The Bose-Einstein condensation in a finite one-dimensional homogeneous system of noninteracting bosons

Condensation of the ideal Bose gas in a closed volume having the shape of a rectangular parallel-epiped of length L with a square base of side length l (L ? l) is theoretically studied within the framework of the Bose-Einstein statistics (grand canonical ensemble) and within the statistics of a canonical ensemble of bosons. Under the condition N(l/L)⁴ ? l, where N is the total number of gas particles, dependence of the average number of particles in the condensate on the temperature T in both statistics is expressed as a function of the ratio t=T/T ₁, where T ₁ is a certain characteristic temperature depending only on the longitudinal size L. Therefore, the condensation process exhibits a one-dimensional (1D) character. In the 1D regime, the average numbers of particles in condensates of the grand canonical and canonical ensembles coincide only in the limiting cases of t → 0 and t → ∞. The distribution function of the number of particles in the condensate of a canonical ensemble of bosons at t ≤1 has a resonance shape and qualitatively differs from the Bose-Einstein distribution. The former distribution begins to change in the region of t ～ 1 and acquires the shape of the Bose-Einstein distribution for t ? 1. This transformation proceeds gradually that is, the 1D condensation process exhibits no features characteristic of the phase transition in a 3D system. For N(l/L)⁴ ? 1, the process acquires a 3D character with respect to the average number of particles in the condensate, but the 1D character of the distribution function of the number of particles in the condensate of a canonical ensemble of bosons is retained at all N values.     

Pre-formed Cooper pairs and Bose-Einstein condensation in cuprate superconductors

A two-dimensional (2D) assembly of noninteracting, temperature-dependent, pre-formed Cooper pairs in chemical/thermal equilibrium with unpaired fermions is examined in a binary boson-fermion statistical model as the Bose-Einstein condensation (BEC) singularity temperature T_c is approached from above. Compared with BCS theory (which is not a BEC theory) substantially higher T_cs are obtained without any adjustable parameters, that fall roughly within the range of empirical T_cs for quasi-2D cuprate superconductors.     

The shear viscosity of a trapped Bose-condensed gas

By obtaining Kubo formula type and using nonequilibrium Green’s functions, we calculate the shear viscosity of a trapped Bose-condensed gas below and above the Bose-Einstein condensation temperature (T_BEC). The contributions of the interactions between condensate and noncondensate atoms and between noncondensate atoms take into account to the viscous relaxation time, by evaluating second order self-energies in Beliaev approximation.     

Instability of dipole magnetoexcitons in quantum wells' and graphene superlattices

We propose the Bose-Einstein condensation and superfluidity of quasi-two-dimensional spatially indirect magnetobiexcitons in a slab of superlattice with alternating electron and hole layers consisting from the semiconducting quantum wells (QWs) and graphene superlattice in high magnetic field. For this system the instability of the ground state of interacting two-dimensional indirect magnetoexcitons in a slab of superlattice with alternating electron and hole layers in high magnetic field is found. The density of superfluid component ns(T) and the temperature of the Kosterlitz-Thouless phase transition to the superfluid state in the system of two-dimensional indirect magnetobiexcitons, interacting as electrical quadrupoles, are obtained for both QW and graphene realizations.     

Spin-gauge symmetry and the supercurrents of the alkali atomic gas in a magnetic trap

We show that the local spin-gauge symmetry and the off-diagonal long-range order of the system of alkali atoms in a magnetic trap at the temperature T < T_BEC (the temperature for the Bose-Einstein condensation transition) leads to a superflow of the atomic gas. The supercurrents are present in the interior of the systems even in the ground state. This effect does not exist at the temperature T > T_BEC.     

Possible mechanism of superconductivity in the CuO-Cu interface

Apparently, a two-dimensional CuO lattice is formed on the surface of copper oxide in the CuO-Cu interface. This lattice consists of Cu²⁺ and O^1? ions, which form a narrow, partially filled two-dimensional band. In this case, local electron pairs (LEPs) can form in the oxygen subsystem as a result of the fulfillment of the Shubin-Vonsovskii conditions. A crude estimate of the formation temperature of LEPs gives T* ～ 10 4 K. At the concentration in the interface layer n～1.6×10²⁰ cm^?3 and the effective mass of carriers m* ～ m _e, the onset temperature of Bose-Einstein condensation may take a value of T _c ～ 1000 K. The estimate obtained for the temperature T _c corresponds to the experimental value by an order of magnitude.     

