Insulating behavior of a trapped ideal Fermi gas

We investigate theoretically and experimentally the center-of-mass motion of an ideal Fermi gas in a combined periodic and harmonic potential. We find a crossover from a conducting to an insulating regime as the Fermi energy moves from the first Bloch band into the band gap of the lattice. The conducting regime is characterized by an oscillation of the cloud about the potential minimum, while in the insulating case the center of mass remains on one side of the potential.     

The two-body problem in Rosen's bimetric theory of gravitation

This is a continuation of a previous paper, in which the field equations in successive approximations and the post-Newtonian equations of motion in Rosen's theory of gravitation were derived. In this paper the energy integral and the center of mass for an insular system with an arbitrary structure are obtained in the post-Newtonian approximation. A many-body system is considered, and in the extreme case of point bodies (particles) the center-of-mass coordinates are found to be identical with the Einsteinian ones. The two-body problem is considered. For a system of two identical neutron stars of mass 1.3M (a possible model of the Hulse-Taylor binary pulsar system) the trajectory and the perihelion precession are calculated. It is found that the expressions obtained depend on the gravitational self-energy of the stars. The relations deduced from Rosen's bimetric gravitation in the case of small velocities and weak fields are compared with those of general relativity.In partial fulfillment of the requirements for Dr.Sc. degree at the Technion-Israel Institute of Technology.     

Particle acceleration in Horava–Lifshitz black holes

In this paper we calculate the center-of-mass energy of two colliding test particles near the rotating and non-rotating Horava–Lifshitz black hole. For the case of a slowly rotating KS solution of Horava–Lifshitz black hole we compare our results with the case of Kerr black holes. We confirm the limited value of the center-of-mass energy for static black holes and unlimited value of the center-of-mass energy for rotating black holes. Numerically, we discuss temperature dependence of the center-of-mass energy on the black hole horizon. We obtain the critical angular momentum of particles. In this limit the center-of-mass energy of two colliding particles in the neighborhood of the rotating Horava–Lifshitz black hole could be arbitrarily high. We found appropriate conditions where the critical angular momentum could have an orbit outside the horizon. Finally, we obtain the center-of-mass energy corresponding to this circle orbit.     

The exciton dead layer revisited

Although the exciton in a quantum well is not a rigid ball but distords when its center of mass gets close to a surface, it is mathematically possible to write the exciton energy change from its bulk value as an effective decrease of the well width in which the center of mass would freely move. In the large well limit, the exciton dead layer defined this way is related to the third order term in the expansion of the exciton energy as a function of the inverse well width. A quite precise calculation of this exciton energy is thus necessary to obtain this dead layer. We present a new calculation which relies on a Born-Oppenheimer procedure to decouple the relative motion of the e-h pair from its center of mass motion. This is associated to a quite precise calculation of the relative motion energy, based on our recent work on the exact envelope function for confined motion. We predict that the dead layer increases with the exciton total mass in contradiction with previous results.     

Dihyperons in chiral color dielectric model

The mass of the dibaryon having spin, parityJ ^π = 0⁺, isospinI = 0 and strangeness—2 is computed using chiral color dielectric model. The bare wave function is constructed as a product of two color-singlet three-quark clusters and then it is properly antisymmetrized by considering appropriate exchange operators for spin, flavor and color. Color magnetic energy due to gluon exchange, meson self energy and energy correction due to center of mass motion are computed. The calculation shows that the mass of the particle is 80 to 160 MeV less than twice λ mass.     

Umklapp collisions and center-of-mass oscillations of a trapped Fermi gas

Starting from the Boltzmann equation, we study the center-of-mass oscillation of a harmonically trapped normal Fermi gas in the presence of a one-dimensional periodic potential. We show that for values of the Fermi energy above the first Bloch band the center of mass motion is overdamped in the collisional regime due to umklapp processes. This should be contrasted with the behavior of a superfluid where one instead expects the occurrence of persistent Josephson-like oscillations.     

Dynamics of bright soliton in a spin–orbit coupled spin-1 Bose–Einstein condensate

We have investigated the dynamics of bright solitons in a spin–orbit coupled spin-1 Bose–Einstein condensate analytically and numerically. By using the hyperbolic sine function as the trial function to describe a plane wave bright soliton with a single finite momentum, we have derived the motion equations of soliton's spin and center of mass, and obtained its exact analytical solutions. Our results show that the spin–orbit coupling couples the soliton's spin with its center-of-mass motion, the spin oscillations induced by the exchange of atoms between components result in the periodical oscillation of center-of-mass, and the motion of center of mass of soliton can be viewed as a superposition of periodical and linear motions. Our analytical results have also been confirmed by the direct numerical simulations of Gross–Pitaevskii equations.     

