Topological states at exceptional points

We consider an N-level non-Hermitian Hamiltonian with an exceptional point of order N. We define adiabatic equivalence in such systems and explore topological phase. We show that the topological exceptional states appear at the interface of topologically distinct systems. We discuss that topological states appear even in closed systems. We explore dynamical robustness of exceptional edge states.     

Fast frictionless expansion of an optical lattice

We investigate fast frictionless expansion of an optical lattice with dynamically variable spacing (accordion lattice). We design an expansion trajectory that yields a final state identical to the initial state up to an irrelevant phase factor. We discuss the effect of additional force and nonlinear interaction on the fast frictionless expansion.     

Two-step condensation of lattice bosons

We present a theoretical study of Bose-Einstein condensation in highly anisotropic harmonic traps. The bosons are considered to be moving in an optical lattice in an overall anisotropic harmonic confining potential. We find that two-step condensation occurs for lattice bosons at much reduced harmonic potential anisotropy when compared to the case of an ideal Bose gas in an anisotropic harmonic confinement. We also show that when the bosons are in an isotropic harmonic confinement but with highly anisotropic hopping in the optical lattice, two-step condensation does not occur. We interpret some of our results using single boson density of energy states corresponding to the potentials faced by the bosons.     

Interaction-induced adiabatic cooling and antiferromagnetism of cold fermions in optical lattices

We propose an interaction-induced cooling mechanism for two-component cold fermions in an optical lattice. It is based on an increase of the spin entropy upon localization, an analogue of the Pomeranchuk effect in liquid helium 3. We discuss its application to the experimental realization of the antiferromagnetic phase. We illustrate our arguments with dynamical mean-field theory calculations.     

A Simple Bimodular Nonlinear Element

We have studied the dynamics of an artificial nonlinear element representing a flexible membrane with oscillation limiters and a static pressing force. Such an element has the property of “bimodularity” and demonstrates “modular” nonlinearity. We have constructed a mathematical model that describes these oscillations. Their shapes have been calculated. We follow the analogy with a classical object—Galileo’s pendulum. We demonstrate that for a low-frequency excitation of the membrane, the level of the harmonics in the spectrum is higher than in the vicinity of the resonance frequency. We have established a strong dependence of the level of the harmonics on the magnitude of the pressing force for a weak perturbation. We propose a design scheme for a device in the quasi-static approximation possessing the property of bimodularity. We perform an experiment that confirms its operability. We show a qualitative coincidence of the experimental results and calculations when detecting an amplitude-modulated signal.     

Spherical Gravitational Collapse: Tangential Pressure and Related Equations of State

We derive an equation for the acceleration of a fluid element in the spherical gravitational collapse of a bounded compact object made up of an imperfect fluid. We show that non-singular as well as singular solutions arise in the collapse of a fluid initially at rest and having only a tangential pressure. We obtain an exact solution of the Einstein equations, in the form of an infinite series, for collapse under tangential pressure with a linear equation of state. We show that if a singularity forms in the tangential pressure model, the conditions for the singularity to be naked are exactly the same as in the model of dust collapse.     

Many-body aspects of coherent atom-molecule oscillations

We study the many-body effects on coherent atom-molecule oscillations by means of an effective quantum field theory that describes Feshbach-resonant interactions in Bose gases in terms of an atom-molecule Hamiltonian. We determine numerically the many-body corrections to the oscillation frequency for various densities of the atomic condensate. We also derive an analytic expression that approximately describes both the density and magnetic-field dependence of this frequency near the resonance. We find excellent agreement with experiment.     

Ultrafast carrier dynamics of resonantly excited InAs/GaAs self-assembled quantum dots

We study theoretically the time development of electronic relaxation in quantum dots. We consider the process of relaxation of the state with an electron prepared at the beginning of relaxation in the electronic ground state. We obtain a fast (in picoseconds) increase of electronic population in the excited state. Also, we consider the process of relaxation of an electron from an excited state in the dot. Here we obtain an incomplete depopulation of the electron from the excited state. We compare these results to experiments in which a fast decrease of luminescence is reported during the first period of relaxation after resonant excitation of the ground state. We estimate numerically the role of electron–LO–phonon (Fröhlich's coupling) mechanism in these processes. We show that this effect may be attributed to the influence of multiple scattering of quantum dot electrons on LO phonons. A single-electron two-energy-level quantum dot model is used to demonstrate this effect in an isolated semiconductor quantum dot.     

Quantum state sharing of an arbitrary qudit state by using nonmaximally generalized GHZ state

We present a scheme for quantum state sharing of an arbitrary qudit state by using nonmaximally entangled generalized Greenberger-Horne-Zeilinger （GHZ） states as the quantum channel and generalized Bell-basis states as the joint measurement basis. We show that the probability of successful sharing an unknown qudit state depends on the joint measurements chosen by Alice. We also give an expression for the maximally probability of this scheme.     

