Complex dynamical invariants for two-dimensional complex potentials

Complex dynamical invariants are searched out for two-dimensional complex potentials using rationalization method within the framework of an extended complex phase space characterized by x?=?x ₁?+?i p ₃,?y?=?x ₂?+?i p ₄, ?p _x ?=?p ₁?+?i x ₃, ?p _y ?=?p ₂?+?i x ₄. It is found that the cubic oscillator and shifted harmonic oscillator admit quadratic complex invariants. The obtained invariants may be useful for studying non-Hermitian Hamiltonian systems.     

Dielectric-barrier discharges in two-dimensional lattice potentials

We use a pin-grid electrode to introduce a corrugated electrical potential into a planar dielectric-barrier discharge (DBD) system, so that the amplitude of the applied electric field has the profile of a two-dimensional square lattice. The lattice potential provides a template for the spatial distribution of plasma filaments in the system and has pronounced effects on the patterns that can form. The positions at which filaments become localized within the lattice unit cell vary with the width of the discharge gap. The patterns that appear when filaments either overfill or underfill the lattice are reminiscent of those observed in other physical systems involving 2D lattices. We suggest that the connection between lattice-driven DBDs and other areas of physics may benefit from the further development of models that treat plasma filaments as interacting particles.     

Tunneling times in complex potentials

Tunneling times in absorptive media, described by complex potentials, are investigated. A general expression relating relevant tunneling times is extended by introducing a new term τa. For both single Dirac δ potential and rectangular potential τa exhibits a maximum for a specific complex potential configuration. The optimal shape of a complex rectangular potential in respect to the maximization of τa differs drastically in the short or long wavelength limits.     

Anomalous diffusion in two-dimensional potentials with hexagonal symmetry

The diffusion process in a Hamiltonian dynamical system describing the motion of a particle in a two-dimensional (2D) potential with hexagonal symmetry is studied. It is shown that, depending on the energy of the particle, various transport processes can exist: normal (Brownian) diffusion, anomalous diffusion, and ballistic transport. The relationship between these transport processes and the underlying structure of the phase space of the Hamiltonian dynamical system is investigated. The anomalous transport is studied in detail in two particular cases: in the first case, inside the chaotic sea there exist self-similar structures with fractal properties while in the second case the transport takes place in the presence of multilayered structures. It is demonstrated that structures of the second type can lead to a physical situation in which the transport becomes ballistic. Also, it is shown that for all cases in which the diffusive transport is anomalous the trajectories of the diffusing particles contain long segments of regular motion, the length of these segments being described by Levy probability density functions. Finally, the numerical values of the parameters which describe the diffusion processes are compared with those predicted by existing theoretical models. (c) 2000 American Institute of Physics.     

Correlated electron states at level crossings of bilayer two-dimensional electron systems in tilted magnetic fields

We have measured the energy-level structure of high mobility, strongly coupled bilayer two-dimensional electron systems in tilted magnetic fields by means of magnetotransport experiments. At tilt angles where single-particle levels with opposite spin and symmetry cross, we observe a surprising sudden broadening of the quantum Hall plateaus and a deepening of the Shubnikov–de Haas minima. This observation is explained by an interaction-induced rearrangement of the energy level structure which strongly increases the energetic splitting of two (anti-)crossing levels.     

Coherent backscattering of Bose-Einstein condensates in two-dimensional disorder potentials

We study quantum transport of an interacting Bose-Einstein condensate in a two-dimensional disorder potential. In the limit of a vanishing atom-atom interaction, a sharp cone in the angle-resolved density of the scattered matter wave is observed, arising from constructive interference between amplitudes propagating along reversed scattering paths. Weak interaction transforms this coherent backscattering peak into a pronounced dip, indicating destructive instead of constructive interference. We reproduce this result, obtained from the numerical integration of the Gross-Pitaevskii equation, by a diagrammatic theory of weak localization in the presence of nonlinearity.     

Localization of matter waves in two-dimensional disordered optical potentials

We consider ultracold atoms in 2D disordered optical potentials and calculate microscopic quantities characterizing matter wave quantum transport in the noninteracting regime. We derive the diffusion constant as a function of all relevant microscopic parameters and show that coherent multiple scattering induces significant weak localization effects. In particular, we find that even the strong localization regime is accessible with current experimental techniques and calculate the corresponding localization length.     

