eigenvalues give quasibound state energies and lifetimes of the system.

Chaos in the band structure of a soft Sinai lattice.

We study the effect of broken spatial and dynamical symmetries on the band structure of two lattices with unit cells that are soft versions of the classic Sinai billiard. We find significant signatures of chaos in the band structure of these lattices, in energy regimes where the underlying classical unit cell undergoes a transition to chaos. Broken dynamical symmetries and the presence of chaos can diminish the feasibility of changing and controlling band structure in a wide variety of two-dimensional lattice-based devices, including two-dimensional solids, optical lattices, and photonic crystals.

Arnold diffusion in a driven optical lattice.

The effect of time-periodic forces on matter has been a topic of growing interest since the advent of lasers. It is known that dynamical systems with 2.5 or more degrees of freedom are intrinsically unstable. As a consequence, time-periodic driven systems can experience large excursions in energy. We analyze the classical and quantum dynamics of rubidium atoms confined to a time-periodic optical lattice with 2.5 degrees of freedom. When the laser polarizations are orthogonal, the system consists of two 1.5 uncoupled dynamical systems. When laser polarizations are turned away from orthogonal, an Arnold web forms and the dynamics undergoes a fundamental change. For parallel polarizations, we find huge random excursions in the rubidium atom energies and significant entanglement of energies in the quantum dynamics.

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 laboratory 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.

Chaos and band structure in a three-dimensional optical lattice.

Classical chaos is known to affect wave propagation because it signifies the presence of broken symmetries. The effect of chaos has been observed experimentally for matter waves, electromagnetic waves, and acoustic waves. When these three types of waves propagate through a spatially periodic medium, the allowed propagation energies form bands. For energies in the band gaps, no wave propagation is possible. We show that optical lattices provide a well-defined system that allows a study of the effect of chaos on band structure. We have determined the band structure of a body-centered-cubic optical lattice for all theoretically possible couplings, and we find that the band structure for those lattices realizable in the laboratory differs significantly from that expected for the bands in an "empty" body-centered-cubic crystal. However, as coupling is increased, the lattice becomes increasingly chaotic and it becomes possible to produce band structure that has behavior qualitatively similar to the "empty" body-centered-cubic band structure, although with fewer degeneracies.

The vibrational dynamics of 3D HOCl above dissociation.

We explore the classical vibrational dynamics of the HOCl molecule for energies above the dissociation energy of the molecule. Above dissociation, we find that the classical dynamics is dominated by an invariant manifold which appears to stabilize two periodic orbits at energies significantly above the dissociation energy. These stable periodic orbits can hold a large number of quantum states and likely can support a significant quasibound state of the molecule, well above the dissociation energy. The classical dynamics and the lifetime of quantum states on the invariant manifold are determined.

Chaotic dynamics in a two-dimensional optical lattice.

The classical nonlinear dynamics of a dilute gas of rubidium atoms in an optical lattice is studied for a range of polarizations of the laser beams forming the lattice. The dynamics ranges from integrable to chaotic, and mechanisms leading to the onset of chaos in the lattice are described.

Transport coefficients from the boson Uehling-Uhlenbeck equation.

Expressions for the bulk viscosity, shear viscosity, and thermal conductivity of a quantum degenerate Bose gas above the critical temperature for Bose-Einstein condensation are derived using the Uehling-Uhlenbeck kinetic equation. For contact potentials and hard sphere interactions, the eigenvalues (relaxation rates) of the Uehling-Uhlenbeck collision operator have an upper cutoff. This cutoff requires summation over all discrete eigenvalues and eigenvectors of the collision operator when computing transport coefficients. 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 of the degenerate boson gas remains identically zero, as it is for the classical gas.

Fractal scattering dynamics of the three-dimensional HOCl molecule.

