Basic properties of cold Bose atoms in optical lattices are reviewed. The main principles correct self-consistent description arbitrary systems with Bose-Einstein condensate formulated. Theoretical methods for describing regular periodic presented. A special attention is paid to the discussion Bose-atom frame boson Hubbard model. Optical strong disorder, induced by random potentials, treated. Possible applications discussed, an emphasis their usefulness quantum information processing and...

Experiments with trapped atomic gases have opened novel possibilities for studying the evolution of nonequilibrium finite quantum systems, which revived necessity reconsidering and developing theory such processes. This review analyzes basic approaches to describing phenomena equilibration, thermalization, decoherence in systems. Isolated, nonisolated, quasi-isolated systems are considered. The relations between decoherence, existence time arrow emphasized. possibility occurrence rare...

One-dimensional Bose gases are considered, interacting either through the hard-core potentials or contact delta potentials. Interest in these gained momentum because of recent experimental realization quasi-one-dimensional traps with tightly confined radial motion, achieving Tonks-Girardeau (TG) regime strongly atoms. For such Fermi-Bose mapping wavefunctions is applicable. The aim present communication to give a brief survey problem and demonstrate generality this by emphasizing that: (i)...

A new method is suggested to approximately find out the limit for a sequence of functions when solely several first terms are known. The seems be very useful those complicated problems mathematical physics, statistical mechanics, and field theory in which, because technical difficulties, one able calculate, using some iteration procedure or perturbation scheme, only approximations quantities interest. As an illustration, quartic oscillator considered, it shown that invoking up second order,...

A survey is given of the present state art in studying Bose-Einstein condensation dilute atomic gases. The bulk attention focused on principal theoretical problems, though related experiments are also mentioned. Both uniform and nonuniform trapped gases considered. Existing contradictions critically analysed. correct understanding problems necessary for gaining a more penetrating insight into with atoms their proper interpretation.

One of the most complex systems is human brain whose formalized functioning characterized by decision theory. We present a "Quantum Decision Theory" decision-making, based on mathematical theory separable Hilbert spaces. This structure captures effect superposition composite prospects, including many incorporated intentions, which allows us to explain variety interesting fallacies and anomalies that have been reported particularize decision-making real beings. The describes entangled...

A generalization for the method of self-similar approximations suggested recently by author is given. Stability conditions are formulated: first, mapping multipliers recurrence relations have to be less than unity; second, Lyapunov exponent differential form has negative. The fixed-point defining governing functions analyzed from point view stability. It shown that condition expressed in principle minimal sensitivity provides a contracting contrary difference. This explains why, general,...

The possibility of creating a Bose condensate trapped atoms in non-ground-state is suggested. Such nonequilibrium can be formed if one first obtains the conventional ground state and then transfers condensed to by means resonance pumping. properties non-ground-states are compared plausible applications such condensates discussed.

An alternative approach for treating strongly interacting statistical systems with singular potentials is developed. This combines both the advantages of decoupling procedures Green functions, which eliminate divergences caused by potentials, and perturbation theory, a regular procedure that makes it possible to construct subsequent approximations above chosen decoupling. The resulting iterative sequence functions generates corresponding sequences observable quantities. To improve...

A survey is given summarizing the state of art describing information processing in Quantum Decision Theory, which has been recently advanced as a novel variant decision making, based on mathematical theory separable Hilbert spaces. This structure captures effect superposition composite prospects, including many incorporated intended actions. The characterizes entangled non-commutativity subsequent decisions, and intention interference. self-consistent procedure frame quantum theory, takes...

The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated the frame a self-consistent stochastic mean-field approximation. General considerations presented, which valid for finite temperatures, arbitrary strengths interaction potential, and arbitrarily strong disorder potentials. special case spatially uncorrelated field is then treated more detail. It shown that system consists three components, condensed particles, uncondensed...

Nonlinear coherent modes are the collective states of trapped Bose atoms, corresponding to different energy levels. These can be created starting from ground state condensate that excited by means a resonant alternating field. A thorough theory for excitation is presented. The necessary and sufficient conditions feasibility this process found. Temporal behaviour fractional populations relative phases exhibits dynamic critical phenomena on line parametric manifold. origin these elucidated...

The fundamental problem is analyzed, the relation between Bose-Einstein condensation and spontaneous gauge symmetry breaking. This largerly misunderstood in physics community. Numerous articles books contain statement that, though breaking helps for describing condensation, but latter, principle, does not require any This, however, correct. analysis based on known mathematical theorems. But order to overcomplicate presentation make it accessible all readers, technical details are often...

A consistent statistical theory of the crystal-liquid phase transition is developed, being based on a method which takes into account liquidlike fluctuations in crystals and solidlike clusters liquids. It shown that degenerate fluidlike droplets have finite number density at zero temperature, while nondegenerate disappear when temperature goes to zero. The existence melting point proved. This method, consideration heterophase fluctuations, provides possibility describing metastable states...

The possibility of realizing the superradiant regime electromagnetic emission by assembly quantum dots is considered. overall dynamical process analyzed in detail. It shown that there can occur several qualitatively different stages evolution. starts with dipolar waves triggering spontaneous radiation individual dots. This corresponds to fluctuation stage, when are not yet noticeably correlated each other. second dot interactions through common field become more important, but coherence...

We have studied a Bose-Einstein condensate of 87 Rb atoms under an oscillatory excitation.For fixed frequency excitation, we explored how the values amplitude and time excitation must be combined in order to produce quantum turbulence condensate.Depending on combination these parameters different behaviors are observed sample.For lowest observe bending main axis cloud.Increasing increasing number vortices.The vortex state can evolve into turbulent regime if driven up certain set...