Scattering of neutrons on a Bose condensate

The spectrum of noncondensate excitations in neutron scattering on bosons is obtained in the framework of the Bogoliubov models both for liquid ⁴He and a dilute gas. The problem is solved using a path-integral representation of the partition function of the system. We describe the influence of scattering of neutrons on a Bose condensate in a stationary (time-independent) picture in the Gibbs equilibrium ensemble. This influence is a stationary boson response, and it depends on the initial neutron momentum k, transfer momentum p, and the neutron-boson interaction λ, which is related to the scattering length. The contribution of the neutrons to the initial Bogoliubov spectrum is found to be important for “quasi-elastic” scattering on the noncondensate, while the contribution of deep inelastic scattering is small; no contribution from elastic scattering on the Bose condensate is found. In the case of liquid Helium, the response is unlikely to be observable for all values p. On the other hand, for a gas one may expect a visible effect, in particular for a small momentum transfer p and a small density of the Bose condensate ϱ.     

The <Superscript>55</Superscript>Mn Spin Echo Test of Magnon BEC State in MnCO<Subscript>3</Subscript>

The coherent quantum state of magnons—Bose–Einstein condensate (BEC) has been observed in several types of antiferromagnets. According to the Bose statistics of magnons, BEC appears when the magnon density exceeds the critical density N _BEC and the magnon gas condenses to a quantum liquid. The BEC state is characterized by a coherent precession of the magnetization. In this paper, the first experiments showing the suppression of the spin echo signal by the magnon BEC is presented. These experiments confirm the coherence of magnetic excitations in the BEC state.     

Bose-Einstein condensation at finite momentum and magnon condensation in thin film ferromagnets

We use the Gross-Pitaevskii equation to determine the spatial structure of the condensate density of interacting bosons whose energy dispersion ϵ _k has two degenerate minima at finite wave-vectors ± q. We show that in general the Fourier transform of the condensate density has finite amplitudes for all integer multiples of q. If the interaction is such that many Fourier components contribute, the Bose condensate is localized at the sites of a one-dimensional lattice with spacing 2 π/|q|; in this case Bose-Einstein condensation resembles the transition from a liquid to a crystalline solid. We use our results to investigate the spatial structure of the Bose condensate formed by magnons in thin films of ferromagnets with dipole-dipole interactions.     

Perturbative calculation of critical exponents for the Bose–Hubbard model

We develop a strategy for calculating critical exponents for the Mott insulator-to-superfluid transition shown by the Bose–Hubbard model. Our approach is based on the field-theoretic concept of the effective potential, which provides a natural extension of the Landau theory of phase transitions to quantum critical phenomena. The coefficients of the Landau expansion of that effective potential are obtained by high-order perturbation theory. We counteract the divergency of the weak-coupling perturbation series by including the seldom considered Landau coefficient a ₆ into our analysis. Our preliminary results indicate that the critical exponents for both the condensate density and the superfluid density, as derived from the two-dimensional Bose–Hubbard model, deviate by less than 1 % from the best known estimates computed so far for the three-dimensional XY universality class.     

Pairing energy of liquid 4He

The two-particle density matrix of a Bose system described by a Jastrow wave function displays off-diagonal long-range order associated with strong correlations between pairs of bosons with non-zero momenta ?q, -?q. In conjunction with the zero-momentum condensate, these correlations give rise to a finite contribution to the energy expectation value per particle, which is calculated for liquid ⁴He at two values of the density.     

Experimental observation of Bose condensation in high-temperature superconductors

Emission Mössbauer spectroscopy on ⁶⁷Cu (⁶⁷Zn) and ⁶⁷Ga (⁶⁷Zn) isotopes was used to show that for the superconductors Nd_1.85Ce_0.15CuO₄, La_1.85 Sr_0.15CuO₄, and Tl₂Ba₂ CaCuO₈ in the temperature range T > T _c the temperature dependence of the center of gravity S of the Mössbauer spectrum is determined by the second-order Doppler shift, while in the range T < T _c the Bose condensation of Cooper pairs influences the value of S (here T _c is the superconducting transition temperature). The spatial nonuniformity produced in the electron density by a Bose condensate of Cooper pairs was observed for La_1.85 Sr_0.15CuO₄.     

BCS-BEC crossover in 2D Fermi gases with Rashba spin-orbit coupling

We present a systematic theoretical study of the BCS-BEC crossover in two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC). By solving the exact two-body problem in the presence of an attractive short-range interaction we show that the SOC enhances the formation of the bound state: the binding energy E(B) and effective mass m(B) of the bound state grows along with the increase of the SOC. For the many-body problem, even at weak attraction, a dilute Fermi gas can evolve from a BCS superfluid state to a Bose condensation of molecules when the SOC becomes comparable to the Fermi momentum. The ground-state properties and the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature are studied, and analytical results are obtained in various limits. For large SOC, the BKT transition temperature recovers that for a Bose gas with an effective mass m(B). We find that the condensate and superfluid densities have distinct behaviors in the presence of SOC: the condensate density is generally enhanced by the SOC due to the increase of the molecule binding; the superfluid density is suppressed because of the nontrivial molecule effective mass m(B).     

