Effect of gravitational force upon traffic flow with gradients

We study the effect of gravitational force upon traffic flow on a highway with sag, uphill, and downhill. We extend the optimal velocity model to take into account the gravitational force which acts on vehicles as an external force. We study the traffic states and jamming transitions induced by the slope of highway. We derive the fundamental diagrams (flow-density diagrams) for the traffic flow on the sag, the uphill, and downhill by using the extended optimal velocity model. We clarify where and when traffic jams occur on a highway with gradients. We show the relationship between densities before and after the jam. We derive the dependence of the fundamental diagram on the slope of gradients.     

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.     

Nonlinear localized modes in Glauber-Fock photonic lattices

We study a nonlinear Glauber-Fock lattice and the conditions for the excitation of localized structures. We investigate the particular linear properties of these lattices, including linear localized modes. We investigate numerically nonlinear modes centered in each site of the lattice. We found a strong disagreement of the general tendency between the stationary and the dynamical excitation thresholds. We define a new parameter that takes into account the stationary and dynamical properties of localized excitations.     

Diffusion controlled multiplicative process: typical versus average behaviour

We investigate the dynamics of the number of particles diffusing in a multiplicative medium. We show that the typical behaviour of the growth process is different from the average. We develop a new formalism to study the average growth process and extend it to the calculation of higher moments and finally of the probability distribution. We show that the fluctuations of the growth process increase exponentially with time. We describe the interesting features of the distribution.     

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.     

Pion Effect of Nuclear Matter in a Chiral Sigma Model

We develop a new framework for the study of the nuclear matter based on the linear sigma model.We introduce a completely new viewpoint on the treatment of the nuclear matter with the inclusion of the pion.We extend the relativistic chiral mean field model by using the similar method in the tensor optimized shell model.We also regulate the pion-nucleon interaction by considering the form-factor and short range repulsion effects.We obtain the equation of state of nuclear matter and study the importance of the pion effect.     

The driven oscillator in the photon-number probability representation of quantum mechanics

We study the evolution of the driven harmonic oscillator in the probability representation of quantum mechanics. We use the photon-number tomographic-probability-distribution function to describe the quantum states of the system. We give a general review of the photon-number tomographic framework, including a discussion on the connection with other representations of quantum mechanics. We find tomograms of coherent states as well as excited states of the harmonic oscillator in an explicit form. We discuss the time evolution of the photon-number tomograms and transforms of the propagators for different representations of quantum mechanics. We obtain the propagator for the photon-number tomographic-distribution function for the case of the driven oscillator in an explicit form.     

Resistive Plates Carrying a Steady Current: Electric Potential and Surface Charges Close to the Battery

We treat the problem of two resistive plates carrying a steady current in the same direction. We consider a linear battery orthogonal to the direction of the current in the middle of the plates. We study the behavior of the surface charges close to the battery. We calculate the potential and electric field in the space outside the plates. We also consider the case of a single resistive plate carrying a steady current.     

Abelian Higgs model with a Chern-Simons term in 3-dimensional gravitation

We consider the Abelian Higgs model with a Chern-Simons term coupled to the Einstein theory of gravitation in 3-dimensional space-time. We seek a finite solution, regular everywhere, having a stationary, cylindrically symmetric metric. We analyze these field equations and we suggest that such a solution exists. We find that the asymptotic metric of this solution corresponds to that which describes gravitationally a massive particle with spin. We obtain explicitly the expression of the spin. We give only the expression of the mass in the first order with respect to the gravitational coupling constant.     

Oblique propagation of longitudinal waves in magnetized spin-1/2 plasmas: Independent evolution of spin-up and spin-down electrons

We consider quantum plasmas of electrons and motionless ions. We describe separate evolution of spin-up and spin-down electrons. We present corresponding set of quantum hydrodynamic equations. We assume that plasmas are placed in an uniform external magnetic field. We account different occupation of spin-up and spin-down quantum states in equilibrium degenerate plasmas. This effect is included via equations of state for pressure of each species of electrons. We study oblique propagation of longitudinal waves. We show that instead of two well-known waves (the Langmuir wave and the Trivelpiece–Gould wave), plasmas reveal four wave solutions. New solutions exist due to both the separate consideration of spin-up and spin-down electrons and different occupation of spin-up and spin-down quantum states in equilibrium state of degenerate plasmas.     

Quantum phase analysis of 1D superconducting quantum dot lattice using extended Bose-Hubbard model

We have obtained the quantum phase diagram of a one-dimensional superconducting quantum dot lattice using the extended Bose-Hubbard model for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from the Mott insulating phase to the superconducting phase for integer band fillings of Cooper pairs. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, besides the charge density wave and superconducting phases for half-integer band fillings. We also predict that extended range interactions are necessary to obtain the correct phase boundary of a one-dimensional interacting Cooper system. We have used the density matrix renormalization group method and Abelian bosonization to study our system.     

