Narrow Results

We consider a gas of interacting bosons trapped in a box of side length one in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s prediction for the ground state energy and the low-energy excitation spectrum. This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein.

An overview of the Bose–Einstein condensation of correlated atoms in a trap is presented by examining the effect of interparticle correlations to one- and two-body properties of the above systems at zero temperature in the framework of the lowest order cluster expansion. Analytical expressions for the one- and two-body properties of the Bose gas are derived using Jastrow-type correlation function. In addition numerical calculations of the natural orbitals and natural occupation numbers are also carried out. Special effort is devoted for the calculation of various quantum information properties including Shannon entropy, Onicescu informational energy, Kullback–Leibler relative entropy and the recently proposed Jensen–Shannon divergence entropy. The above quantities are calculated for the trapped Bose gases by comparing the correlated and uncorrelated cases as a function of the strength of the short-range correlations. The Gross–Piatevskii equation is solved, giving the density distributions in position and momentum space, which are employed to calculate quantum information properties of the Bose gas.

Fifty years ago, Yang and I worked on the dilute hard-sphere Bose gas, which has been experimentally realized only relatively recently. I recount the background of that work, subsequent developments, and fresh understanding. In the original work, we had to rearrange the perturbation series, which was equivalent to the Bogoliubov transformation. A deeper reason for the rearrangement has been a puzzle. I can now explain it as a crossover from ideal gas to interacting gas behavior, a phenonmenon arising from Bose statistics. The crossover region is infinitesimally small for a macroscopic system, and thus unobservable. However, it is experimentally relevant in mesoscopic systems, such as a Bose gas trapped in an external potential, or on an optical lattice.

We study properties of charge fluids with random impurities or heavy polarons using a microscopic Hamiltonian with the full many-body Coulomb interaction. At zero temperature and high enough density the bosonic fluid is superconducting, but when density decreases the Coulomb interaction will be strongly over-screened and impurities or polarons begin to trap charge carriers forming bound quasiparticle like clusters, which we call Coulomb bubbles or clumps. These bubbles are embedded inside the superconductor and form nuclei of a new insulating state. The growth of a bubble is terminated by the Coulomb force. The fluid contains two groups of charge carriers associated with free and localized states. The insulating state arises via a percolation of the insulating islands of bubbles, which cluster and prevent the flow of the electrical supercurrent through the system.

Our results are applicable to HTSC. There the Coulomb fluids discussed in the paper correspond to mobile holes located on Cu sites and heavy polarons or charged impurities located on Oxygen sites. As a result of our calculations the following two-componet picture of two competing orders in cuprates arise. The mobile and localized states are competing with each other and their balance is controlled by doping. At high doping a large Fermi surface is open. There the density of real charge carriers is significantly larger than the density of the doped ones. When doping decreases more and more carriers are localized as Coulomb clumps which are creating around heavy polarons localized on Oxygen sites and forming a regular lattice. The picture is consistent with the Gorkov and Teitelbaum (GT) analysis ^1,2 of the transport, Hall effect data and the ARPES spectra as well as with nanoscale superstructures observed in Scanning Tunneling Microscope(STM) experiments [3-8]. The scenario of the clump formation may be also applicable to pnictides, where two types of clumps may arise even at very high temperatures.

Reasons have been found for thinking that the minimum diameter of channels of a given length to support superconductivity through films of oxidized atactic polypropylene (OAPP) at room temperature is considerably larger than that found in a model for Bose condensation in an array of nanofilaments [D. M. Eagles, Philos. Mag.85, 1931 (2005)] used previously. This model was introduced to interpret experimental results dating from 1988 on OAPP. The channels are thought to be of larger diameter than believed before because, for an N–S–N system where the superconductor consists of an array of single-walled carbon nanotubes, the resistance, for good contacts, is R_Q/2N, where N is the number of nanotubes and R_Q = 12.9 kΩ [see e.g., M. Ferrier et al., Solid State Commun.131, 615 (2004)]. We assume this would be 2R_Q/N for a triplet superconductor with all spins in the same direction and no orbital degeneracy, which may be the case for nanofilaments in OAPP. Hence one may infer a minimum number of filaments for a given resistance. In the present model, the E(K) curve for the bosons is taken to be of a Bogoliubov form, but with a less steep initial linear term in the dispersion at T_c than the one at low T. This form is different from the simple linear plus quadratic dispersion, with a steeper initial slope, used in my 2005 paper. A combination of theory and experimental data has been used to find approximate constraints on parameters appearing in the theory.

The thermodynamics of a free Bose gas with effective temperature scale and hard-sphere Bose gas with the scale are studied. arises as the temperature experienced by a single particle in a quantum gas with 2-body harmonic oscillator interaction V_osc, which at low temperatures is expected to simulate, almost correctly, the attractive part of the interatomic potential V_He between ⁴He atoms. The repulsive part of V_He is simulated by a hard-sphere (HS) potential. The thermodynamics of this system of HS bosons, with the temperature scale (HSET), and particle mass and density equal to those of ^4He, is investigated, first, by the Bogoliubov–Huang method and next by an improved version of this method, which describes He II in terms of dressed bosons and takes approximate account of those terms of the 2-body repulsion which are linear in the zero-momentum Bose operators a₀, (originally rejected by Bogoliubov). Theoretical heat capacity C_V(T) exhibits good agreement, below 1.9 K, with the experimental heat capacity graph observed in ⁴He at saturated vapour pressure. The phase transition to the He II phase, occurs in the HSET at T_λ = 2.17 K, and is accompanied, in the modified HSET version, by a singularity of C_V(T). The fraction of atoms in the momentum condensate at 0 K equals 8.86% and agrees with other theoretical estimates for He II. The fraction of normal fluid falls to 8.37% at 0 K which exceeds the value 0% found in He II.

