35 research outputs found
Method of self-similar factor approximants
The method of self-similar factor approximants is completed by defining the
approximants of odd orders, constructed from the power series with the largest
term of an odd power. It is shown that the method provides good approximations
for transcendental functions. In some cases, just a few terms in a power series
make it possible to reconstruct a transcendental function exactly. Numerical
convergence of the factor approximants is checked for several examples. A
special attention is paid to the possibility of extrapolating the behavior of
functions, with arguments tending to infinity, from the related asymptotic
series at small arguments. Applications of the method are thoroughly
illustrated by the examples of several functions, nonlinear differential
equations, and anharmonic models.Comment: Latex file, 21 pages, 4 tables, 4 figure
Cannon for Neutral Particles
Dynamics of spin-polarized neutral particles, such as neutrons or neutral
atoms and molecules, in magnetic fields is studied. A new regime of motion is
found where particles move mainly in one direction forming a well-collimated
beam. This regime suggests a mechanism for creating devices emitting directed
beams of neutral particles.Comment: 1 file, 7 pages, RevTex, no figures, final versio
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
Regulating atomic imbalance in double-well lattices
An insulating optical lattice with double-well sites is considered. In the
case of the unity filling factor, an effective Hamiltonian in the pseudospin
representation is derived. A method is suggested for manipulating the
properties of the system by varying the shape of the double-well potential. In
particular, it is shown that the atomic imbalance can be varied at will and a
kind of the Morse-alphabet sequences can be created.Comment: Latex file, 12 pages, 3 figure
Algebraic Self-Similar Renormalization in Theory of Critical Phenomena
We consider the method of self-similar renormalization for calculating
critical temperatures and critical indices. A new optimized variant of the
method for an effective summation of asymptotic series is suggested and
illustrated by several different examples. The advantage of the method is in
combining simplicity with high accuracy.Comment: 1 file, 44 pages, RevTe
Chaotic Lattice - Gas Model
A nonuniform system is considered consisting of two phases with different
densities of particles. At each given time the distribution of the phases in
space is chaotic: each phase filling a set of regions with random shapes and
locations. A chaotic diffusion process intermixes these regions by varying
their shapes and locations in a random way. To investigate the statistical
properties of such a system, it is exemplified by a lattice-gas model.
Conditions are analysed when this chaotic lattice-gas model can become
thermodynamically more stable than the usual model describing a pure one-phase
system.Comment: 1 file, 23 pages, LaTex, no figure
Coherent spin radiation by magnetic nanomolecules and nanoclusters
The peculiarities of coherent spin radiation by magnetic nanomolecules is
investigated by means of numerical simulation. The consideration is based on a
microscopic Hamiltonian taking into account realistic dipole interactions.
Superradiance can be realized only when the molecular sample is coupled to a
resonant electric circuit. The feedback mechanism allows for the achievement of
a fast spin reversal time and large radiation intensity. The influence on the
level of radiation, caused by sample shape and orientation, is analysed. The
most powerful coherent radiation is found to occur for an elongated sample
directed along the resonator magnetic field.Comment: Latex file, 11 figure
Multichannel Approach to Clustering Matter
An approach is developed, combining the ideas of quantum statistical
mechanics and multichannel theory of scattering, for treating statistical
systems whose constituents can possess different bound states realized as
compact clusters. The main principles for constructing multichannel cluster
Hamiltonians are formulated: principle of statistical correctness, principle of
cluster coexistence, and principle of potential scaling. The importance of the
principle of statistical correctness is emphasized by showing that when it does
not hold the behaviour of thermodynamic functions becomes essentially
distorted. And moreover, unphysical instabilities can appear. The ideas are
carefully illustrated by a statistical model of hot nuclear matter.Comment: 1 file, LaTex, no figure
Temporal Dynamics in Perturbation Theory
Perturbation theory can be reformulated as dynamical theory. Then a sequence
of perturbative approximations is bijective to a trajectory of dynamical system
with discrete time, called the approximation cascade. Here we concentrate our
attention on the stability conditions permitting to control the convergence of
approximation sequences. We show that several types of mapping multipliers and
Lyapunov exponents can be introduced and, respectively, several types of
conditions controlling local stability can be formulated. The ideas are
illustrated by calculating the energy levels of an anharmonic oscillator.Comment: 1 file, 21 pages, RevTex, 2 table
Evaporation and Condensation of Clusters
Influence of surrounding matter on the properties of clusters is considered
by an approach combining the methods of statistical and quantum mechanics. A
cluster is treated as a bound N-particle system and surrounding matter as
thermostat. It is shown that, despite arbitrary strong interactions between
particles, cluster energy can be calculated by using the controlled
perturbation theory. The accuracy of the latter is found to be much higher than
that of the quasiclassical approximation. Spectral distribution is obtained by
minimizing conditional entropy. Increasing the thermostat temperature leads to
the depletion of bound states. The characteristic temperature when bound states
become essentially depleated defines the temperature of cluster evaporation.
The inverse process of lowering the thermostate temperature, yielding the
filling of bound states, corresponds to cluster condensation.Comment: 1 file, 15 pages, RevTex, 4 table