Non-translation-invariant states in two dimensions

We construct a class of models with translation-invariant interaction for which in dimension two there already exist non-periodic Gibbs states at low temperatures.     

Bose condensation in biosystems

A microscopic approach to Fröhlich's theory of Bose condensation in biological systems is discussed. The conclusions from this microscopic analysis offer further support for Fröhlich's hypothesis.     

Critical temperature of interacting Bose gases in two and three dimensions

We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.     

Cooper pairing and superfluidity in the Emery model

The energy E of the system as a function of the gauge phase Φ is calculated by exact diagonalization in a two-dimensional Cu₄O₈ cluster and by the slave-boson method for large systems. It is shown that motion of carriers with charge 2e, i.e., Cooper pairs, is observed for certain values of the parameters in the Hamiltonian. This motion is identified from the onset of a characteristic maximum of E(Φ) at Φ≈Φ₀/2, where Φ₀ is the flux quantum. The phase diagram is constructed and the range of values of the model parameters where the effect is observed is determined. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 2, 78–82 (25 January 1996)     

Evolution of fermion pairing from three to two dimensions

We follow the evolution of fermion pairing in the dimensional crossover from three-dimensional to two-dimensional as a strongly interacting Fermi gas of ^{6}Li atoms becomes confined to a stack of two-dimensional layers formed by a one-dimensional optical lattice. Decreasing the dimensionality leads to the opening of a gap in radio-frequency spectra, even on the Bardeen-Cooper-Schrieffer side of a Feshbach resonance. The measured binding energy of fermion pairs closely follows the theoretical two-body binding energy and, in the two-dimensional limit, the zero-temperature mean-field Bose-Einstein-condensation to Bardeen-Cooper-Schrieffer crossover theory.     

Bose condensation in strongly monideal systems

The possibility of the formation of a condensate with a finite absolute value of the momentum k₀ in a strongly nonideal Bose system is considered. Such a condensate comes into existence when the one-particle spectrum of a normal system touches zero in the point k₀ ≠ 0. The form of a correlation function below the condensation point shows the appearance of a long-range order, but not the infinite long-range one. In the case of liquid ⁴He estimates show that $\text{k}{}_0\text{? 1}\text{A}\text{?}{}^{\mathrm{?1}}$, and at the temperature T>₀ ～ 1 K this unusual condensate with a finite magnitude of the momentum turns into the conventional Bose-Einstein condensate with the zero momentum. The properties of correlation functions in the spaces of different dimensions are discussed.     

Cooper pairing in the presence of antiferromagnetism

With a BCS interaction, the free energy for usual BCS pairing of electrons but in the presence of antiferromagnetism is shown to be lower than for a different pairing scheme where pairs are formed from electron eigenstates of the antiferromagnet. In both pairing schemes, super-conductivity in the presence of antiferromagnetism is always a mixture of spin-singlet-even-parity-orbital and spin-triplet-odd-parity-orbital electron pairs.     

Topological spin Hall states, charged skyrmions, and superconductivity in two dimensions

We study the properties of two dimensional topological spin Hall insulators which arise through spontaneous breakdown of spin symmetry in systems that are spin rotation invariant. Such a phase breaks spin rotation but not time reversal symmetry and has a vector order parameter. Skyrmion configurations in this vector order parameter are shown to have an electric charge that is twice the electron charge. When the spin Hall order is destroyed by condensation of Skyrmions superconductivity results. This may happen either through doping or at fixed filling by tuning interactions to close the Skyrmion gap. In the latter case the superconductor-spin Hall insulator quantum phase transition can be second order even though the two phases break distinct symmetries.     

