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The energies of Bose–Einstein condensate of 85 Rb atoms confined by the 3-dimensional parabolic and quartic trap are investigated. The two-body correlations among atoms are taken into calculation in many-body approach. We increase the number of bosons within the anharmonic trap and study the behaviour of different zero-temperature energies in detail. The interatomic interaction strongly depends on the anharmonic coefficient (λ ) as the collapsing point is observed to be varying for different values of λ . For weak values of λ , we observe similar behaviour of energies, as studied for harmonically trapped attractive condensate. However, when the anharmonic distortion is high, dramatic behaviour of energies near the collapsing point is observed. It is shown that the anharmonic effect is very crucial to propel the condensate towards collapsing. [ABSTRACT FROM AUTHOR]

We consider the attractive Bose–Einstein condensate (BEC) of Rb atoms, which is confined in a harmonic plus quartic trap [ V (r) = 1 2 m ω 2 r 2 + λ r 4 ] . We slowly tune the coefficient of quartic term (λ ) to see how the metastable region (MSR) in the outer part of the trap is modified. The MSR is always bounded by a left intermediate barrier (IB) and a deep but narrow attractive well (NAW) appears on the left of this barrier. For λ < 0 , the MSR is bounded by an additional right IB. A dramatic behaviour (compared with the attractive BEC in a harmonic trap) of interaction energy, kinetic energy, trap energy along with the total ground-state energy of the condensate is observed in this different metastability. For λ ≥ 0 , the outer wall of the MSR increases steeply as λ increases. Dynamical responses of the zero point energies of the condensate are explored also. Observations are interesting as we find a critical value of anharmonicity ( λ cr ) to collapse the condensate. We slightly increase the strength of λ (close to λ cr ) and investigate the significant increase of the quantum tunnelling probability through the left IB into an inner core (NAW). [ABSTRACT FROM AUTHOR]

Spinel ZnMn2O4 nanoparticles (ZMONPs) were successfully synthesized using a microwave-assisted chemical route. X-ray diffraction (XRD) revealed the growth of ZMONPs along the (211) plane with a tetragonal structure. The crystallite size was ~ 14 nm, estimated using the XRD data. Vibrational analysis confirmed the tetragonal structure of ZMONPs. Scanning electron microscopy images showed nanometer-sized particles, which was in agreement with the XRD results. EDX investigation of the samples demonstrated the good stoichiometric ratio of Zn, Mn, and O (1:2:4). The surface area and pore radius were also investigated in detail through Brunauer–Emmett–Teller analysis and were found to be 10.385 m2/g and 16.24 Å, respectively. The direct band gap for the ZMONPs was estimated using Tauc's relation and was found to be 2.07 eV, which is larger than that of bulk ZMO (1.91 eV). Dielectric constant and loss values decreased with increasing frequency, while conductivity increased with increasing frequency. The dielectric constant was found to be in the range of 17–25 considering the entire testing range. The dielectric constant value was larger than expected, which could be the result of quantum confinement. [ABSTRACT FROM AUTHOR]

Structural, electronic, elastic and thermodynamic properties of Ni2LaZ (Z = As, Sb and Bi) Heusler alloys based on rare earth element have been investigated using full-potential linear muffin-tin orbital (FP-LMTO) method within generalized gradient approximation (GGA) in the frame of density functional theory (DFT). By using total energy variations, the independent elastic constants and their pressure dependence have been determined. Also, anisotropic parameter (A), shear modulus (G), Young modulus (E), Poisson's ratio (ν), ratio (B/G) are calculated. Using quasi-harmonic Debye model, thermodynamic properties of Ni2LaZ (Z = As, Sb and Bi) Heusler alloys are investigated in temperature range 0–1200 K and pressure range 0–50 GPa. The temperature and pressure effects on the unit cell volume, bulk modulus (B), heat capacities (Cv) at stable volume, (Cp), Debye temperatures (θD), Gibbs energies (G), thermal expansion coefficients (α) and entropies (S) are determined from non-equilibrium Gibbs functions. This study allows to understand deeply the structural and thermodynamic properties of Ni2LaZ (Z = As, Sb and Bi) Heusler alloys in shortest time and cost-effective. [ABSTRACT FROM AUTHOR]

