On the Stability of a Quantum Dynamics of a Bose-Einstein Condensate Trapped in a One-Dimensional Toroidal Geometry

We rigorously analyze the stability of the “quasi-classical” dynamics of a Bose-Einstein condensate with repulsive and attractive interactions, trapped in an effective 1D toroidal geometry. The “classical” dynamics, which corresponds to the Gross-Pitaevskii mean field theory, is stable in the case of repulsive interaction, and unstable (under some conditions) in the case of attractive interaction. The corresponding quantum dynamics for observables is described by using a closed system of linear partial differential equations. In both cases of stable and unstable quasi-classical dynamics the quantum effects represent a singular perturbation to the quasi-classical solutions, and are described by the terms in these equations which consist of a small quasi-classical parameter which multiplies high-order “spatial” derivatives. We demonstrate that as a result of the quantum singularity for observables a convergence of quantum solutions to the corresponding classical solutions exists only for limited times, and estimate the characteristic time-scales of the convergence.     

Study of a Long Range Perturbation of a One-Dimensional Kac Model

We consider a one dimensional ferromagnetic Ising spin system with interactions that correspond to a 1/r ² long range perturbation of the usual Kac model. We apply a coarse graining procedure widely used for higher-dimensional finite range Kac potentials to describe the basic properties of the system and the relation with the mean field theory.     

The Spectrum of the Billiard Laplacian of a Family of Random Billiards

Random billiards are billiard dynamical systems for which the reflection law giving the post-collision direction of a billiard particle as a function of the pre-collision direction is specified by a Markov (scattering) operator P. Billiards with microstructure are random billiards whose Markov operator is derived from a “microscopic surface structure” on the boundary of the billiard table. The microstructure in turn is defined in terms of what we call a billiard cellQ, the shape of which completely determines the operator P. This operator, defined on an appropriate Hilbert space, is bounded self-adjoint and, for the examples considered here, a Hilbert-Schmidt operator. A central problem in the statistical theory of such random billiards is to relate the geometric characteristics of Q and the spectrum of P. We show, for a particular family of billiard cell shapes parametrized by a scale invariant curvature K (Fig. 2), that the billiard Laplacian P−I is closely related to the ordinary spherical Laplacian, and indicate, by partly analytical and partly numerical means, how this provides asymptotic information about the spectrum of P for small values of K. It is shown, in particular, that the second moment of scattering about the incidence angle closely approximates the spectral gap of P.     

Classical and Non-relativistic Limits of a Lorentz-Invariant Bohmian Model for a System of Spinless Particles

A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating the squared norm of the wave function as a space-time probability density. The particle’s configurations evolve in space-time in terms of a parameter σ with dimensions of time. In this work this model is further analyzed and extended to the case of an interaction with an external electromagnetic field. The physical meaning of σ is explored. Two special situations are studied in depth: (1) the classical limit, where the Einsteinian Mechanics of Special Relativity is recovered and the parameter σ is shown to tend to the particle’s proper time; and (2) the non-relativistic limit, where it is obtained a model very similar to the usual non-relativistic Bohmian Mechanics but with the time of the frame of reference replaced by σ as the dynamical temporal parameter.     

Quantum Dynamics of a Harmonic Oscillator in a Deformed Bath

The dissipative quantum dynamics of a harmonic oscillator in the presence of a deformed bath is investigated. The deformed bath is modelled by a collection of deformed quantum harmonic oscillators as a generalization of Hopfield model. The transition probabilities between energy levels of the oscillator are obtained perturbatively and discussed.     

Radiation Laws of a Kerr Nonlinear Blackbody in a Moving Frame of Reference

A Kerr nonlinear blackbody (KNB) is a new kind of blackbody in which bare photons with opposite wave vectors and helicities are bound into pairs and unpaired photons are transformed into nonpolaritons. In the present paper, the radiation of a KNB is considered from the viewpoint of an observer in arbitrary uniform motion with respect to a rest frame of reference of the radiation. It is found that the radiation laws, which include the distribution of nonpolaritons and so forth, are modified due to the motion. Moreover, under a special condition, we notice that the only effect of the motion is to introduce an angle-dependent directional temperature, which replaces the rest-frame temperature of the cavity. Besides, we try to extend the model of a KNB to the whole Universe and apply the modified radiation laws to the question of 2.7 K cosmic microwave background radiation (CMBR).     