Evolution from BCS superconductivity to Bose condensation: analytic results for the crossover in three dimensions

We provide an analytic solution for the mean-field equations and for the relevant physical quantities at the Gaussian level, in terms of the complete elliptic integrals of the first and second kinds, for the crossover problem from BCS superconductivity to Bose-Einstein condensation of a three-dimensional system of free fermions interacting via an attractive contact potential at zero temperature. This analytic solution enables us to follow the evolution between the two limits in a particularly simple and transparent way, as well as to verify the absence of singularities during the evolution. Received: 9 May 1997 / Revised: 4 August 1997 / Accepted: 6 November 1997     

Bose-Einstein condensation and Casimir effect of trapped ideal Bose gas in between two slabs

We study the Bose-Einstein condensation for a 3-d system of ideal Bose gas which is harmonically trapped along two perpendicular directions and is confined in between two slabs along the other perpendicular direction. We calculate the Casimir force between the two slabs for this system of trapped Bose gas. At finite temperatures this force for thermalized photons in between two plates has a classical expression which is independent of ħ. At finite temperatures the Casimir force for our system depends on ħ. For the calculation of Casimir force we consider only the Dirichlet boundary condition. We show that below condensation temperature (T_c) the Casimir force for this non-interacting system decreases with temperature (T) and at , it is independent of temperature. We also discuss the Casimir effect on 3-d highly anisotropic harmonically trapped ideal Bose gas.     

Bound two-pion Cooper pairs in nuclei?

The possibility of bound two-pion (Cooper) pairs in a nuclear medium and their eventual Bose condensation is pointed out. This stems from the fact that freeπ —π scattering in theI=0,l=0 channel shows attraction and that the kinetic energy is strongly suppressed in matter through coupling to Δ —h intermediate states. Connections to theσ meson in effective field theories for nuclear matter are discussed.     

Local-field correction of the charged Bose condensate for two and three dimensions

The local-field correction for the dielectric function of the two-dimensional and of the three-dimensional Bose condensate is calculated within a sum-rule version of the Singwi et al. (Phys. Rev.176, 589 (1968)) approach. We derive analytical expressions for small and large wave numbers and give analytical expressions for the density dependence. We compare the results of the groundstate energy for the three-dimensional system with Monte-Carlo computations. In two dimensions a roton structure in the plasmon dispersion is found at low boson density. The plasmon density of states is calculated. A correlation induced charge-density-wave instability in layered structures of two-dimensional Bose gases is discussed.     

Bose condensation,solitons and canonical transformations in quantum field theory

In an quantum sine-Gordon model in 1+1 dimensions, the condition that the vacuum expectation value of the Heisenberg scalar field reproduces static soliton solution to the classical equation is satisfied when the LSZ asymptotic quantum field undergoes a canonical transformation. This can be viewed as a quantum image of the Bäcklund transformation and the soliton is described in terms of condensation of quanta. Their confinement is ascribed to the non-implementability of unitary transformations among unitary inequivalent representations of the canonical commutation relations.Invited talk at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–21, 1981.It is a pleasure to thank Professor J. Niederle and the Organizing Committee for the opportunity of participating in this Symposium and for the kind hospitality.     

Generalized thermostatistics and Bose–Einstein condensation

Analytical expressions for Bose–Einstein condensation of an ideal Bose gas analyzed within the strictures of nonextensive, generalized thermostatistics are here obtained.     

Vortex states in soft magnets in two and three dimensions

The magnetization curves of arrays of near-spherical soft ferromagnetic particles are compared with those of quasi-two-dimensional dots with similar radius prepared by a rapid e-beam lithographic technique. Curves for the three-dimensional particles are anhysteretic and fit a M(H)/M_s=tanh(cμ₀H) law, whereas the two-dimensional arrays show irreversible segments in the first and third quadrants where the planar vortex state transforms to a collinear state by discontinuous rotation of magnetization about an axis perpendicular to the vortex axis. The additional symmetry of the spherical particle allows this rotation to occur continuously, without energy barriers due to the demagnetizing field.     

Microchip traps and Bose–Einstein condensation

The article gives an overview of the rapidly evolving field of magnetic microchip traps (also called ‘atom chips’) for neutral atoms. Special attention is given to Bose–Einstein condensation in such traps, to the particular properties of microchip trap potentials, and to practical considerations in their design. Scaling laws are developed, which lead to an estimate of the ultimate confinement that chip traps can provide. Future applications such as integrated atom interferometers are discussed. Received: 28 March 2002 / Published online: 14 May 2002     

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.