Three ReN2 phases (Pbcn, C2/m and P4/mbm) are searched to be stable under different pressures by the swarm-intelligence-based CALYPSO method. Pressure-induced phase transitions from Pbcn phase to C2/m phase at 68.5 GPa and C2/m phase to P4/mbm phase at 138.8 GPa are firstly observed. The calculated results of density of state show all the three phases are metallic conductor. And elastic constant calculations confirm their mechanical stabilities. The high bulk and shear moduli of C2/m and P4/mbm phases indicate their high hardness. The total and partial electron densities of states and electron localization functions indicate that the covalent bonding of Re–N in ReN2 makes great contributions to the structural stability and high hardness. [ABSTRACT FROM AUTHOR]

In one-dimensional (anti)-de Sitter background, all commutation relations are modified and the Heisenberg uncertainty principle is changed to the so-called extended uncertainty principle. In this scenario, the commutator between position and momentum operators contains a linear power of coordinate, instead of a constant, and the coordinate representation of the momentum operators for this model becomes coordinate dependent. In this paper, we present an exact solution of the one-dimensional harmonic oscillator in Ads and dS spaces. The eigenfunctions are determined for both cases, and the energy eigenvalues equation is obtained. From the obtained spectrum energy, the thermodynamic properties of the harmonic oscillator in AdS space are then analyzed. [ABSTRACT FROM AUTHOR]

Static and dynamic properties of Bose-Einstein condensates in annular traps are investigated by solving the many-boson Schrödinger equation numerically accurately using the multiconfigurational time-dependent Hartree for bosons method. We concentrate on weakly-interacting bosons exhibiting low depletion. Analysis of the mean-field position variance, which accounts for the shape of the density only, and the many-body position variance, which incorporates a tiny amount of excitations through the reduced two-particle density matrix, shows that the former behaves essentially as a quasi-one-dimensional quantity whereas the latter as a two-dimensional quantity. This brings another dimension to the physics of bosons in ring-shaped traps. [ABSTRACT FROM AUTHOR]

On the basis of spectroscopic studies of (NH2(C2H5)2)2CoCl4 crystals, the absorption bands corresponding to the internal electronic transitions in the Co2+ ion were identified. The values of the crystal field and Racah parameters were calculated. The temperature evolution of the absorption spectra of (NH2(C2H5)2)2CoCl4 crystals reveals the anomalies of their parameters at the points of phase transitions. The corresponding changes of the absorption spectra were discussed in terms of distortion of the metal-halogen complex. The temperature dependences of the absorption spectra of (NH2(C2H5)2)2CoCl4 crystals confirm the presence of the thermochromic phase transitions at 255 and 330 K. [ABSTRACT FROM AUTHOR]

Noncentrosymmetric superconductors (NCSs) with broken inversion symmetry can have spin-dependent order parameters (OPs) with mixed parity which can also have nodes in the pair potential as well as the energy spectra. These nodes are distinct features that are not present in conventional superconductors. They appear as points or lines in the momentum space where the latter can have angular or radial geometries dictated by the dimensionality, the lattice structure and the pairing interaction. In this work we study the nodes in time reversal symmetry (TRS) preserving NCSs at the OP, the pair potential, and the energy spectrum levels. Nodes are examined by using spin independent pairing interactions respecting the rotational C ∞ v symmetry in the presence of spin-orbit coupling (SOC). The pairing symmetries and the nodal topology are affected by the relative strength of the pairing channels which is studied for the mixed singlet-triplet, pure singlet, and pure triplet. Complementary to the angular line nodes widely present in the literature, the C ∞ v symmetry here allows radial line nodes (RLNs) due to the nonlinear momentum dependence in the OPs. The topology of the RLNs in the mixed case shows a distinctly different characterization than the half-spin quantum vortex at the Dirac point. We apply this NCS physics to the inversion symmetry broken exciton condensates (ECs) in double quantum wells where the point and the RLNs can be found. On the other hand, for a pure triplet condensate, two fully gapped and topologically distinct regimes exist, separated by a QSHI-like zero energy superconducting state with even number of Majorana modes. We also remark on how the point and the RLNs can be manipulated, enabling an external control on the topology. [ABSTRACT FROM AUTHOR]