Exact quantum critical points and phase separation instabilities in Betts Hubbard nanoclusters

Spontaneous phase separation instabilities with the formation of various types of charge and spin pairing (pseudo)gaps in U>0 Hubbard model including the next nearest neighbor coupling are calculated with the emphasis on the two-dimensional (square) lattices generated by 8- and 10-site Betts unit cells. The exact theory yields insights into the nature of quantum critical points, continuous transitions, dramatic phase separation instabilities and electron condensation in spatially inhomogeneous systems. The picture of coupled antiparallel (singlet) spins and paired charged holes suggests full Bose condensation and coherent pairing in real space at zero temperature of electrons complied with the Bose-Einstein statistics. Separate pairing of charge and spin degrees at distinct condensation temperatures offers a new route to superconductivity different from the BCS scenario. The conditions for spin liquid behavior coexisting with unsaturated and saturated Nagaoka ferromagnetism due to spin-charge separation are established. The phase separation critical points and classical criticalities found at zero and finite temperatures resemble a number of inhomogeneous, coherent and incoherent nanoscale phases seen near optimally doped high-T_c cuprates, pnictides and CMR nanomaterials.     

Disorder effects in the BCS-BEC crossover region of the attractive Hubbard model

We study the disorder effects upon superconducting transition temperature T _c and the number of local pairs within the attractive Hubbard model in the combined Nozieres-Schmitt-Rink and DMFT + Σ approximations. We analyze the wide range of attractive interaction U, from the weak coupling region, where instability of the normal phase and superconductivity are well described by the BCS model, to the limit of strong coupling, where superconducting transition is determined by Bose-Einstein condensation of compact Cooper pairs, forming at temperatures much higher than superconducting transition temperature. It is shown that disorder can either suppress T _c in the weak coupling limit, or significantly enhance T _c in the case of strong coupling. However, in all cases we actually prove the validity of generalized Anderson theorem, so that all changes in T _c are related to change in the effective bandwidth due to disorder. Similarly, disorder effects on the number of local pairs are only due to these band-broadening effects.     

On the correlation between order parameter, superconducting volume fraction and critical current density in R: 123 superconductors

Resistivity and low field ac susceptibility measurements are made on R: 123 superconducting samples with different rare earth elements R. The order parameter dimensionality OPD is deduced from resistivity versus temperature plot using the Aslamazov and Larkin expression, while the analysis of the temperature dependence of ac susceptibility is done employing Beans’ critical state model and with the help of the Ravi expression. With increasing R, the critical temperatures T_c are nearly kept constant (∼90 K), while the crossover temperatures T_o are shifted to lower values. Moreover, the superconducting order parameter OPD is shifted toward 2D behavior. On the other hand, the values of superconducting volume fraction f_g decrease with increasing ac field amplitude H_m for all samples and it is higher in Er: 123 sample than in Nd: 123 sample. Although the values of critical current density J_c at the peak temperature T_m are nearly unchanged with increasing R, the values of J_c(T), at T<T_m and T>T_m, are found to be dependent on the chosen R. The correlation between the above calculated parameters against R is also mentioned.     

Bose-Einstein condensation in a cavity

The effect of the physically correct boundary conditions and the nonvanishing ground state energy on Bose-Einstein condensation of quantum particles confined to a cubic volumeV=L ³ is evaluated. The transition point is shifted towards higher temperatures by the confinement, the specific heat below the onset of condensation is no longer proportional toT ^3/2, and the pressure does depend on the volume. Precise expressions for the modification of the ground state population and for the shift of the condensation temperature are derived, together with an expansion of the internal energy and of the specific heat. Numerical computations confirm the accuracy of our analytical approximations.Dedicated to Herbert Wagner, whose work on quantum Fermi liquids proved to be also very stimulating for quantum Bose liquids.     