Bragg quantum wells in weak confinement regime

The optical properties of Bragg quantum wells are studied for exciton confinement under center-of-mass quantization. A variational model of Wannier exciton envelope function, that embodies the correct boundary conditions for center-of-mass, is adopted for calculation. The present non-adiabatic exciton model is compared with adiabatic results and with heuristic “hard sphere” model. The radiative self-energy of a single-quantum well (SQW) and multi-quantum wells (MQWs) are computed in the semiclassical framework, and in effective mass approximation, by self-consistent solution of Schroedinger and Maxwell equations. This microscopic solution is free from “fitting” parameter values, except for the non-radiative broadening, and also the exciton dead-layer and the additional boundary condition are not taken ad hoc, but come coherently from the variational principle and self-consistent Schroedinger-Maxwell solution. Dispersion curves of exciton-polariton propagating in a MQW, under Bragg condition, are studied by selected numerical examples. The case of optical gap in correspondence of higher excited states is studied, and, moreover, the interesting effect of gap enhancement or inhibition, in correspondence of non-resonant Bragg energy, will be addressed.     

Multiply-charged magnetoexcitons in low-dimensional structures

The frequencies and intensities of absorption lines of a “hole + Nelectrons” complex in a magnetic field are found. The motion of all particles is assumed to be two-dimensional, and the electron and hole quantum wells are assumed to be spatially separated. It is shown how Kohn’s theorem can be extended to the case of a system with a finite total mass. The energy of a N-electron complex in a quantum ring oscillates as a function of the magnetic flux with a period that depends on N and the ratio of the masses. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 6, 423–427 (25 September 1997)     

Center-of-mass motion of a system of relativistic Dirac particles

The relativistic center-of-mass motion for a system ofN fermions can be exactly separated because of the linearity of the Dirac operators in momenta which is not possible for quadratic Klein-Gordon particles. The covariant equations derived from Maxwell-Dirac field theory are considered. The center-of-mass equation is still a 4 ^N -component spinor equation. We solve these equations for two- and three-body systems, as well as the relative motion for the non-interacting case, and discuss the quantum numbers and identification of eigenstates and eigenvalues. The results apply for both bound and scattering states. Dedicated to the Third Centenary of the Publication of Principia: Corollary IV.... and therefore the common center of gravity of all bodies acting upon each other (excluding external actions and impediments) is either at rest, or moves uniformly in a right line. Is. Newton, Philosophiae Naturalis Principia Mathematica (S. Pepys, Julii 5, 1686, Londini)     

Multicenter Higgs oscillators and Calogero model

We show that the spherical part of N-particle Calogero model describes, after exclusion of the center of mass, the motion of the particle on (N − 2)-dimensional sphere interacting with N(N − 1)/2 force centers with Higgs oscillator potential. In the case of four-particle system these force centers are located at the vertexes of cuboctahedron. The geometry of the five-particle case is also investigated.     

Revisiting the Balazs thought experiment in the presence of loss: electromagnetic-pulse-induced displacement of a positive-index slab having arbitrary complex permittivity and permeability

Over a half-century ago, Balazs proposed a thought experiment to deduce the form of electromagnetic momentum in a lossless and non-dispersive slab by imposing conservation of global momentum and system center-of-mass velocity after a pulse has traveled through the slab. Here, we revisit the Balazs thought experiment by explicit calculations of momentum transfer and center-of-mass displacement of a non-dispersive, positive-index slab of arbitrary complex permittivity and permeability using a set of postulates consisting only of Maxwell’s equations, a generalized Lorentz force law, the Abraham form of the electromagnetic momentum density, and conservation of both pulse and slab mass. In the case where the slab is lossless, we show that a pulse of arbitrary shape incident onto the slab conserves both global momentum and system center-of-mass velocity, consistent with the starting postulates of the Balazs thought experiment. In the case where the slab is lossy, we show, within the context of the above postulates, that global momentum is always conserved and that system center-of-mass velocity is conserved only when mass transfer from the pulse to the slab is described by an incremental pulse-mass-transfer model, proposed here, in which the pulse deposits mass in the slab with a distribution corresponding to the instantaneous mass density profile of the pulse.     

Double S- and P-wave charmonium production in e+e? annihilation

On the basis of perturbative QCD and the relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of S-wave and P-wave charmonium states. Relativistic factors in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave function to the reference frame of the moving S- and Pwave mesons are taken into account. For the gluon and quark propagators entering the production vertex function we use a truncated expansion in the ratio of the relative quark momenta to the center-of-mass energy $ \sqrt s $ \sqrt s up to the second order. Relativistic corrections to the quark bound state wave functions in the rest frame are considered by means of the Breit-like potential. It turns out that the examined effects change essentially the nonrelativistic results of the cross section for the considered reactions at the center-of-mass energy $ \sqrt s $ \sqrt s = 10.6 GeV.     

Hydrodynamic and viscoelastic effects in polymer diffusion

We develop a fluctuating hydrodynamics approach to study the impact of the hydrodynamic and viscoelastic interactions on the motion of the center of mass of a polymer as well as on the relaxation of Rouse modes, either in a Θ solvent or in a melt of identical unentangled chains. We show that this method allows us to describe the effect of hydrodynamic interactions beyond the Zimm (for a single chain in a Θ solvent) or the Rouse models (for an unentangled melt). In the latter case, we recover the same important effect of the viscoelastic hydrodynamic interactions on the center-of-mass diffusion, first described in Farago et?al (2011 Phys. Rev. Lett. 107 178301).     