The bilinear form of the nonisospectral generalized Sawada-Kotera equation is derived. With the aid of the Wronskian technique, the Wronskian solution is presented for this equation. The soliton resonance is discussed in inhomogeneous media. Negatons and positons are also obtained. [ABSTRACT FROM AUTHOR]

The full-potential linear augmented plane wave plus local orbital method has been used to study the structural, electronic and thermodynamic properties of LaMgX (X = Ga, In, Tl). The equilibrium structural properties viz. lattice parameters ( a , c), bulk modulus ( B) and its first order pressure derivative ( $$ B_{0}^{\prime } $$ ) have been calculated in the parent hexagonal P-62m phase. The electronic behavior has been shown in terms of band structure and density of states histograms, indicating dominant character of '5 d' orbital electrons of Tl in electronic contribution to LaMgTl. Effects of temperature and pressure on unit cell volume ( V), bulk modulus ( B), Debye temperature ( θ), Grüneisen parameter ( γ), specific heat ( C) and thermal expansion coefficient (α) have been investigated in wide temperature range and pressure range. The calculated parameters are in good agreement with available experimental/theoretical literature values. [ABSTRACT FROM AUTHOR]

The low-temperature properties of certain quantum magnets can be described in terms of a Bose–Einstein condensation (BEC) of magnetic quasiparticles (triplons). Some mean-field approaches (MFA) to describe these systems, based on the standard grand canonical ensemble, do not take the anomalous density into account and leads to an internal inconsistency, as it has been shown by Hohenberg and Martin, and may therefore produce unphysical results. Moreover, an explicit breaking of the U(1) symmetry as observed, for example, in TlCuCl _3 makes the application of MFA more complicated. In the present work, we develop a self-consistent MFA approach, similar to the Hartree–Fock–Bogolyubov approximation in the notion of representative statistical ensembles, including the effect of a weakly broken U(1) symmetry. We apply our results on experimental data of the quantum magnet TlCuCl _3 and show that magnetization curves and the energy dispersion can be well described within this approximation assuming that the BEC scenario is still valid. We predict that the shift of the critical temperature T _c due to a finite exchange anisotropy is rather substantial even when the anisotropy parameter γ is small, e.g., ${\rm{\Delta }}{T}_{{c}}\approx 10 \% $ of T _c in H = 6 T and for $\gamma \approx 4$ $\mu \mathrm{eV}$ .

We study one-dimensional (1D) strongly interacting Bose–Fermi mixtures by both the exact Bethe-ansatz method and variational perturbation theory within the degenerate ground state subspace of the system in the infinitely repulsive limit. Based on the exact solution of the 1D Bose–Fermi gas with equal boson–boson and boson–fermion interaction strengths, we demonstrate that the ground state energy is degenerate for different Bose–Fermi configurations and the degeneracy is lifted when the interaction deviates the infinitely interacting limit. We then show that the ground properties in the strongly interacting regime can be well characterized by using the variational perturbation method within the degenerate ground state subspace, which can be applied to deal with more general cases with anisotropic interactions and in external traps. Our results indicate that the total ground-state density profile in the strongly repulsive regime behaves like the polarized non-interacting fermions, whereas the density distributions of bosons and fermions display different properties for different Bose–Fermi configurations and are sensitive to the anisotropy of interactions.

We theoretically investigate the dynamic structure factor of a strongly interacting Fermi gas at the crossover from Bardeen–Cooper–Schrieffer superfluids to Bose–Einstein condensates, by developing an improved random phase approximation within the framework of a density functional theory (DFT)—the so-called superfluid local density approximation. Compared with the previous random-phase-approximation studies based on the standard Bogoliubov–de Gennes equations, the use of the DFT greatly improves the accuracy of the equation of state at the crossover, and leads to a better description of both collective Bogoliubov-Anderson-Goldstone phonon mode and single-particle fermionic excitations at small transferred momentum. Near unitarity, where the s -wave scattering length diverges, we show that the single-particle excitations start to significantly contribute to the spectrum of dynamic structure factor once the frequency is above a threshold of the energy gap at $2{\rm{\Delta }}$ . The sharp rise in the spectrum at this threshold can be utilized to measure the pairing gap Δ. Together with the sound velocity determined from the phonon branch, the dynamic structure factor provides us some key information of the crossover Fermi superfluid. Our predictions could be examined in experiments with ^6 Li or ^40 K atoms using Bragg spectroscopy.