A recently developed formalism for Helium II is generalized by introducing a 2-body interaction of spheres with diameter depending on the momentum exchanged between two atoms in an interaction process. A larger class of atomic collisions is also admitted. These modifications allow to account for some details of the interatomic potential V_He(r) between two ⁴He atoms, which were previously disregarded, and to improve the theoretical graphs of Helium II momentum distribution and normal fluid fraction.

We study the Bardeen–Cooper–Shrieffer (BCS) pairing state of a two-component Bose gas with a symmetric spin–orbit coupling (SOC). In the dilute limit at low temperature, this system is essentially a dilute gas of diatomic molecules. We compute the effective mass of the molecule and find that it is anisotropic in momentum space. The critical temperature of the pairing state is about eight times smaller than the Bose–Einstein condensation (BEC) transition temperature of an ideal Bose gas with the same density.

We discuss the construction of the exactly solvable pairing models for bosons in the framework of the Quantum Inverse Scattering method. It is stressed that this class of models naturally appears in the quasiclassical limit of the algebraic Bethe ansatz transfer matrix. We propose the new pairing Hamiltonians for bosons, depending on the additional parameters. It is pointed out that the new class of the pairing models can be obtained from the fundamental transfer-matrix. The possible new application of the pairing models for confined bosons in the physics of helium nanodroplets is pointed out.

In this paper, we investigate the Landau and Baliaev damping of the collective modes in a two-component Bose gas using the mean-field approximation. We show that due to the two body atom–atom interaction, oscillations of each component is coupled to the thermal excitations of the other component which gives rise to creation or destruction of the elementary excitations that can take place in the two separate components. In addition, we find that the damping is also enhanced due to inter-component coupling.

Weakly interacting Bose gases confined in a one-dimensional harmonic trap are studied using microcanonical ensemble approaches. Combining number theory methods, I present a new approach to calculate the particle number counting statistics of the ground state occupation. The results show that the repulsive interatomic interactions increase the ground state fraction and suppresses the fluctuation of ground state at low temperature.

In this paper, we investigate the spectral function of the Higgs mode in a two-dimensional Bose gas by using the effective field theory in the zero-temperature limit. Our approach explains the experimental feature that the peak of the spectral function is a soft continuum rather than a sharp peak, broadens and vanishes in the superfluid phase, which cannot be explained in terms of the $O(2)$ model. We also find that the scalar susceptibility is the same as the longitudinal susceptibility.

A Hartree–Fock mean-field theory of a weakly interacting Bose-gas in a quenched white noise disorder potential is presented. A direct continuous transition from the normal gas to a localized Bose-glass phase is found which has localized short-lived excitations with a gapless density of states and vanishing superfluid density. The critical temperature of this transition is as for an ideal gas undergoing Bose–Einstein condensation. Increasing the particle-number density a first-order transition from the localized state to a superfluid phase perturbed by disorder is found. At intermediate number densities both phases can coexist.

Fifty years ago, Yang and I worked on the dilute hard-sphere Bose gas, which has been experimentally realized only relatively recently. I recount the background of that work, subsequent developments, and fresh understanding. In the original work, we had to rearrange the perturbation series, which was equivalent to the Bogoliubov transformation. A deeper reason for the rearrangement has been a puzzle. I can now explain it as a crossover from ideal gas to interacting gas behavior, a phenonmenon arising from Bose statistics. The crossover region is infinitesimally small for a macroscopic system, and thus unobservable. However, it is experimentally relevant in mesoscopic systems, such as a Bose gas trapped in an external potential, or on an optical lattice.

The dilute Bose gas is studied in the large-N limit using functional integration.

We introduce a stochastic field equation based on the P-representation of the grand canonical density operator of a Bose gas which is free from ultraviolet problems. Numerical simulations for a harmonic trap potential are presented. Although strictly valid for an ideal gas only, we argue that the behavior of weakly interacting Bose gases at finite temperatures may also be described.

We study properties of charge fluids with random impurities or heavy polarons using a microscopic Hamiltonian with the full many-body Coulomb interaction. At zero temperature and high enough density the bosonic fluid is superconducting, but when density decreases the Coulomb interaction will be strongly over-screened and impurities or polarons begin to trap charge carriers forming bound quasiparticle like clusters, which we call Coulomb bubbles or clumps. These bubbles are embedded inside the superconductor and form nuclei of a new insulating state. The growth of a bubble is terminated by the Coulomb force. The fluid contains two groups of charge carriers associated with free and localized states. The insulating state arises via a percolation of the insulating islands of bubbles, which cluster and prevent the flow of the electrical supercurrent through the system.

Our results are applicable to HTSC. There the Coulomb fluids discussed in the paper correspond to mobile holes located on Cu sites and heavy polarons or charged impurities located on Oxygen sites. As a result of our calculations the following two-componet picture of two competing orders in cuprates arise. The mobile and localized states are competing with each other and their balance is controlled by doping. At high doping a large Fermi surface is open. There the density of real charge carriers is significantly larger than the density of the doped ones. When doping decreases more and more carriers are localized as Coulomb clumps which are creating around heavy polarons localized on Oxygen sites and forming a regular lattice. The picture is consistent with the Gorkov and Teitelbaum (GT) analysis ^1,2 of the transport, Hall effect data and the ARPES spectra as well as with nanoscale superstructures observed in Scanning Tunneling Microscope(STM) experiments [3-8]. The scenario of the clump formation may be also applicable to pnictides, where two types of clumps may arise even at very high temperatures.