Boltzmann Limit for a Homogeneous Fermi Gas with Dynamical Hartree-Fock Interactions in a Random Medium

We study the dynamics of the thermal momentum distribution function for an interacting, homogeneous Fermi gas on ℤ³ in the presence of an external weak static random potential, where the pair interactions between the fermions are modeled in dynamical Hartree-Fock theory. We determine the Boltzmann limits associated to different scaling regimes defined by the size of the random potential, and the strength of the fermion interactions.     

Measures on Classes of Subspaces Affiliated with a von Neumann Algebra

Let ℳ be a von Neumann algebra acting on a Hilbert space H and let S be a dense lineal in H that is affiliated with a von Neumann algebra ℳ. The “topological” definition of measures on the classes of orthoclosed and splitting subspaces of S affiliated with a von Neumann algebra ℳ is given and results on the relationships of these measures to measures on orthoprojections of the algebra ℳ are presented.     

Geometric Phase in a Time-Dependent System with Laguerre Polynomial State

By using of the invariant theory, we have studied the geometric phase in a time-dependent system with Laguerre polynomial state, the dynamical and geometric phases are given, respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.     

Tunable diode laser spectroscopy of benzene near 1684 nm with a low-temperature VCSEL

We describe the application of a long-wavelength vertical-cavity surface-emitting laser (VCSEL) with extended tuning range to the detection of benzene vapor at atmospheric pressure. A benzene absorption feature centered at 1684.24 nm was accessed by reducing the heat sink temperature of a VCSEL designed for room-temperature operation to −55°C. This allowed us to increase the injection current and thus to extend a single-scan tuning interval up to 46.4 cm⁻¹ or 13.2 nm around a central wavelength of 1687.4 nm. Five absorption lines of methane in the 5903–5950 cm⁻¹ range could be acquired within single laser scans at a repetition rate of 500 Hz. A benzene absorption feature between 5926 and 5948 cm⁻¹ was recorded for concentration measurements at atmospheric pressure using a single-pass 1.2 m absorption cell. A 50 ppmv mixture of CH₄ in N₂ was introduced into the cell along with benzene vapor to calibrate benzene concentration measurements. Benzene mixing ratios down to ∼90 ppmv were measured using a direct absorption technique. The minimum detectable absorbance and detection limit of benzene were estimated to be ∼10⁻⁴ and 30 ppmv, respectively. Using the wavelength modulation technique, we measured a second harmonic sensor response to benzene vapor absorption in air at atmospheric pressure as a function of modulation index. We conclude that a low-temperature monolithic VCSEL operating near 1684 nm can be employed in compact benzene sensors with a detection limit in the sub-ppm range.     

Dirac-Type Equations in a Gravitational Field,with Vector Wave Function

An analysis of the classical-quantum correspondence shows that it needs to identify a preferred class of coordinate systems, which defines a torsionless connection. One such class is that of the locally-geodesic systems, corresponding to the Levi-Civita connection. Another class, thus another connection, emerges if a preferred reference frame is available. From the classical Hamiltonian that rules geodesic motion, the correspondence yields two distinct Klein-Gordon equations and two distinct Dirac-type equations in a general metric, depending on the connection used. Each of these two equations is generally-covariant, transforms the wave function as a four-vector, and differs from the Fock-Weyl gravitational Dirac equation (DFW equation). One obeys the equivalence principle in an often-accepted sense, whereas the DFW equation obeys that principle only in an extended sense. Part of this work was done while the author was at Dipartimento di Fisica, Università di Bari and INFN Bari, Italy.     

Phase transitions in a holographic s $$$$ p model with back-reaction

In a previous paper (Nie et al. in JHEP 1311:087, arXiv:1309.2204 [hep-th], 2013), we presented a holographic s \(+\) p superconductor model with a scalar triplet charged under an SU(2) gauge field in the bulk. We also study the competition and coexistence of the s-wave and p-wave orders in the probe limit. In this work we continue to study the model by considering the full back-reaction. The model shows a rich phase structure and various condensate behaviors such as the “n-type” and “u-type” ones, which are also known as reentrant phase transitions in condensed matter physics. The phase transitions to the p-wave phase or s \(+\) p coexisting phase become first order in strong back-reaction cases. In these first order phase transitions, the free energy curve always forms a swallow tail shape, in which the unstable s \(+\) p solution can also play an important role. The phase diagrams of this model are given in terms of the dimension of the scalar order and the temperature in the cases of eight different values of the back-reaction parameter, which show that the region for the s \(+\) p coexisting phase is enlarged with a small or medium back-reaction parameter but is reduced in the strong back-reaction cases.     

