Bosonization rules in 12 + 1 dimensions

We derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system with a boundary. We compute the fermion determinant of the fermionic fluctuations for a system with a boundary using Forman's approach. We find that the degrees of freedom induced at the boundary do not to modify the commutation relations of the bulk. We give an explicit derivation of the bosonization rules for the fermion operators for a system with boundaries. We derive a set of bosonization rules for the Fermi operators which include the explicit effect of the boundaries and of boundary degrees of freedom. As a byproduct, we calculate the one-particle Green function and determine the effects of the boundaries on its analytic structure.     

Bosonization rules in dimensions

We derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system with a boundary. We compute the fermion determinant of the fermionic fluctuations for a system with a boundary using Forman's approach. We find that the degrees of freedom induced at the boundary do not to modify the commutation relations of the bulk. We give an explicit derivation of the bosonization rules for the fermion operators for a system with boundaries. We derive a set of bosonization rules for the Fermi operators which include the explicit effect of the boundaries and of boundary degrees of freedom. As a byproduct, we calculate the one-particle Green function and determine the effects of the boundaries on its analytic structure.     

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.     

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.     

Double-Pulse Spectra and Closed-Orbits: Photodetachment of H-in Parallel Electric and Magnetic Fields

We derive a formula for double-pulse spectra from closed-orbit theory. We then calculate the double-pulsephotodetachment spectra of H- in the presence of parallel electric and magnetic fields. We analyze the spectra in termsof closed-orbits of the system. We suggest a method for the measurement of a phase associated with each closed-orbit.     

Nonmarkovian dynamics of stochastic differential equations with quadratic noise

We consider a stochastic differential equation with a quadratic nonlinearity in the noise. We derive equations for the steady state probability density and joint probability distribution valid beyond a markovian approximation. We do not assume that the strength of the random term is small. The equations are derived for the case of an Ornstein-Uhlenbeck noise and also for a dichotomic noise. A comparison is made. We discuss some examples for which correlation functions and the associated relaxation times are calculated.     

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 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.     

Unextendible Product Bases,Uncompletable Product Bases and Bound Entanglement

We report new results and generalizations of our work on unextendible product bases (UPB), uncompletable product bases and bound entanglement. We present a new construction for bound entangled states based on product bases which are only completable in a locally extended Hilbert space. We introduce a very useful representation of a product basis, an orthogonality graph. Using this representation we give a complete characterization of unextendible product bases for two qutrits. We present several generalizations of UPBs to arbitrary high dimensions and multipartite systems. We present a sufficient condition for sets of orthogonal product states to be distinguishable by separable superoperators. We prove that bound entangled states cannot help increase the distillable entanglement of a state beyond its regularized entanglement of formation assisted by bound entanglement.     

Leibniz and Lie Algebra Structures for Nambu Algebra

We canonically associate a Leibniz algebra with every Nambu algebra. We show how various homological and cohomological complexes for a Nambu algebra can be naturally obtained from its structure as a module over the Leibniz algebra. We also present a generalization of a classical Lie--Berezin construction for Nambu algebras and extend these results for Nambu superalgebras.     

Secure information transfer based on computing reservoir

There is a broad area of research to ensure that information is transmitted securely. Within this scope, chaos-based cryptography takes a prominent role due to its nonlinear properties. Using these properties, we propose a secure mechanism for transmitting data that relies on chaotic networks. We use a nonlinear on–off device to cipher the message, and the transfer entropy to retrieve it. We analyze the system capability for sending messages, and we obtain expressions for the operating time. We demonstrate the system efficiency for a wide range of parameters. We find similarities between our method and the reservoir computing.     

Collections of heteroclinic cycles in the Kuramoto-Sivashinsky equation

We study the Kuramoto-Sivashinky equation with periodic boundary conditions in the case of low-dimensional behavior. We analyze the bifurcations that occur in a six-dimensional (6D) approximation of its inertial manifold. We mainly focus on the attracting and structurally stable heteroclinic connections that arise for these parameter values. We reanalyze the ones that were previously described via a 4D reduction to the center-unstable manifold (Ambruster et al., 1988, 1989). We also find a parameter region for which a manifold of structurally stable heteroclinic cycles exist. The existence of such a manifold is responsible for an intermittent behavior which has some features of unpredictability.     