Wavelength-independent all-optical synchronization of a Q-switched 100-ps microchip laser to a femtosecond laser reference source

We present a Q-switched microchip laser emitting 1064-nm pulses as short as 100 ps synchronized to a cavity dumped femtosecond laser emitting 800-nm pulses as short as 80 fs. The synchronization is achieved by presaturating the saturable absorber of the microchip laser with femtosecond pulses even though both lasers emit at widely separated wavelengths. The mean timing jitter is 40 ps and thus considerably shorter than the pulse duration of the microchip laser.     

Representation of Quantum States as Points in a Probability Simplex Associated to a SIC-POVM

The quantum state of a d-dimensional system can be represented by a probability distribution over the d ² outcomes of a Symmetric Informationally Complete Positive Operator Valued Measure (SIC-POVM), and then this probability distribution can be represented by a vector of \mathbb R^d2-1\mathbb {R}^{d^{2}-1} in a (d ²−1)-dimensional simplex, we will call this set of vectors Q\mathcal{Q}. Other way of represent a d-dimensional system is by the corresponding Bloch vector also in \mathbb R^d2-1\mathbb {R}^{d^{2}-1}, we will call this set of vectors B\mathcal{B}. In this paper it is proved that with the adequate scaling B=Q\mathcal{B}=\mathcal{Q}. Also we indicate some features of the shape of Q\mathcal{Q}.     

Ultrashort-pulse laser irradiation of metal films: the effect of a double-peak laser pulse

The optical properties of blue-violet InGaN light-emitting diodes under normal and reversed polarizations are numerically studied. The best light-emitting performance under normal and reversed polarization is obtained in a single quantum-well structure and double quantum-well structure, respectively. The key factors responsible for these phenomena are presumably the carrier concentration distribution and the amount of carriers in quantum wells. The turn-on voltage of light-emitting diodes under reversed polarization is lower than that of light-emitting diodes under normal polarization, due mainly to lower potential heights for electrons and holes in the active region.     

Quasi-Stationary Regime of a Branching Random Walk in Presence of an Absorbing Wall

A branching random walk in presence of an absorbing wall moving at a constant velocity v undergoes a phase transition as the velocity v of the wall varies. Below the critical velocity v _c , the population has a non-zero survival probability and when the population survives its size grows exponentially. We investigate the histories of the population conditioned on having a single survivor at some final time T. We study the quasi-stationary regime for v<v _c when T is large. To do so, one can construct a modified stochastic process which is equivalent to the original process conditioned on having a single survivor at final time T. We then use this construction to show that the properties of the quasi-stationary regime are universal when v→v _c . We also solve exactly a simple version of the problem, the exponential model, for which the study of the quasi-stationary regime can be reduced to the analysis of a single one-dimensional map.     

Propagation of general-type of phase-locked beam array in a turbulent atmosphere

The propagation of a general-type of phase-locked beam array in a turbulent atmosphere is studied, in which four practical issues, i.e., apertured, conformal, partially coherent, and flattened beam array is taken into consideration for accurate modeling of beam array in power beaming applications. The average intensity distribution in the receiving plane is deduced analytically based on extended Huygens–Fresnel principle. The influence of beam order, transverse coherence length, and truncation ratio is briefly discussed.     

On azimuthal anisotropy in fragmentation of a classical relativistic string

A fragmenting relativistic string is widely used for modeling particle production via quark–gluon strings formed in hadronic and nuclear inelastic interactions at high energies. In this note we focus on motion and fragmentation of a relativistic string with non-zero transverse separation of its ends and study this scenario as a possible mechanism for bringing anisotropy into the azimuthal angle distribution of produced particles in inelastic interactions of hadrons.     

Annealed Lower Tails for the Energy of a Charged Polymer

We consider a randomly charged polymer. Each monomer carries a random charge, and only charges on the same site interact pairwise. We study the lower tails of the energy, when averaged over both randomness, in dimension three or more. As a corollary, we obtain the correct temperature-scale for the Gibbs measure.     