The Transformation Properties at the Quantum Level in Field Theories for a Gauge-Invariant System with a Higher-Order Lagrangian

Based on the configuration-space generating functional of the Green functions for the gauge-invariant system in higher-order derivatives theories, the equations of the transformation properties at the quantum level have been derived. It follows that the sufficient conditions are found which implies that there exists the conservation laws and the expressions of the quantal conserved laws are also given. Applying the results to the non-Abelian Chern-Simons higher-order derivatives theories, the quantal BRST conserved charge and other conserved charges are found, the transformation properties of the conformal transformation at the quantum level is discussed, the quantal conserved angular momentum is derived, it is pointed out that fractional spin in this system may be also preserved in quantum theories. But the connection between the symmetries and conservation laws in classical theories are not always preserved in quantum theories.     

Cosmological constant in a model with superstring-inspired E 6 unification and shadow θ-particles

We have developed the concept of parallel existence of the ordinary (O-) and mirror (M-), or shadow (Sh-) worlds. In the first part of the paper we consider a mirror world with broken mirror parity and the breaking E ₆→SU(3)³ in both worlds. We show that in this case the evolutions of coupling constants in the O- and M-worlds are not identical, having different parameters for similar evolutions. E ₆ unification, inspired by superstring theory, restores the broken mirror parity at the scale ～10¹⁸ GeV. With the aim to explain the tiny cosmological constant, in the second part we consider the breakings: E ₆→SO(10)×U(1) _Z in the O-world, and E′₆→SU(6)′×SU(2)′ _θ in the Sh-world. We assume the existence of shadow θ-particles and the low-energy symmetry group SU(3)′ _C ×SU(2)′ _L ×SU(2)′ _θ ×U(1)′ _Y in the shadow world, instead of the Standard Model. The additional non-Abelian SU(2)′ _θ group with massless gauge fields, “thetons”, has a macroscopic confinement radius 1/Λ′ _θ . The assumption that Λ′ _θ ≈2.3?10^?3 eV explains the tiny cosmological constant given by recent astrophysical measurements. In this way the present work opens the possibility to specify a grand unification group, such as E ₆, from cosmology.     

Magnetic moment generation from non-minimal couplings in a scenario with Lorentz-symmetry violation

This paper deals with situations that illustrate how the violation of Lorentz symmetry in the gauge sector may contribute to magnetic moment generation of massive neutral particles with spin- and spin-1. The procedure we adopt here is based on Relativistic Quantum Mechanics. We work out the non-relativistic regime that follows from the wave equation corresponding to a certain particle coupled to an external electromagnetic field and a background that accounts for the Lorentz-symmetry violation, and we thereby read off the magnetic dipole moment operator for the particle under consideration. We keep track of the parameters that govern the non-minimal electromagnetic coupling and the breaking of Lorentz symmetry in the expressions we get for the magnetic moments in the different cases we contemplate. Our claim is that the tiny magnetic dipole moment of truly-elementary neutral particles might signal Lorentz-symmetry violation.     

Conformal anisotropic relativistic charged fluid spheres with a linear equation of state

We obtain two new families of compact solutions for a spherically symmetric distribution of matter consisting of an electrically charged anisotropic fluid sphere joined to the Reissner–Nordstrom static solution through a zero pressure surface. The static inner region also admits a one parameter group of conformal motions. First, to study the effect of the anisotropy in the sense of the pressures of the charged fluid, besides assuming a linear equation of state to hold for the fluid, we consider the tangential pressure p _⊥ to be proportional to the radial pressure p _r , the proportionality factor C measuring the grade of anisotropy. We analyze the resulting charge distribution and the features of the obtained family of solutions. These families of solutions reproduce for the value C=1, the conformal isotropic solution for quark stars, previously obtained by Mak and Harko. The second family of solutions is obtained assuming the electrical charge inside the sphere to be a known function of the radial coordinate. The allowed values of the parameters pertained to these solutions are constrained by the physical conditions imposed. We study the effect of anisotropy in the allowed compactness ratios and in the values of the charge. The Glazer’s pulsation equation for isotropic charged spheres is extended to the case of anisotropic and charged fluid spheres in order to study the behavior of the solutions under linear adiabatic radial oscillations. These solutions could model some stage of the evolution of strange quark matter fluid stars.     

A Lattice Hierarchy with a Free Function and Its Reductions to the Ablowitz-Ladik and Volterra Hierarchies

By embedding a free function into a compatible zero curvature equation, we propose a lattice hierarchy with the free function which still admits zero curvature representation. It is interesting that the hierarchy can reduce the Ablowitz-Ladik hierarchy, the Volterra hierarchy and a new hierarchy by properly choosing the embedded function. Moreover, the new hierarchy is integrable in Liouville’s sense and possess multi-Hamiltonian structure.     