Simulation of influence ternary AlGaN and quaternary AlInGaN blocking layers on temperature characteristic of double quantum well violet InGaN laser diodes

Although of the potential advantages of quaternary AlInGaN as a blocking layer (BL) in double quantum well (QW) violet InGaN laser diode (LD), simulation results indicated that the temperature characteristic (T_o value) of the LD with a quaternary AlInGaN BL is lower than the T_o value of the LD with a conventional ternary AlGaN BL, whereas the T_o value of the LD with quaternary AlInGaN BL is 180 K and the T_o value with ternary AlGaN BL it is 194 K. This is due to the enhance carrier holes distribution between the double QWs with using the quaternary BL.     

On Isotropic Distributional Solutions to the Boltzmann Equation for Bose-Einstein Particles

The paper considers the spatially homogeneous Boltzmann equation for Bose-Einstein particles (BBE). In order to include the hard sphere model, the equation is studied in a weak form and its solutions (including initial data) are set in the class of isotropic positive Borel measures and therefore called isotropic distributional solutions. Stability of distributional solutions is established in the weak topology, global existence of distributional solutions that conserve the mass and energy is proved by weak convergence of approximate L ¹-solutions, and moment production estimates for the distributional solutions are also obtained. As an application of the weak form of the BBE equation, it is shown that a Bose-Einstein distribution plus a Dirac dt-function is an equilibrium solution to the BBE equation in the weak form if and only if it satisfies a low temperature condition and an exact ratio of the Bose-Einstein condensation.     

Gentile statistics with a large maximum occupation number

In Gentile statistics the maximum occupation number can take on unrestricted integers: 1<n<∞. It is usually believed that Gentile statistics will reduce to Bose-Einstein statistics when n equals the total number of particles in the system N. In this paper, we will show that this statement is valid only when the fugacity z<1; nevertheless, if z>1 the Bose-Einstein case is not recovered from Gentile statistics as n goes to N. Attention is also concentrated on the contribution of the ground state which was ignored in related literature. The thermodynamic behavior of a ν-dimensional Gentile ideal gas of particle of dispersion E=p^s/2m, where ν and s are arbitrary, is analyzed in detail. Moreover, we provide an alternative derivation of the partition function for Gentile statistics.     

Electron hopping mechanism in hematite (α-Fe2O3)

The frequency dependence of the real (?′) and imaginary (?″) parts of the dielectric constant of polycrystalline hematite (α-Fe₂O₃) has been investigated in the frequency range 0-100 kHz and the temperature range 190-350 K, in order to reveal experimentally the electron hopping mechanism that takes place during the Morin transition of spin-flip process. The dielectric behaviour is described well by the Debye-type relaxation (α-dispersion) in the temperature regions T<233 K and T>338 K. In the intermediate temperature range 233 K<T<338 K a charge carrier mechanism takes place (electron jump from the O²⁻ ion into one of the magnetic ions Fe³⁺) which gives rise to the low frequency conductivity and to the Ω-dispersion. The temperature dependence of relaxation time (τ) in the −ln τ vs 10³/T plot shows two linear regions. In the first, T<238 K, τ increases with increasing T implying a negative activation energy −0.01 eV, and in the second region T>318 K τ decreases as the temperature increases implying a positive activation energy 0.12 eV. The total reorganization energy (0.12-0.01) 0.11 eV is in agreement with the adiabatic activation energy 0.11 eV given by an ab initio model in the literature. The temperature dependence of the phase shift in the frequencies 1, 5, 10 kHz applied shows clearly an average Morin temperature T_Mo=284±1 K that is higher than the value of 263 K corresponding to a single crystal due to the size and shape of material grains.     

Translationally noninvariant path integral for Bose-Einstein condensate

The Bogolyubov [Hartree-Fock-Bogolyubov (HFB)] method performs the one-particle (mean-field) approximation in the theory of Bose-Einstein condensation (BEC). Various generalizations of this method are possible. Apart from a nonlinear theory, taking the correlation effects into consideration, the HFB approximation for translationally noninvariant systems describes an instructive phenomenon. This paper is devoted to the treatment of two cases: superfluid ⁴He in porous media and atomic BEC in traps subjected to the gravitational field. Both these systems show the dependence of a critical BEC temperature T _c on their nonuniform properties in space.     