We have analytically explored the temperature dependence of critical number of particles for the collapse of a harmonically trapped attractively interacting Bose gas below the condensation point by introducing a kinetic approach within the Hartree-Fock approximation. The temperature dependence obtained by this easy approach is consistent with that obtained from the scaling theory. [ABSTRACT FROM AUTHOR]

Abstract: We study triaxial bright solitons made of attractive Bose-condensed atoms characterized by the absence of confinement in the longitudinal axial direction but trapped by an anisotropic harmonic potential in the transverse plane. By numerically solving the three-dimensional Gross–Pitaevskii equation we investigate the effect of the transverse trap anisotropy on the critical interaction strength above which there is the collapse of the condensate. The comparison with previous predictions [A. Gammal, L. Tomio, T. Frederico, Phys. Rev. A 66 (2002) 043619] shows significant differences for large anisotropies. [Copyright &y& Elsevier]

Abstract: The ground state energy of ideal α-matter at is analyzed within the framework of variational theory of Bose quantum liquids. Calculations are done for three local α–α potentials with positive volume integrals and two-body correlation functions obtained from the Pandharipande–Bethe equation. The energy per particle of α matter is evaluated in the cluster expansion formalism up to four-body diagrams, and using the HNC/0 and HNC/4 approximation for a Bose liquid. At low densities the two methods predict similar EOS whereas at higher densities they are sensitively different, the HNC approximation providing saturation at lower density, bellow the saturation value of nuclear matter. Inclusion of higher-order terms in the cluster expansion of the condensate fraction is leading to a stronger depletion of the alpha condensate with the density compared to the two-body approximation prediction. [Copyright &y& Elsevier]

Abstract: The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with δ-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering method. Many interesting features appear in the system. For example, the wave function has the supersymmetry. It is also found that the ground state of the system is partial polarized, where the fermions form a spin singlet state and the bosons are totally polarized. From the solution of Bethe ansatz equations, it is shown that all the momentum, spin and isospin rapidities at the ground state are real if the interactions between the particles are repulsive; while the fermions form two-particle bounded states and the bosons form one large bound state, which means the bosons condensed at the zero momentum point, if the interactions are attractive. The charge, spin and isospin excitations are discussed in detail. The thermodynamic Bethe ansatz equations are also derived and their solutions at some special cases are obtained analytically. [Copyright &y& Elsevier]

Abstract: We prove that the ground state momentum distribution of a one-dimensional system of impenetrable bosons exhibits a tail for any confining potential. We also derive an expression for easily computing the asymptotic occupation numbers and verify our results with an exact numerical approach. [Copyright &y& Elsevier]

We consider the quantum above-barrier reflection of a particle by the one-dimensional Rosen-Morse potential well, for the nonlinear Schrödinger equation (the Gross-Pitaevskii equation) with a small nonlinearity. The most interesting case is realized in resonances when the reflection coefficient is exactly equal to zero for the linear Schrödinger equation. Then the reflection is determined by only a small nonlinear term in the Gross-Pitaevskii equation. The simple analytic expression is obtained for the reflection coefficient produced only by the nonlinearity. The analytic condition is found for the common action of the potential well and the nonlinearity to produce the zero reflection coefficient. The reflection coefficient is also derived analytically in the vicinity of a resonance shifted by the nonlinearity. [ABSTRACT FROM AUTHOR]

Abstract: Motivated by recent experimental observations, we study theoretically multiple bright solitary waves of trapped Bose–Einstein condensates. Through variational and numerical analyses, we determine the threshold for collapse of these states. Under -phase differences between adjacent waves, we show that the experimental states lie consistently at the threshold for collapse, where the corresponding in-phase states are highly unstable. Following the observation of two long-lived solitary waves in a trap, we perform detailed three-dimensional simulations which confirm that in-phase waves undergo collapse while a -phase difference preserves the long-lived dynamics and gives excellent quantitative agreement with experiment. Furthermore, intermediate phase differences lead to the growth of population asymmetries between the waves, which ultimately triggers collapse. [Copyright &y& Elsevier]