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.     

Deformed Subadditivity Condition for Qudit States and Hybrid Positive Maps

We extend the subadditivity condition for q-deformed entropy of a bipartite quantum system to the case of an arbitrary quantum system including the single qudit state. We present the subadditivity condition for the density matrix of the single qutrit state in an explicit form. We obtain the inequality for the purity parameters of a bipartite quantum system and its subsystems. We propose a positive map construction using the fiducial density matrix.     

The Nonsymmetric Kaluza–Klein Theory and Modern Physics A Novel Approach

We consider in the paper the Nonsymmetric Kaluza–Klein Theory finding a condition for a color confinement in the theory. We consider also a Kerner–Wong–Kopczyński equation in this theory. The Nonsymmetric Kaluza–Klein Theory with a spontaneous symmetry breaking and Higgs' mechanism is examined. We find a mass spectrum for a broken gauge bosons and Higgs' particles. We derive a generalization of Kerner–Wong–Kopczyński equation in the presence of Higgs' field. A new term in the equation is a generalization of a Lorentz force term for a Higgs' field. We consider also a bosonic part of GSW (Glashow–Salam–Weinberg) model in our theory, getting masses for W, Z bosons and for a Higgs' boson agreed with an experiment. We consider Kerner–Wong–Kopczyński equation in GSW model obtaining some additional charges coupled to Higgs' field.     

Transport in a fluctuating potential

We study the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. The potential has no inversion symmetry, and the fluctuations are correlated in time. At finite temperatures, a stationary current is induced. The amplitude and the direction of the current depend on the details of the noise process that is responsible for the potential fluctuations. We discuss several limiting situations for a general case. Furthermore we calculate the current in the case of a piecewise linear potential for different noise processes and parameters. A detailed discussion of the results is given, including a discussion of the mechanism that is responsible for the current reversal. We compare the present results with results for transport in a ratchet-like potential due to a fluctuating force. We also discuss the biological relevance of the present models for molecular motors. We present a model for the motion of molecular motors that explains why similar molecular motors can move in different directions.     

Generalized Second Law of Thermodynamics in Parabolic LTB Inhomogeneous Cosmology

We study thermodynamics of the parabolic Lemaitre-Tolman-Bondi(LTB) cosmology supported by a perfect Suid source.This model is the natural generalization of the Sat Friedmann-Robertson-Walker(FRW) universe,and describes an inhomogeneous universe with spherical symmetry.After reviewing some basic equations in the parabolic LTB cosmology,we obtain a relation for the deceleration parameter in this model.We also obtain a condition for which the universe undergoes an accelerating phase at the present time.We use the first law of thermodynamics on the apparent horizon together with the Einstein field equations to get a relation for the apparent horizon entropy in LTB cosmology.We find out that in LTB model of cosmology,the apparent horizon's entropy could be feeded by a term,which incorporates the effects of the inhomogeneity.We consider this result and get a relation for the total entropy evolution,which is used to examine the generalized second law of thermodynamics for an accelerating universe.We also verify the validity of the second law and the generalized second law of thermodynamics for a universe filled with some kinds of matters bounded by the event horizon in the framework of the parabolic LTB model.     

An unconditionally gradient stable numerical method for solving the Allen-Cahn equation

We consider an unconditionally gradient stable scheme for solving the Allen-Cahn equation representing a model for anti-phase domain coarsening in a binary mixture. The continuous problem has a decreasing total energy. We show the same property for the corresponding discrete problem by using eigenvalues of the Hessian matrix of the energy functional. We also show the pointwise boundedness of the numerical solution for the Allen-Cahn equation. We describe various numerical experiments we performed to study properties of the Allen-Cahn equation.