Phase-function method for complex potentials

We consider the scattering problem for absorptive interactions within the framework of phase-function method. A Green’s function approach is used to derive the phase equation. As a case study we apply the algorithm presented on a shallow α-α potential, the real and imaginary parts of which have been deduced from experimental data. The real and imaginary parts of theS-wave phase shift are found to vary smoothly with energy while those forD andG waves show some fluctuations in the low-energy region. It is shown that studies in spatial behaviour of the phase function provide a plausible explanation for the dynamical origin of these fluctuations.     

Molecular dynamics of two-dimensional gases with realistic potentials

Molecular dynamics calculations have mainly used hard-core interactions because of computational simplicity and increased speed. Algorithms for realistic intermolecular potentials have been used in studies of solids and liquids. By combining both techniques, an algorithm which can reasonably study dilute gases with realistic potentials has been achieved. The BoltzmannH-function is calculated for a hard-core and Lennard-Jones gas, and the latter is found to decrease more rapidly to equilibrium.Work supported in part by the National Science Foundation under Grant No. NSF-USDP GU-1598 and the U. S. Air Force Office of Scientific Research under Grant No. AF-AFOSR 1257-67.     

Stable surface solitons in truncated complex potentials

We show that surface solitons in the one-dimensional nonlinear Schr?dinger equation with truncated complex periodic potential can be stabilized by linear homogeneous losses, which are necessary to balance gain in the near-surface channel arising from the imaginary part of potential. Such solitons become stable attractors when the strength of homogeneous losses acquires values from a limited interval and they exist in focusing and defocusing media. The domains of stability of the surface solitons shrink with an increase in the amplitude of the imaginary part of complex potential.     

Level effects in complex stimulus discrimination

The dependence of spectral-shape discriminations upon presentation level was studied using stimuli consisting of a bandpass noise and a less intense pure tone. The level of the noise band was held constant (+10 dB) relative to the level of the tone, and the minimum change in the intensity of the tone was measured across a range of presentation levels. The results demonstrated that, for tonal frequencies located near the upper edge of the noise band, subject's optimal performance occurred at intermediate presentation levels and became considerably poorer at high levels. This result is in accordance with upward spread of masking and emphasizes that presentation level is an important parameter to consider when measuring discriminations of complex spectral shapes.     

Microrheological consequences of attractive colloid-colloid potentials in a two-dimensional Brownian fluid

By using microrheological methods commonly employed in videomicroscopy experiments, we study the rheology of a two-dimensional computational fluid formed by Brownian disks with the aim of exploring the influence of some effective colloid-colloid attractive interactions. The model of fluid is developed by Brownian dynamics simulations without hydrodynamical interactions, and it is characterized by calculating its equation of state from the pair distribution function. Micromechanical properties, relative and intrinsic viscosity and freezing are discussed. Then, we include attractive forces such a Asakura-Oosawa depletion force or an empiric expression proposed by Grier and Hal (GH) for an anomalous electrostatic potential observed in confined and charged colloids. By using both potentials, viscosity is clearly increased, but when the GH potential is included, viscoelastic gel state is reached for intermediate values of surface concentration. Finally, we analyse the influence of the attractive potentials in the breaking-up by thermal fluctuations of linear chains formed by 2D particles, finding that the GH potential reduces the characteristical time at which the disks can be considered as disaggregated. In this work, we employ an experimental-like methodology for the study of a Brownian hard-disk fluid, providing a very useful link with experimental procedures.     

Quantum mechanics with complex injecting potentials

We show the construction of a time-dependent source potential that injects a desired state into a quantum system. The applicability and validity of the approach is demonstrated through a series of examples. Both bound and scattering states can be injected with a prescribed energy. Electron transport in multi-terminal devices are used to show the power of the proposed method.     

Diffusion of two-dimensional excitons in pseudo-random potentials embedded in quantum well structures

Diffusion processes of excitons are investigated in quantum well structures where AlAs islands are embedded at the center of wells. The diffusion constant is measured by the transient grating method. It is found that with the AlAs insertion the diffusion is suppressed strongly at low temperatures and is anisotropic. Its dependence on carrier density is also revealed. A model calculation is discussed and compared with the experiment.