Abstract: We investigate effects of the application of a kick to one-dimensional matter-wave solitons in a self-attractive Bose–Einstein condensate trapped in an optical lattice. The resulting soliton’s dynamics is studied within the framework of the time-dependent nonpolynomial Schrödinger equation. The crossover from the pinning to quasi-free motion crucially depends on the size of the kick, strength of the self-attraction, and parameters of the optical lattice. [Copyright &y& Elsevier]

Abstract: We review recent studies of the effects of disorder on an atomic Bose–Einstein condensate (BEC). We focus particularly on our own experiments with 7Li BECs in laser speckle. Both the interaction, which gives rise to the nonlinearity in a BEC, and the disorder can be tuned experimentally. This opens many opportunities to study the interplay of interaction and disorder in both condensed matter physics and nonlinear science. [Copyright &y& Elsevier]

Abstract: We introduce a new confining potential which simulates preferably the realistic near-harmonic trap for a quasi-one-dimensional (1D) Bose–Einstein condensate (BEC). An exact transmission state of the BEC system is found and the corresponding spatial configurations, metastability, superfluidity and the transport properties are analyzed. Resonant transmission through the potential is predicted from the exact solution. [Copyright &y& Elsevier]

Abstract: We show through a novel general field theory argument that for the very same reason that excitons are bright, i.e. emitting photons, they have a higher energy than dark excitons, whatever the carrier spatial configurations is, i.e., even in stressed geometry or for electrons well separated from holes as in a double quantum well structure. Indeed, the same channel which produces the necessary finite electron–hole effective overlap to make them bright, allows for Coulomb interband exchange processes, which are nothing but a sequence of virtual recombination and creation of one electron–hole pair, a fact known in relativistic quantum field theory but never extended to semiconductor physics. The repulsive electron–hole Coulomb exchange interaction, which exists for bright excitons, but not for dark excitons, pushes the bright exciton energy up. If we now remember that dark excitons with spins are formed in a natural way through carrier exchange between opposite spin bright excitons, we here predict that in a double quantum well sample with one parabolic trap–a configuration quite appropriate to get a high density–exciton Bose–Einstein condensation should appear, when cooling down the sample, as a dark spot made of excitons at the center of the trap. In this paper, we also suggest a possible link between the observed ring structure in a double quantum well and the formation of dark exciton condensate. [Copyright &y& Elsevier]

Abstract: Approximate solutions of the Gross–Pitaevskii (GP) equation, obtained upon neglection of the kinetic energy, are well known as Thomas–Fermi solutions. They are characterized by the compensation of the local potential by the collisional energy. In this article we consider exact solutions of the GP-equation with this property and definite values of the kinetic energy, which suggests the term “kinetic Thomas–Fermi” (KTF) solutions. Despite their formal simplicity, KTF-solutions can possess complex current density fields with unconventional topology. We point out that a large class of light-shift potentials gives rise to KTF-solutions. As elementary examples, we consider one-dimensional and two-dimensional optical lattice scenarios, obtained by means of the superposition of two, three and four laser beams, and discuss the stability properties of the corresponding KTF-solutions. A general method is proposed to excite two-dimensional KTF-solutions in experiments by means of time-modulated light-shift potentials. [Copyright &y& Elsevier]

One-dimensional (1D) dipolar quantum gases are characterized by a very special condition where super-strong correlations occur to significantly affect the static and dynamical low-energy behavior. This behavior is accurately described by the Luttinger Liquid theory with parameter K < 1. Dipolar Bose gases are routinely studied in laboratory with Chromium atoms. On the other hand, 1D realizations with molecular quantum gases can be at reach of current experimental expertises, allowing to explore such extreme quantum degenerate conditions which are the bottom line for designing technological devices. Aim of the present contribution is to focus on the possible probes expected to signal the reach of Luttinger-Liquid behavior in 1D dipolar gases. [ABSTRACT FROM AUTHOR]