We compare the 2D and 3D classical fractal scattering dynamics of Cl and HO for energies just above dissociation of the HOCl molecule, using a realistic potential energy surface for the HOCl molecule and techniques developed to analyze 3D chaotic scattering processes. For parameter regimes where the HO dimer initially has small vibrational energy, only small intervals of initial conditions show fractal scattering behavior and the scattering process is well described by a 2D model. For parameter regimes where the HO dimer initially has large vibrational energy, the scattering process is fully 3D and is dominated by fractal behavior.

Relaxation rates of the linearized Uehling-Uhlenbeck equation for bosons.

We linearize the Uehling-Uhlenbeck equation for bosonic gases close to thermal equilibrium under the assumption of a contact interaction characterized by a scattering length a. We show that the spectrum of relaxation rates is similar to that of a classical hard-sphere gas. However, the relaxation rates show a significant dependence on the fugacity z of the gas, increasing by as much as 60% of their classical value for z approaching 1. The relaxation modes are also significantly altered at higher values of z. The relaxation rates and modes are determined by the eigenvalues and eigenvectors of a Fredholm integral operator of the second kind. We derive an analytical form for the kernel of this operator and present numerical results for the first few eigenvalues and eigenvectors.

Chaotic scattering in a molecular system.

We study the classical dynamics of bound state and scattering trajectories of the chlorine atom interacting with the HO molecule using a two-dimensional model in which the HO bond length is held fixed. The bound state system forms the HOCl molecule and at low energies is predominantly integrable. Below dissociation a number of bifurcations are observed, most notably a series of saddle-center bifurcations related to a 2:1 and at higher energies 3:1 resonance between bend and stretch motions. At energies above dissociation the classical phase space becomes dominated by a homoclinic tangle which induces a fractal distribution of singularities in all scattering functions. The structure of the homoclinic tangle is examined directly using Poincaré surfaces of section as well as indirectly through its influence on the time delay of the scattered chlorine atom and the angular momentum of the scattered HO molecule.

Molecular dynamics simulation of collision operator eigenvalues.

We simulate numerically the time evolution of 1000 interacting hard spheres in a finite box with periodic boundary conditions, and repeat the simulations many times for a selected random distribution of initial conditions. We use the resulting data to compute, directly, the smallest nonzero eigenvalue of the collision operator for this gas. We also give exact expressions for the transport coefficients and compare them to approximate expressions commonly seen in the literature.

Dynamics of quasibound state formation in the driven Gaussian potential.

The quasibound states of a particle in an inverted-Gaussian potential interacting with an intense laser field are studied using complex coordinate scaling and Floquet theory. The dynamics of the driven system is different depending on whether the driving field frequency is less than or greater than the ionization frequency. As the laser field strength is increased, a new quasibound state emerges as the result of a pitchfork bifurcation in the classical phase space. Changes in the time-averaged "dressed potential" appear related to this bifurcation and provide additional confirmation of the role of the bifurcation on the emergence of a new quasibound state. The Husimi plots of the quasibound state residues reveal strong support on the periodic orbits of the bifurcation at frequencies above the ionization frequency.

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.

Localization of Floquet states along a continuous line of periodic orbits.

A periodically driven particle in an infinite square well is shown to exhibit quantum localization due to a continuous line of periodic orbits in the classical system. Individual Floquet eigenstates localized along this line of periodic orbits are identified. The enhanced localization persists for field strengths beyond that at which the continuous line of orbits is destroyed in the classical dynamics. These results may be relevant to experiments involving trapping potentials with flat regions.

Nonlinear dynamics of gravity and matter creation in a cosmology with an unbounded Hamiltonian.

Nonlinear dynamics and stability properties of a cosmological model of spatially homogeneous coupled gravity and matter fields is analyzed using methods of classical mechanics. The system exhibits regions of chaos and dramatic changes in structural stability as the strength of the coupling between the fields is varied. Numerical simulations suggest that Hamiltonian systems with structure appropriate for describing matter-gravity interaction constitute a new class of nonlinear systems with very unusual and rich dynamics.

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 Poincaré 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.

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.