Bose-Einstein condensation of an ideal gas in a parabolic trap

The temperature-dependent velocity distribution function is found for the case of Bose-Einstein condensation of a finite number of noninteracting atoms trapped in a three-dimensional anisotropic parabolic trap. It is shown that at a temperature T of the order of the condensation temperature T ₀ the velocity distribution consists of an anisotropic part, reflecting the population of the ground state, and an isotropic part above the condensate. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 8, 559–563 (25 October 1997)     

Current transport mechanism in Al/Si3N4/p-Si (MIS) Schottky barrier diodes at low temperatures

The current-voltage (I-V) and capacitance-voltage (C-V) characteristics of metal-insulator-semiconductor (Al/Si₃N₄/p-Si) Schottky barrier diodes (SBDs) were measured in the temperature range of 80-300 K. By using the thermionic emission (TE) theory, the zero-bias barrier height Φ_B0 calculated from I-V characteristics was found to increase with increasing temperature. Such temperature dependence is an obvious disagreement with the negative temperature coefficient of the barrier height calculated from C-V characteristics. Also, the ideality factor decreases with increasing temperature, and especially the activation energy plot is nonlinear at low temperatures. Such behaviour is attributed to Schottky barrier inhomogeneties by assuming a Gaussian distribution of barrier heights (BHs) at interface. We attempted to draw a Φ_B0 versus q/2kT plot to obtain evidence of a Gaussian distribution of the BHs, and the values of Φ_Bo = 0.826 eV and α_o = 0.091 V for the mean barrier height and standard deviation at zero-bias, respectively, have been obtained from this plot. Thus, a modified ln(I_o/T²) − q²σ_o²/2(kT)² versus q/kT plot gives Φ_B0 and Richardson constant A^* as 0.820 eV and 30.273 A/cm² K², respectively, without using the temperature coefficient of the barrier height. This value of the Richardson constant 30.273 A/cm² K² is very close to the theoretical value of 32 A/cm² K² for p-type Si. Hence, it has been concluded that the temperature dependence of the forward I-V characteristics of the Al/Si₃N₄/p-Si Schottky barrier diodes can be successfully explained on the basis of TE mechanism with a Gaussian distribution of the barrier heights. In addition, the temperature dependence of energy distribution of interface state density (N_SS) profiles was determined from the forward I-V measurements by taking into account the bias dependence of the effective barrier height and ideality factor.     

Electronic transport and magnetic studies of La1−xCax−0.08Sr0.04Ba0.04MnO3

Lanthanum based mixed valence manganite system La_1−xCa_x−0.08Sr_0.04Ba_0.04MnO₃ (LCSBMO; x=0.15, 0.24 and 0.33) synthesized through the sol-gel route is systematically investigated in this paper. The electronic transport and magnetic susceptibility properties are analyzed and compared, apart from the study of unit cell structure, microstructure and composition. Second order phase transition is observed in all the samples and significant difference is observed between the insulator to metal transition temperature (T_MI) and paramagnetic (PM) to ferromagnetic (FM) transition temperature (T_C). In contrast to the insulating FM behaviour usually observed in La_1−xCa_xMnO₃ (LCMO) for x=0.15, a clear insulator to metal transition is observed for LCSBMO for the same percentage of lanthanum. The temperature dependent resistivity of polycrystalline pellets, when obeying the well studied law ρ=ρ_o+ρ₂T² for T<T_MI, is observed to differ significantly in the values of ρ_o and ρ₂, with the electrical conductivity increasing with x. The variable range hopping model has been found to fit resistivity data better than the small polaron model for T>T_MI. AC magnetic susceptibility study of the polycrystalline powders of the manganite system shows the highest PM to FM transition of 285 K for x=0.33.     

Temperature dependence of Johnson noise

Johnson noise is usually considered to measure the absolute, thermodynamic temperature. A careful analysis of data on copper to 1.7 mK suggests that a kinetic temperature T_o coth T_o/T is measured, where T_o = 1.98 mK, and so reflects a zero-point energy.     

Phase transitions in a system of coupled Boson oscillators on a sphere

The solutions of mean-field equations for a system of coupled Boson oscillators on an infinite k-dimensional sphere are discussed in the low density - high temperature region and high density — low temperature region. It is shown that for k = 2 the system exhibits only spatial condensation, whereas for k ⩾ 3 both spatial condensation and Bose-Einstein condensation.