We numerically study properties of the dynamics of vortices in nonrotating Bose-Einstein condensates in the Thomas-Fermi regime. On the one hand, we compute the vortex energy as a function of its position and we predict, using the expression of the Magnus force, the vortex precession velocity. On the other hand, we calculate the temporal evolution of the vortex-state and test the accuracy of the previous prediction. We also investigate the validity of analytical formulae of this velocity involving the healing length. In addition, we analyze the velocity field and the angular momentum and we compare them to available analytical expressions. [ABSTRACT FROM AUTHOR]

Bose systems, subject to the action of external random potentials, are considered. For describing the system properties, under the action of spatially random potentials of arbitrary strength, the stochastic mean-field approximation is employed. When the strength of disorder increases, the extended Bose-Einstein condensate fragments into spatially disconnected regions, forming a granular condensate. Increasing the strength of disorder even more transforms the granular condensate into the normal glass. The influence of time-dependent external potentials is also discussed. Fastly varying temporal potentials, to some extent, imitate the action of spatially random potentials. In particular, strong time-alternating potential can induce the appearance of a nonequilibrium granular condensate. [ABSTRACT FROM AUTHOR]

We review some recent theoretical work on the phase transition of interacting Bose gases in the presence of external trapping potentials. A general framework for the study of such questions is presented which is based on the application of perturbative momentum-shell renormalization group methods to the trapped gas in the uncondensed phase. After giving an overview of this approach, we first establish its validity by comparing to previous results for homogeneous and harmonically trapped gases. Using this theoretical framework, we then examine various aspects of how external potentials influence the physics of condensation. (i) By studying the case of general power-law potentials and complemented by arguments from variational perturbation theory, it is quantitatively worked out how a growing inhomogeneity of the trapping potential diminishes nonperturbative effects at the transition. (ii) It is shown how by superimposing a weak periodic potentials on the homogeneous system, the characteristic nonperturbative momentum scale of critical interacting Bose gases can be probed. (iii) For a gas in a random potential, it is studied how condensation is affected by the combined influence of disorder effects and particle interactions. [ABSTRACT FROM AUTHOR]

Propagation of monochromatic linearly polarized plane electromagnetic wave through resonantly absorbing anisotropic medium with frequency-modulated response is studied analytically and numerically. Frequency modulation is assumed to be provided by means of either mechanical vibration of a solid sample or modulation of quantum transition frequency by a driving low-frequency electromagnetic field. Possibility of generation of train of pulses with polarization of the incident field as well as with orthogonal polarization is shown. For each polarization, optimal combinations of values of four parameters that provide maximal ratio of peak pulse intensity to the average output intensity is found numerically. Possible realization of this resonant method of pulse shaping in laser crystal Dy2+:CaF2 is discussed. [ABSTRACT FROM AUTHOR]

Abstract: We theoretically study the influence of an external static magnetic field on the slowing of electromagnetic pulses in a Bose–Einstein condensate of hydrogenlike atoms. The description is based on the analysis of the Zeeman splitting of hyperfine levels corresponding to the ground and excited states of alkali-metal atoms. We find the dependencies of the group velocity and absorption rate of the pulses on the intensity of the magnetic field for two-component Bose condensate of sodium atoms. The possibility of controlling the ultraslow light phenomenon in this system by the external static magnetic field is discussed. [Copyright &y& Elsevier]

It is shown analytically that, in a trap filled by a Bose-Einstein condensate of atoms with a negative S-scattering length, there exists an instability caused by the nonlocal interaction of atoms. For this effect to be efficiently discovered experimentally, it is necessary to considerably decrease the absolute value of the scattering length using the Feshbach effect. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the crossover from three to two dimensions for harmonically trapped hard-sphere Bose gases by varying the aspect ratio of the trapping potential. The diffusion Monte Carlo method is used to calculate both the ground-state energy and structural properties. The effect of trap anisotropy, interparticle interaction, and number of particles on the ground-state properties is discussed. Our results show that the minimum value of the aspect ratio at which the system reaches an asymptotic equilibrium distribution in the weakly confined direction decreases with increasing scattering length, while the minimum value of the aspect ratio at which the system enters the quasi-two-dimensional (2D) regime increases as both the scattering length and the number of particles increase. Additionally, the role played by particle correlations is proved to be more pronounced in the quasi-2D system than in the three-dimensional (3D) system by directly comparing the ground-state properties for the two cases. [Copyright &y& Elsevier]