Dynamics of a vertical flight in the stationary gravitational field of a celestial body: Post-newtonian corrections and gravitational redshift

The standard problem of a radial motion of test particles in the stationary gravitational field of a spherically symmetric celestial body is solved and is used to determine the time features of this motion. The problem is solved for the equations of motion of general relativity (GR), and the time features are obtained in the post-Newtonian approximation, with linear GR corrections proportional to r _g /r and β ² (in the solution being considered, they are of the same order of smallness) being taken rigorously into account. Total times obtained by integrating the time differentials along the trajectories of motion are considered as the time features in question. It is shown that, for any parameters of the motion, the proper time (which corresponds to watches comoving with a test particle) exceeds the time of watches at rest (watches at the surface of the celestial body being considered). The mass and the radius of the celestial body, as well as the initial velocity of the test particle, serve as arbitrary parameters of the motion. The time difference indicated above implies a leading role of the gravitational redshift, which decreases somewhat because of the opposite effect of the Doppler shift. The results are estimated quantitatively for the important (from the experimental point of view) case of vertical flights of rockets starting from the Earth’s surface. In this case, the GR corrections, albeit being extremely small (a few microseconds for several hours of the flight), aremeasurable with atomic (quantum) watches.     

Magnetoexcitons in nanostructures exhibiting cylindrical symmetry

The problem of an exciton in the cylindrical nanostructure exposed to an external static magnetic field is investigated. The theoretical model assumes anisotropic masses which are different inside and outside the nanostructure. The confinement potential has finite value at the boundaries and magnetic field is parallel to the axis of the cylinder. The screened Coulomb interaction between an electron and a hole is assumed. The consistent mathematical procedure is developed to calculate the magnetoexciton eigenfunctions and eigenenergies. Our method applies to the systems exhibiting cylindrical symmetry where, due to confinement effects accompanied by the e-h Coulomb interaction, the separation of relative- and center-of-mass motion is not possible. Numerical calculations have been performed for the quantum disk, the cylinder and the quantum rod. The magnetic field dependent energy spectrum and corresponding wave functions, expressed in terms of known one-particle electron and hole eigenfunctions, are calculated. Additionally, we point out the different role of Coulomb interaction in every case.     

Ionic recombination in a weakly ionized gas : I. A stochastic approach to the recombination rate problem

Using the framework of a stochastic approach to the reaction-kinetic problem originating from Teramoto and Shigesada equations for the phase-space evolution of the ionic part in a diluted ternary gas mixture composed of positively and negatively charged ions as well as of neutrals are derived. On the basis of the stationary solution of the reactive ion-pair equation an operator expression for the recombination constant α is defined and discussed with regard to the effect of the center-of-mass motion. By iteration a formally exact α-expansion in terms of multiple ion-pair neutral collisions is derived for the case that non-thermal center-of-mass effects can be neglected. This expansion has to be specified to meet the conditions of well-known models for ion-pair stabilization (absorbing sphere, critical energy barrier).     

Signatures of nonlocality in the first-order coherence of scattered light

The spatial coherence of an atomic wavepacket can be detected in scattered photons, even when the center-of-mass motion is in the quantum coherent superposition of two distant, nonoverlapping wavepackets. Spatial coherence manifests itself in the power spectrum of the emitted photons, whose spectral components can exhibit interference fringes as a function of the emission angle. The contrast and the phase of this interference pattern provide information about the quantum state of the center of mass of the scattering atom.     

Jet quenching pattern at LHC in PYQUEN model

The first LHC data on high transverse momentum hadron and dijet spectra in PbPb collisions at center-of-mass energy 2.76 TeV per nucleon pair are analyzed in the frameworks of PYQUEN jet quenching model. The presented studies for the nuclear modification factor of high-p _T hadrons and the imbalance in dijet transverse energy support the supposition that the intensive wide-angular (“out-of-cone”) medium-induced partonic energy loss is seen in central PbPb collisions at the LHC.     

晶格振动对激子运动的影响

在本文中用Haga研究极化子时提出的微扰法讨论晶格振动对激子运动的影响。把作者过去的工作推广到电子和空穴质量不相等的普遍情形。在忽略反冲效应中不同波矢的声子之间的相互作用时,导出了激子的基态能量、有效质量、约化质量和内部势能。指出:激子的有效质量和电子、空穴与声子的相互作用有关;激子的约化质量不仅和电子、空穴与声子的相互作用有关,而且还和电子空穴质量比有关;激子形成自陷态的条件并非由电子、空穴与声子相互作用的大小,而是由电子、空穴质量比决定。形成激子自陷的条件是电子、空穴质量比0.261<μ_e/μ_h<3.83。在μ_e/μ_h<0.261或μ_e/μ_h>3.83的情形,激子极化晶体中并不形成自陷态。 关键词：