Spin superradiance versus atomic superradiance

A comparative analysis is given of spin superradiance and atomic superradiance. Their similarities and distinctions are emphasized. It is shown that, despite a close analogy, these phenomena are fundamentally different. In atomic systems, superradiance is a self-organized process, in which both the initial cause, being spontaneous emission, as well as the collectivizing mechanism of their interactions through the common radiation field, are of the same physical nature. Contrary to this, in actual spin systems with dipole interactions, the latter are the major reason for spin motion. Electromagnetic spin interactions through radiation are negligible and can never produce collective effects. The possibility of realizing superradiance in molecular magnets by coupling them to a resonant circuit is discussed.Comment: Latex file, 12 pages, no figure

Dynamics of Nonground-State Bose-Einstein Condensates

Dilute Bose gases, cooled down to low temperatures below the Bose-Einstein condensation temperature, form coherent ensembles described by the Gross-Pitaevskii equation. Stationary solutions to the latter are topological coherent modes. The ground state, corresponding to the lowest energy level, defines the standard Bose-Einstein condensate, while the states with higher energy levels represent nonground-state condensates. The higher modes can be generated by alternating fields, whose frequencies are in resonance with the associated transition frequencies. The condensate with topological coherent modes exhibits a variety of nontrivial effects. Here it is demonstrated that the dynamical transition between the mode-locked and mode-unlocked regimes is accompanied by noticeable changes in the evolutional entanglement production.Comment: latex file, 5 pages, 2 figures, Figs. 1,2 are not include

Absence of spin superradiance in resonatorless magnets

A spin system is considered with a Hamiltonian typical of molecular magnets, having dipole-dipole interactions and a single-site magnetic anisotropy. In addition, spin interactions through the common radiation field are included. A fully quantum-mechanical derivation of the collective radiation rate is presented. An effective narrowing of the dipole-dipole attenuation, due to high spin polarization is taken into account. The influence of the radiation rate on spin dynamics is carefully analysed. It is shown that this influence is completely negligible. No noticeable collective effects, such as superradiance, can appear in molecular magnets, being caused by electromagnetic spin radiation. Spin superradiance can arise in molecular magnets only when these are coupled to a resonant electric circuit, as has been suggested earlier by one of the authors in Laser Phys. {\bf 12}, 1089 (2002).Comment: Latex file, 14 pages, 5 figure

From Coherent Modes to Turbulence and Granulation of Trapped Gases

The process of exciting the gas of trapped bosons from an equilibrium initial state to strongly nonequilibrium states is described as a procedure of symmetry restoration caused by external perturbations. Initially, the trapped gas is cooled down to such low temperatures, when practically all atoms are in Bose-Einstein condensed state, which implies the broken global gauge symmetry. Excitations are realized either by imposing external alternating fields, modulating the trapping potential and shaking the cloud of trapped atoms, or it can be done by varying atomic interactions by means of Feshbach resonance techniques. Gradually increasing the amount of energy pumped into the system, which is realized either by strengthening the modulation amplitude or by increasing the excitation time, produces a series of nonequilibrium states, with the growing fraction of atoms for which the gauge symmetry is restored. In this way, the initial equilibrium system, with the broken gauge symmetry and all atoms condensed, can be excited to the state, where all atoms are in the normal state, with completely restored gauge symmetry. In this process, the system, starting from the regular superfluid state, passes through the states of vortex superfluid, turbulent superfluid, heterophase granular fluid, to the state of normal chaotic fluid in turbulent regime. Both theoretical and experimental studies are presented.Comment: Latex file, 25 pages, 4 figure

Anomalous Transient Current in Nonuniform Semiconductors

Nonequilibrium processes in semiconductors are considered with highly nonuniform initial densities of charge carriers. It is shown that there exist such distributions of charge densities under which the electric current through a sample displays quite abnormal behaviour flowing against the applied voltage. The appearance of this negative electric current is a transient phenomenon occurring at the initial stage of the process. After this anomalous negative fluctuation, the electric current becomes normal, i.e. positive as soon as the charge density becomes more uniform. Several possibilities for the practical usage of this effect are suggested.Comment: 1 file, 11 pages, RevTex, no figure

Self-Similar Factor Approximants

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving a novel type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are named the self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of the self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions which include a variety of transcendental functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties.Comment: 22 pages + 11 ps figure

Self-similar Approximants of the Permeability in Heterogeneous Porous Media from Moment Equation Expansions

We use a mathematical technique, the self-similar functional renormalization, to construct formulas for the average conductivity that apply for large heterogeneity, based on perturbative expansions in powers of a small parameter, usually the log-variance $\sigma_Y^2$ of the local conductivity. Using perturbation expansions up to third order and fourth order in $\sigma_Y^2$ obtained from the moment equation approach, we construct the general functional dependence of the transport variables in the regime where $\sigma_Y^2$ is of order 1 and larger than 1. Comparison with available numerical simulations give encouraging results and show that the proposed method provides significant improvements over available expansions.Comment: Latex, 14 pages + 5 ps figure

Particle fluctuations in nonuniform and trapped Bose gases

The problem of particle fluctuations in arbitrary nonuniform systems with Bose-Einstein condensate is considered. This includes the case of trapped Bose atoms. It is shown that the correct description of particle fluctuations for any nonuniform system of interacting atoms always results in thermodynamically normal fluctuations.Comment: Latex file, 16 page

Fluctuation indices for atomic systems with Bose-Einstein condensate

The notion of fluctuation indices, characterizing thermodynamic stability of statistical systems, is advanced. These indices are especially useful for investigating the stability of nonuniform and trapped atomic assemblies. The fluctuation indices are calculated for several systems with Bose-Einstein condensate. It is shown that: the ideal uniform Bose-condensed gas is thermodynamically unstable; trapped ideal gases are stable for the confining dimension larger than two; trapped gases, under the confining dimension two, are weakly unstable; harmonically trapped gas is stable only for the spatial dimension three; one-dimensional harmonically trapped gas is unstable; two-dimensional gas in a harmonic trap represents a marginal case, being weakly unstable; interacting nonuniform three-dimensional Bose-condensed gas is stable. There are no thermodynamically anomalous particle fluctuations in stable Bose-condensed systems.Comment: Latex file, 12 page

Nonequilibrium Bose systems and nonground-state Bose-Einstein condensates

The theory of resonant generation of nonground-state Bose-Einstein condensates is extended to Bose-condensed systems at finite temperature. The generalization is based on the notion of representative statistical ensembles for Bose systems with broken global gauge symmetry. Self-consistent equations are derived describing an arbitrary nonequilibrium nonuniform Bose system. The notion of finite-temperature topological coherent modes, coexisting with a cloud of noncondensed atoms, is introduced. It is shown that resonant generation of these modes is feasible for a gas of trapped Bose atoms at finite temperature.Comment: Latex file, 16 pages, no figure