Abstract: We present a quantum many body approach with van der Waal type of interaction to achieve 85Rb Bose–Einstein condensate with tunable interaction which has been produced by magnetic field induced Feshbach resonance in the JILA experiment. [Copyright &y& Elsevier]

Basic properties of cold Bose atoms in optical lattices are reviewed. The main principles of correct self-consistent description of arbitrary systems with Bose-Einstein condensate are formulated. Theoretical methods for describing regular periodic lattices are presented. A special attention is paid to the discussion of Bose-atom properties in the frame of the boson Hubbard model. Optical lattices with arbitrary strong disorder, induced by random potentials, are treated. Possible applications of cold atoms in optical lattices are discussed, with an emphasis of their usefulness for quantum information processing and quantum computing. An important feature of the present review article, distinguishing it from other review works, is that theoretical fundamentals here are not just mentioned in brief, but are thoroughly explained. This makes it easy for the reader to follow the principal points without the immediate necessity of resorting to numerous publications in the field. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the dynamic response of population transfer between two components of a finite temperature spinor Bose condensed gas to a time-dependent coupling potential. Comparison between the results obtained in the Bogoliubov–Popov approximation (BPA) and in the generalized random phase approximation (GRPA) shows noticeable discrepancies. In particular, the inter-component current response function calculated in the GRPA displays a gapped spectrum due to the exchange interaction energy whereas the corresponding density response function is gapless. We verify that, contrary to the BPA, the GRPA preserves the symmetry and the -sum rule associated to the spinor gas. In order to validate the approximation, we propose an experimental setup that allows the observation of the predicted gap. [Copyright &y& Elsevier]

Abstract: Nuclear Magnetic Resonance (NMR) cryoporometry is a technique for non-destructively determining pore size distributions in porous media through the observation of the depressed melting point of a confined liquid. It is suitable for measuring pore diameters in the range 2 nm–1 μm, depending on the absorbate. Whilst NMR cryoporometry is a perturbative measurement, the results are independent of spin interactions at the pore surface and so can offer direct measurements of pore volume as a function of pore diameter. Pore size distributions obtained with NMR cryoporometry have been shown to compare favourably with those from other methods such as gas adsorption, DSC thermoporosimetry, and SANS. The applications of NMR cryoporometry include studies of silica gels, bones, cements, rocks and many other porous materials. It is also possible to adapt the basic experiment to provide structural resolution in spatially-dependent pore size distributions, or behavioural information about the confined liquid. [Copyright &y& Elsevier]

Abstract: S-wave pairing in neutron matter is studied within an extension of correlated basis function (CBF) theory to include the strong, short range spatial correlations due to realistic nuclear forces and the pairing correlations of the Bardeen, Cooper and Schrieffer (BCS) approach. The correlation operator contains central as well as tensor components. The correlated BCS scheme of [S. Fantoni, Nucl. Phys. A 363 (1981) 381], developed for simple scalar correlations, is generalized to this more realistic case. The energy of the correlated pair condensed phase of neutron matter is evaluated at the two-body order of the cluster expansion, but considering the one-body density and the corresponding energy vertex corrections at the first order of the Power Series expansion. Based on these approximations, we have derived a system of Euler equations for the correlation factors and for the BCS amplitudes, resulting in correlated nonlinear gap equations, formally close to the standard BCS ones. These equations have been solved for the momentum independent part of several realistic potentials (Reid, Argonne and Argonne ) to stress the role of the tensor correlations and of the many-body effects. Simple Jastrow correlations and/or the lack of the density corrections enhance the gap with respect to uncorrelated BCS, whereas it is reduced according to the strength of the tensor interaction and following the inclusion of many-body contributions. [Copyright &y& Elsevier]

