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.     

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.     

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.     

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.     

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.     

Constructing quantum games from symmetric non-factorizable joint probabilities

We construct quantum games from a table of non-factorizable joint probabilities, coupled with a symmetry constraint, requiring symmetrical payoffs between the players. We give the general result for a Nash equilibrium and payoff relations for a game based on non-factorizable joint probabilities, which embeds the classical game. We study a quantum version of Prisoners' Dilemma, Stag Hunt, and the Chicken game constructed from a given table of non-factorizable joint probabilities to find new outcomes in these games. We show that this approach provides a general framework for both classical and quantum games without recourse to the formalism of quantum mechanics.     

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     

Moment problem for effect algebras

We present a solution to the moment problem for effect algebras, concerning mean values of all powers of an observable concentrated on the interval [0, 1] for states from a convex set. We give a solution for particular examples, e.g., for the set of all effect operators. We examine how this problem is related to a socalled E-property. Finally, we give a solution for observables studied in the operational approach to physical theories.     

Relativistic compact stars with charged anisotropic matter

In this article, we perform a detailed theoretical analysis of new exact solutions with anisotropic fluid distribution of matter for compact objects subject to hydrostatic equilibrium. We present a family solution to the Einstein-Maxwell equations describing a spherically symmetric, static distribution of a fluid with pressure anisotropy. We implement an embedding class one condition to obtain a relation between the metric functions. We generalize the properties of a spherical star with hydrostatic equilibrium using the generalised Tolman-Oppenheimer-Volkoff (TOV) equation. We match the interior solution to an exterior Reissner-Nordström one, and study the energy conditions, speed of sound, and mass-radius relation of the star. We also show that the obtained solutions are compatible with observational data for the compact object Her X-1. Regarding our results, the physical behaviour of the present model may serve for the modeling of ultra compact objects.     

Multiplexing encryption technique by combining random amplitude and phase masks

We propose and demonstrate an encryption-selectable undercover multiplexing. We encrypt and multiplex images for storage by means of a random phase mask common to every image, covered with random amplitude masks different for each image. In order to get a correct decryption of the encoded information, we have to use the appropriate random amplitude mask; otherwise fake information is recovered. We employ a phase conjugation scheme to generate the recovering wavefronts. We analyze and compare the different alternatives and degrees of complexity this combination of masks brings to enhance the security of optical encrypting techniques. We also include an analysis on the advantages and disadvantages this undercover multiplexing protocol offers. We present digital simulations to demonstrate the soundness of the proposal.     

Entanglement of a two-particle Gaussian state interacting with a heat bath

The effect of a thermal reservoir is investigated on a bipartite Gaussian state. We derive a pre-Lindblad master equation in the non-rotating wave approximation for the system. We then solve the master equation for a bipartite harmonic oscillator Hamiltonian with entangled initial state. We show that for strong damping the loss of entanglement is the same as for freely evolving particles. However, if the damping is small, the entanglement is shown to oscillate and eventually tend to a constant non-zero value.     

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.     

Surface and curvature properties of neutron-rich nuclei

We use the extended Thomas-Fermi approximation and Skyrme-type interactions to describe the energy density of a semi-infinite slab of neutron-rich nuclear matter at zero temperature. We allow for the existence of a drip phase at low proton fractions in addition to the more dense nuclear phase. We determine various bulk properties of both phases when the system is in equilibrium. We extend the usual definition of the surface energy to apply to the case where drip is present. Assuming the density profile has the form of a Fermi function to a power, we perform a constrained variational calculation to determine the parameters of the density profile. The surface and curvature energies are calculated for proton fractions ranging from 0.5 (symmetric nuclear matter) to 0 (pure neutron matter) for typical Skyrme-type interactions. We find significantly different asymmetry dependences for different interactions. For proton fractions close to 0.5, our results are in close agreement with the predictions of the droplet model. We also present results of calculations for fission barrier properties and phase transitions between nuclei and bubbles to highlight the role of surface and curvature energies in the neutron-rich regime.     

Modular forms and three-loop superstring amplitudes

We study a proposal of D'Hoker and Phong for the chiral superstring measure for genus three. A minor modification of the constraints they impose on certain Siegel modular forms leads to a unique solution. We reduce the problem of finding these modular forms, which depend on an even spin structure, to finding a modular form of weight 8 on a certain subgroup of the modular group. An explicit formula for this form, as a polynomial in the even theta constants, is given. We checked that our result is consistent with the vanishing of the cosmological constant. We also verified a conjecture of D'Hoker and Phong on modular forms in genus 3 and 4 using results of Igusa.     

Kinetic Arrest Originating in Competition Between Attractive Interaction and Packing Force

We discuss the situation where attractive and repulsive portions of the interparticle potential both contribute significantly to glass formation. We introduce the square-well potential as prototypical model for this situation, and reject the Baxter model as a useful model for comparison to experiment on glasses, based on our treatment within mode coupling theory. We present explicit results for various well widths, and show that, for narrow wells, there is a useful analytical formula that would be suitable for experimentalists working in the field of colloidal science. We raise the question as to whether, in a more exact treatment, the sticky-sphere limit might have an infinite glass transition temperature or a high but finite one.     

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.     

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 fluid source. This model is the natural generalization of the flat 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.     

Holomorphic representation of coherent states of a singular oscillator and their Darboux representation

We consider the coherent states of a singular oscillator; these states are defined to be the characteristic states of an operator that reduces the number of basis functions for a discrete spectrum to one. We use the Darboux transform to study the coherent states of a transformed Hamiltonian. We obtain an expression for measures that can be used to decompose unity. We construct a holomorphic representation for the state vectors in the space of functions holomorphic everywhere in the complex plane, including vectors for discrete spectra and coherent states. We obtain a holomorphic representation of the Darboux transformation operators. Tomsk State University. Institute of High-Energy Electronics. Siberian Division of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 46–53, February, 1998.     

Variational self-consistent theory for trapped Bose gases at finite temperature

We apply the time-dependent variational principle of Balian-Vénéroni to a system of self-interacting trapped bosons at finite temperature. The method leads to a set of coupled non-linear time dependent equations for the condensate density, the thermal cloud and the anomalous density. We solve numerically these equations in the static case for a harmonic trap. We analyze the various densities as functions of the radial distance and the temperature. We find an overall good qualitative agreement with recent experiments as well as with the results of many theoretical groups. We also discuss the behavior of the anomalous density at low temperatures owing to its importance to account for many-body effects.