Density,phase and coherence properties of a low dimensional Bose-Einstein systems moving in a disordered potential

We present a detailed numerical study of the dynamics of a disordered one-dimensional Bose-Einstein condensates in position and momentum space. We particularly focus on the region where non-linearity and disorder simultaneously effect the time propagation of the condensate as well as the possible interference between various parts of the matter wave. We report oscillation between spatially extended and localized behavior for the propagating condensate which dies down with increasing non-linearity. We also report intriguing behavior of the phase fluctuation and the coherence properties of the matter wave. We also briefly compare these behavior with that of a two-dimensional condensate. We mention the relevance of our results to the related experiments on Anderson localization and indicate the possibility of future experiments     

Consistent treatment of charm evolution in deep inelastic scattering

We present a formulation which allows heavy quark mass effects to be explicitly incorporated in both the coefficient functions and the splitting functions in the parton evolution equations. We obtain a consistent procedure for evolution through the threshold regions for and production in deep inelastic scattering, which allows the prediction of the charm and bottom quark densities. We use the new formulation to perform a next-to-leading order global parton analysis of deep inelastic and related hard scattering data. We find that the optimum fit has . We give predictions for the charm components of the proton structure functions and as functions of and and, in particular, find that is in good agreement with the existing measurements. We examine the range of validity of the photon-gluon fusion model for electroproduction. We emphasize the value of a precision measurement of the charm component at HERA. Received: 12 May 1997 / Revised version: 12 June 1997     

Quantum phase diagram of granular superconducting quantum dots array

We study the quantum phase diagram of granular superconducting quantum dots (GSQD) array. We implement the physics of granularity by considering site dependent Josephson couplings, on-site charging energies and the intersite interactions. We predict dimer density wave and staggered phases at the insulating state for higher order commensurability. Several parts of the quantum phase diagram of GSQD are in contrast with the clean superconducting quantum dots array. We also obtain the superconducting phase of GSQD. We develop the theory for weak tunneling conductance and the Coulomb energy is smaller than the superconducting gap.     

Exactly solvable models of nonstationary turbulence in Bose condensate

In this Letter we study a turbulence decay mechanism in the superfluid liquid. We proceed with developement of master equation approach introduced Copeland, Kibble, Steer and Nemirovskii. We obtain the full rate of reconnection in presence of normal component. We also discuss different random-walk models of vortex filaments. We obtain the expression for the reconnection rate in the nonstationary vortex tangle for these models. The equation for the full number of vortex loops is derived. We also obtain the expression for the relaxation time.     

Controlling soliton explosions

We investigate the dynamics of solitons in generalized Klein–Gordon equations in the presence of nonlinear damping and spatiotemporal perturbations. We will present different mechanisms for soliton explosions. We show (both analytically and numerically) that some space-dependent perturbations or nonlinear damping can make the soliton internal mode unstable leading to soliton explosion. We will show that, in some cases, while some conditions are satisfied, the soliton explodes becoming a permanent, extremely complex, spatiotemporal dynamics. We believe these mechanisms can explain some of the phenomena that recently have been reported to occur in excitable media. We present a method for controlling soliton explosions.     

Interacting Tachyon Dark Energy Model in Gauss-Bonnet Cosmology

We investigate the tachyon scalar filed model of dark energy in the framework of Gauss-Bonnet cosmology. We consider a spatially non-flat universe containing interacting tachyon dark energy with pressureless dark matter. We obtain the equation of state and deceleration parameters. We also reconstruct the potential and the dynamics for the tachyon scalar field model, which describe accelerated expansion of the universe.     

Universality of entropy scaling in one dimensional gapless models

We consider critical models in one dimension. We study the ground state in the thermodynamic limit (infinite lattice). We are interested in an entropy of a subsystem. We calculate the entropy of a part of the ground state from a space interval (0,x). At zero temperature it describes the entanglement of the part of the ground state from this interval with the rest of the ground state. We obtain an explicit formula for the entropy of the subsystem at any temperature. At zero temperature our formula reproduces a logarithmic formula, discovered by Vidal, Latorre, Rico, and Kitaev for spin chains. We prove our formula by means of conformal field theory and the second law of thermodynamics. Our formula is universal. We illustrate it for a Bose gas with a delta interaction and for the Hubbard model.     

Resonant X-ray diffraction: Basic theoretical principles

We present the main steps governing the theory of resonant X-ray diffraction (RXD). We focus on the derivation of the anomalous scattering amplitude from perturbation theory and starting from the low-energy expansion of the Dirac Hamiltonian. We give the main ingredients of the multipolar expansion in term of electric and magnetic transitions. We also show the expansion in terms of scattering tensors of the material. We end by giving the RXD formula necessary to simulate in practice this spectroscopy.     

Flavor changing neutral currents and a Z′

We consider a non-universal Z′ that affects primarily the third generation fermions as an example of new physics associated with the top-quark. We first discuss constraints on the mass and coupling strength of such a Z′. We then turn our attention to the flavor changing neutral currents (FCNC) present in the model. We discuss the experimental constraints and their implications. We propose an ansatz to understand the smallness of the FCNC in terms of the CKM matrix.