Abstract: We investigate analytically the thermodynamical stability of vortices in the ground state of rotating 2D Bose–Einstein condensates confined in asymptotically homogeneous trapping potentials in the Thomas–Fermi regime. Our starting point is the Gross–Pitaevskii energy functional in the rotating frame. By estimating lower and upper bounds for this energy, we show that the leading order in energy and density can be described by the corresponding Thomas–Fermi quantities and we derive the next order contributions due to vortices. As an application, we consider a general potential of the form with slope and anisotropy which includes the harmonic () and ‘flat’ () traps, respectively. For this potential, we derive the critical angular velocities for the existence of vortices and show that all vortices are single-quantized. Moreover, we derive relations which determine the distribution of the vortices in the condensate i.e. the vortex pattern. [Copyright &y& Elsevier]

Abstract: Bose–Einstein statistics is derived in the thermodynamic limit when the ratio of system size to thermal de Broglie wavelength goes to infinity. However, according to the experimental setup of Bose–Einstein condensation of harmonically trapped Bose gas of alkali atoms, the ratio near the condensation temperature () is 30–50. And, at ultralow temperatures well below , this ratio becomes comparable to 1. We argue that finite size as well as the ultralow temperature induces corrections to Bose–Einstein statistics. From the corrected statistics we plot condensation fraction versus temperature graph. This theoretical plot satisfies well with the experimental plot [A. Griesmaier et al., Phys. Rev. Lett. 94 (2005) 160401]. [Copyright &y& Elsevier]

We investigate the stability of the first excited state, the so-called “π-state,” of Bose-Einstein condensates in a double-well potential. From the condition of complex excitation energies, we determine the critical barrier height, above which the π-state is dynamically unstable. We find that the critical barrier height decreases monotonically as the number of condensate atoms increases. We also simulate the dynamics of the π-state by solving the time-dependent Gross-Pitaevskii equation. Our simulation results show that the π-state in the dynamically unstable region exhibits distinctively different behavior from that in the dynamically stable region. [ABSTRACT FROM AUTHOR]

We study the superfluid-to-Mott insulator transition of bosons in a two-legged ladder optical lattice of a type accessible in current experiments on double-well optical lattices. The zero-temperature phase diagram is mapped out, with a focus on its dependence upon interchain hopping and the tilt between double wells. We find that the unit-filling Mott phase exhibits a nonmonotonic behavior as a function of the tilt parameter, producing a reentrant phase transition between the Mott insulator and superfluid phases. [ABSTRACT FROM AUTHOR]

We investigate Bose-Einstein condensation of noninteracting gases in a harmonic trap with an offcenter dimple potential. We specifically consider the case of a tight and deep dimple potential, which is modeled by a point interaction. This point interaction is represented by a Dirac delta function. The atomic density, chemical potential, critical temperature and condensate fraction, and the role of the relative depth and the position of the dimple potential are analyzed by performing numerical calculations. [ABSTRACT FROM AUTHOR]

Abstract: Neutron diffraction is a standard method for determining the structure of matter on an atomic scale; NMR cryoporometry is a recent widely applicable technique for characterising structure on a 2nm to scale. An extension of these techniques is described, Neutron Diffraction Cryoporometry (NDC). The information from a set of neutron diffraction measurements of liquids and their crystalline forms in meso-pores, as a function of temperature, is displayed as a cryoporometry graph. The data may then be conveniently interpreted using the Gibbs–Thomson relationship by analogy with the existing technique, NMR cryoporometry. Clear information is thus obtained on the relationship between phase and nano-structure, in a form well suited to further analysis. This method is applied to an equilibrium study of water/ice in SBA-15 templated silicas, as model nano- to meso-structured systems. The method described here uses global pattern matching (a one-dimensional morphing algorithm inside a linear least-squares fitting algorithm) applied to the full range of the diffraction data. This is a rapid method by comparison with the conventional method of fitting individual (overlapping) peaks, and has already led to NMR observations indicating plastic (rotator phase) ice in the same system. [Copyright &y& Elsevier]

The Bose condensation of two-dimensional dipolar excitons in quantum wells is numerically studied by the diffusion Monte Carlo simulation method. The correlation, microscopic, thermodynamic, and spectral characteristics are calculated. It is shown that, in structures of coupled quantum wells, in which low-temperature features of exciton luminescence have presently been observed, dipolar excitons form a strongly correlated system. [ABSTRACT FROM AUTHOR]