Measurements of cavitation bubble dynamics based on a beam-deflection probe

We present an optodynamic measurement of a laser-induced cavitation bubble and its oscillations based on a scanning technique using a laser beam-deflection probe. The deflection of the beam was detected with a fast quadrant photodiode which was built into the optical probe. The applied experimental setup enabled us to carry out one- or two-dimensional scanning of the cavitation bubble, automatic control of the experiment, data acquisition and data processing. Shadow photography was used as a comparative method during the experiments.     

Numerical study of the expansion of metallic vapor plasma by a nanosecond laser pulse

The interaction between a laser-produced aluminum plasma and the ambient air, at a pressure of 173.3 Pa, is studied at the plasma thermalization stage. A two-dimensional approach is developed to solve the Navier–Stokes equations, where a finite volume discretization allows for obtaining a numerical solution. The simulation runs over a time representing 10 μs of plasma expansion. It is shown that the shock and drag models are good approximations for the two successive regimes after the initial strong expansion stage, and the calculation makes evident the plume sharpening on the axial direction before its confinement by the ambient gas, which is in good agreement with the experimental observation.     

Wave Localization Does not Affect the Breakdown of a Schrödinger-Type Amplifier Driven by the Square of a Gaussian Field

We study the divergence of the solution to a Schrödinger-type amplifier driven by the square of a Gaussian noise in presence of a random potential. We follow the same approach as Mounaix, Collet, and Lebowitz (MCL) in terms of a distributional formulation of the amplified field and the use of the Paley-Wiener theorem (Mounaix et al. in Commun. Math. Phys. 264:741–758, 2006, Erratum: ibid. 280:281–283, 2008). Our results show that the divergence is not affected by the random potential, in the sense that it occurs at exactly the same coupling constant as what was found by MCL without a potential. It follows a fortiori that the breakdown of the amplifier is not affected by the possible existence of a localized regime in the amplification free limit.     

Breaking of Global Gauge Symmetries on a Spatial-temporal Subdomain

It is generally considered that global gauge symmetry of an action integral over a finite spatial-temporal domain as a whole holds in any subdomain of this domain. However, in this paper we demonstrate that when the so-called localized assumption is no longer valid, the global gauge symmetry will break in the subdomain of this spatial-temporal domain, due to occurrence of a new source called the nonlocal residual. The nonlocal residual is correlated with a gauge field and satisfies the zero mean condition with respect to whole spatial-temporal domain. An example is given to support this conclusion.     

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.     

Inequivalent Quantization in the Field of a Ferromagnetic Wire

We argue that it is possible to bind neutral atom (NA) to the ferromagnetic wire (FW) by inequivalent quantization of the Hamiltonian. We follow the well known von Neumann’s method of self-adjoint extensions (SAE) to get this inequivalent quantization, which is characterized by a parameter Σ∈ℝ(mod2π). There exists a single bound state for the coupling constant η ²∈[0,1). Although this bound state should not occur due to the existence of classical scale symmetry in the problem. But since quantization procedure breaks this classical symmetry, bound state comes out as a scale in the problem leading to scaling anomaly. We also discuss the strong coupling region η ²<0, which supports bound state making the problem re-normalizable.     

Topos-Theoretic Extension of a Modal Interpretation of Quantum Mechanics

This paper deals with topos-theoretic truth-value valuations of quantum propositions. Concretely, a mathematical framework of a specific type of modal approach is extended to the topos theory, and further, structures of the obtained truth-value valuations are investigated. What is taken up is the modal approach based on a determinate lattice , which is a sublattice of the lattice of all quantum propositions and is determined by a quantum state e and a preferred determinate observable R. Topos-theoretic extension is made in the functor category of which base category is determined by R. Each true atom, which determines truth values, true or false, of all propositions in , generates also a multi-valued valuation function of which domain and range are and a Heyting algebra given by the subobject classifier in , respectively. All true propositions in are assigned the top element of the Heyting algebra by the valuation function. False propositions including the null proposition are, however, assigned values larger than the bottom element. This defect can be removed by use of a subobject semi-classifier. Furthermore, in order to treat all possible determinate observables in a unified framework, another valuations are constructed in the functor category . Here, the base category includes all ’s as subcategories. Although has a structure apparently different from , a subobject semi-classifier of gives valuations completely equivalent to those in ’s.