Inequivalent quantizations of the rational Calogero model with a Coulomb type interaction

We consider the inequivalent quantizations of a N-body rational Calogero model with a Coulomb type interaction. It is shown that for a certain range of the coupling constants, this system admits a one-parameter family of self-adjoint extensions. We analyze both the bound and scattering state sectors and find novel solutions of this model. We also find the ladder operators for this system, with which the previously found solutions can be constructed.     

Accelerating Universe with a Special Form of Decelerating Parameter

In this article, we try to investigate the quintessence model with a minimally coupled scalar field by taking a special form of decelerating parameter q in such a way that which provides an early deceleration and late time acceleration for barotropic fluid and Chaplygin gas dominated models. We have shown that the potential function V(φ) is always decreases with the scalar field φ for barotropic and Chaplygin both models. The {r,s} diagram shows the behaviour of the universe in different stages during the evolution.     

Perturbation Theory for a Stochastic Process with Ornstein-Uhlenbeck Noise

The Ornstein-Uhlenbeck process may be used to generate a noise signal with a finite correlation time. If a one-dimensional stochastic process is driven by such a noise source, it may be analysed by solving a Fokker-Planck equation in two dimensions. In the case of motion in the vicinity of an attractive fixed point, it is shown how the solution of this equation can be developed as a power series. The coefficients are determined exactly by using algebraic properties of a system of annihilation and creation operators.     

Soliton Structures in a Molecular Chain Model with Saturation

In the present work, we study, by means of a one-dimensional lattice model, the collective excitations corresponding to intra molecular ones of a chain like proteins. It is shown that such excitations are described by the nonlinear Schrödinger equation with saturation. The solutions obtained here are the bell solitons, bubbles, kinks and crowdons. Since they belong to different sectors on the parametric space, the bubble condensation could give rise to some important changes of phase in this nonlinear system. Additionally, it is shown that the limiting velocity of the solitons is the velocity of sound waves corresponding to longitudinal vibrations of molecules.     

The Effects of Time Delay on Stochastic Resonance in a Bistable System with Correlated Noises

The effects of time delay on stochastic resonance (SR) in a bistable system with time delay, correlated noises and periodic signal are studied by using the theory of signal-to-noise ratio (SNR). The expression of the SNR is derived under the adiabatic limit and the small delay time approximation. It is found that: (i) For the case of no correlations between multiplicative and additive noise, the delay time τ can enhance the SNR as a function of the multiplicative noise intensity α and it can restrain the SNR as a function of the additive noise intensity D; (ii) For the case of correlations between multiplicative and additive noise, τ can induce a minimum and maximum in curve of the SNR as a function of α, and can intensively restrain the SNR as a function of the D and there is a critical value of delay tim τ _c =0.1 in the height of the SNR peak with change of τ, i.e., when τ takes value blow τ _c , the τ boosts up the SNR as a function of the strength λ of correlations between multiplicative and additive noise, however, when τ takes value above τ _c , the τ restrains that.     

Dissipative solitons compounds in a fiber laser. Analogy with the states of the matter

We investigate experimentally ordered and disordered pattern formation of solitons in a double-clad fiber laser. We point out an analogy between the different states of matter and the states of a set of dissipative solitons. In particular, we have identified a gas, a supersonic gas flow, a liquid, a polycrystal and a crystal of solitons. The different states are obtained only by adjustment of the intracavity phase plates.     

Wegner-type Bounds for a Multi-particle Continuous Anderson Model with an Alloy-type External Potential

We consider an N-particle quantum systems in ? ^d , with interaction and in presence of a random external alloy-type potential (a continuous N-particle Anderson model). We establish Wegner-type bounds (inequalities) for such models, giving upper bounds for the probability that random spectra of Hamiltonians in finite volumes intersect a given set.     

Rigorous Treatment of the Liquid-Vapor Transition in a Polydisperse System with Kac Interaction

Within the canonical formalism, we consider a polydisperse lattice-gas model and a polydisperse continuous system interacting with the Kac potential. We obtain rigorous expressions for free energy densities. We also exhibit phase diagrams of the bidisperse lattice-gas model.     

Precise predictions for Higgs production in association with a W-boson pair at ILC

Higgs-boson production in association with a W-boson pair at e ⁺ e ⁻ linear colliders is one of the important processes in probing the coupling between the Higgs boson and vector gauge bosons and discovering the signature of new physics. We describe the impact of the complete electroweak (EW) radiative corrections of to this process in the standard model (SM) at the International Linear Collider (ILC), and investigate the dependence of the lowest-order (LO) and EW next-to-leading order (NLO) corrected cross sections on the colliding energy and the Higgs-boson mass. The LO and NLO EW corrected distributions of the invariant mass of the W-boson pair and the transverse momenta of the final W-boson and Higgs boson are presented. Our numerical results show that the relative EW radiative correction (δ _ew) varies from −19.4% to 0.2% when m _H=120 GeV and grows from 300 GeV to 1.2 TeV.