Empirical analysis of the evolution of a scientific collaboration network

We present an analysis of the temporal evolution of a scientific coauthorship network, the genetic programming network. We find evidence that the network grows according to preferential attachment, with a slightly sublinear rate. We empirically find how a giant component forms and develops, and we characterize the network by several other time-varying quantities: the mean degree, the clustering coefficient, the average path length, and the degree distribution. We find that the first three statistics increase over time in the growing network; the degree distribution tends to stabilize toward an exponentially truncated power-law. We finally suggest an effective network interpretation that takes into account the aging of collaboration relationships.     

Hamilton's equations for constrained dynamical systems

We derive expressions for the conjugate momenta and the Hamiltonian for classical dynamical systems subject to holonomic constraints. We give an algorithm for correcting deviations of the constraints arising in numerical solution of the equations of motion. We obtain an explicit expression for the momentum integral for constrained systems.     

Energy phase correlation and pulse dynamics in short bunch high gain FELs

We analyze the dynamics of Free Electron Laser (FEL) devices, operating with a bunched beam exhibiting a longitudinal phase space correlation. We show that the presence of an energy-position correlation term is responsible for very interesting effects like an enhancement of the peak output power, a shortening of the laser pulses and an increase of the non linearly generated harmonic intensities. We conjecture that the mechanism is due to a kind of energy tapering effect associated with the correlation. We discuss the difference of the dynamics with respect to an ordinary undulator tapering and the relative advantages.     

Hydrodynamics and rheology of active liquid crystals: a numerical investigation

We report numerical studies of the hydrodynamics and rheology of an active liquid crystal. We confirm the existence of a transition between a passive and an active phase, with spontaneous flow in steady state. We explore how the velocity profile changes with activity, and we point out the difference in behavior for flow-aligning and tumbling materials. We find that an active material can thicken or thin under a flow, or even exhibit both behaviors as the forcing changes.     

Flapping states of a flag in an inviscid fluid: bistability and the transition to chaos

We investigate the "flapping flag" instability through a model for an inextensible flexible sheet in an inviscid 2D flow with a free vortex sheet. We solve the fully-nonlinear dynamics numerically and find a transition from a power spectrum dominated by discrete frequencies to an apparently continuous spectrum of frequencies. We compute the linear stability domain which agrees with previous approximate models in scaling but differs by large multiplicative factors. We also find hysteresis, in agreement with previous experiments.     

Relation between local temperature gradients and the direction of heat flow in quantum driven systems

We introduce thermometers to define the local temperature of an electronic system driven out-of-equilibrium by local ac fields. We discuss the behavior of the local temperature along the sample, showing that it exhibits spatial fluctuations following an oscillatory pattern. We show explicitly that the local temperature is the correct indicator for heat flow.     

Differential operators on the superline,Berezinians, and Darboux transformations

We consider differential operators on a supermanifold of dimension 1|1. We define non-degenerate operators as those with an invertible top coefficient in the expansion in the ‘superderivative’ D (which is the square root of the shift generator, the partial derivative in an even variable, with the help of an odd indeterminate). They are remarkably similar to ordinary differential operators. We show that every non-degenerate operator can be written in terms of ‘super Wronskians’ (which are certain Berezinians). We apply this to Darboux transformations (DTs), proving that every DT of an arbitrary non-degenerate operator is the composition of elementary first-order transformations. Hence every DT corresponds to an invariant subspace of the source operator and, upon a choice of basis in this subspace, is expressed by a super Wronskian formula. We consider also dressing transformations, i.e., the effect of a DT on the coefficients of the non-degenerate operator. We calculate these transformations in examples and make some general statements.     

Dynamics of an Orientational-Kink Pair in a Hydrogen-Bonded Chain in an External Field

We discuss dynamic properties of an orientational-kink pair in hydrogen-bonded chains in the presence of an external force and damping, based on a new two-component soliton model. We study the scattering of an electromagnetic wave by an orientational-kink pair. Finally, we find the expressions of the scattering cross-section of an orientational-kink pair for an electromagnetic wave and the mobility of the orientational-kink pair.     

Laser picosecond acoustics in isotropic and anisotropic materials

We present experimental results concerning the laser generation of picosecond acoustic pulses and their propagation in isotropic and anisotropic materials. We make use of a conventional reflectance detection technique as well as interferometric detection to probe the real and imaginary changes in reflectance. We also demonstrate the detection of transverse acoustic waves by mode conversion at an interface between an isotropic polycrystalline film and an anisotropic substrate.     

The control of high-dimensional chaos in time-delay systems to an arbitrary goal dynamics

We present the control of high-dimensional chaos, with possibly a large number of positive Lyapunov exponents, of unknown time-delay systems to an arbitrary goal dynamics. We give an existence-and-uniqueness theorem for the control force. In the case of an unknown system, a formula to compute a model-based control force is derived. We give an example by demonstrating the control of the Mackey-Glass system toward a fixed point and a Rossler dynamics. (c) 1999 American Institute of Physics.