Zero-sound condensate in a Fermi liquid

We consider a normal Fermi liquid with a local scalar interaction given by the Landau parameter f₀. The system becomes unstable for f₀ < ?1 against a growth of scalar-mode excitations (Pomeranchuk instability). We show that the instability may be tamed by the formation of a static Bose condensate of the scalar modes. We study a possible reconstruction of the isospin-symmetric nuclear matter owing to the appearance of the condensate. Possibility of a novel metastable state at subnuclear densities is demonstrated.     

Saturation and condensate fraction reduction of cold alpha matter

The ground state energy of ideal α  -matter at T=0$T=0$ 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.     

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.     

Superconducting plate in a transverse magnetic field: New state

A model is proposed for describing Cooper pairs near the transition (in temperature and magnetic field) point when their spacing is larger than their size. The essence of the model is as follows: the Ginzburg-Landau functional is written in operator form in terms of field operators of the Bose type so that the average value of the density operator gives the concentration of Cooper pairs, and the same Ginzburg-Landau expression is obtained for the Bose condensate. The model is applied to a superconducting plate with a thickness smaller than the size of a pair in a transverse magnetic field near its upper critical value H _c2. A new state is discovered that is energetically more advantageous in a certain interval in the vicinity of the transition point as compared to the Abrikosov vortex state. The wavefunction of the system in this state is of the type of the Laughlin function used in the fractional quantum Hall effect (naturally, as applied to Cooper pairs as Bose particles in our case) and corresponds to a homogeneous incompressible fluid. The energy of this state is proportional to the first power of quantity (1 ? H/H _c2) in contrast to the energy of the vortex state containing the square of this quantity. The interval of the existence of the new state is the larger, the dirtier the sample.     

Instability of layered quantum liquids: 6. Strongly correlated bosons

We calculate the local-field corrections G(q, q _z) for charged bosons at zero temperature in a superlattice with interlayer distance d. An analytical expression for the local-field correction is described. The sum-rule version of the self-consistent approach for the local-field correction is used to discuss the effects of correlation. The RPAparameter r _s and the ratio d/a* determine correlation effects. a* is the effective Bohr radius. The stability region for the Bose condensate r _s < r _sc as a function of d/a* is determined: r _sc ≈ (d/a*)^3/4. The ground-state energy of the layered Bose condensate is calculated and optical and acoustical plasmons are discussed. We predict a roton structure for optical plasmons for r _s > r _sr with r _sr ≈ 0.5 (d/a*)^3/4.     

Dynamic d-symmetry Bose condensate of a planar-large-bipolaron liquid in cuprate superconductors

Abstract

Planar-large-bipolarons can form if the ratio of the surrounding mediums’ static to high-frequency dielectric constants is especially large, ε₀/ε_∞ >> 2. A large-bipolaron in p-doped La₂CuO₄ is modelled as two electrons being removed from the out-of-plane orbitals of four oxygen ions circumscribed by four copper ions of a CuO₂ layer. These oxygen dianions relax inwardly as they donate electrons to the surrounding outwardly relaxing copper cations. This charge transfer generates the strong in-plane electron–lattice interaction needed to stabilise a large-bipolaron with respect to decomposing into polarons. The lowest-energy radial in-plane optic vibration of a large-bipolaron’s four core oxygen ions with their associated electronic charges has d-symmetry. Electronic relaxation in response to multiple large-bipolarons’ atomic vibrations lowers their frequencies to generate a phonon-mediated attraction among them which fosters their condensation into a liquid. This liquid features distinctive transport and optical properties. A large-bipolaron liquid’s superconductivity can result when it undergoes a Bose condensation yielding macroscopic occupation of its ground state. The synchronised vibrations of large-bipolarons’ core-oxygen ions with their electronic charges generate this Bose condensate’s dynamic global d-symmetry.     

Emission of Cu<Subscript>2</Subscript>O Paraexcitons Confined by a Strain Trap: Hints of a Bose–Einstein Condensate?

We monitor the phonon sideband emission from paraexcitons confined in a strain trap in cuprous oxide at T = 1.25 K. On the low energy ank of the optical phonon replicas, both of Γ ₅ ^? and Γ ₃ ^? symmetry (the latter activated by application of a magnetic field), we detect sharp peaks that might represent indications for a paraexciton Bose–Einstein condensate. In contrast, such peaks are absent in the phonon-mediated emission of the orthoexcitons, and they also disappear at elevated temperatures. The results challenge our understanding of the involved physics, e.g., of the Auger recombination of excitons, which has so far been believed to prevent crossing the border to a condensate.     

Long Cycles in a Perturbed Mean Field Model of a Boson Gas

In this paper we give a precise mathematical formulation of the relation between Bose condensation and long cycles and prove its validity for the perturbed mean field model of a Bose gas. We decompose the total density ρ=ρ_short+ρ_long into the number density of particles belonging to cycles of finite length (ρ_short) and to infinitely long cycles (ρ_long) in the thermodynamic limit. For this model we prove that when there is Bose condensation, ρ_long is different from zero and identical to the condensate density. This is achieved through an application of the theory of large deviations. We discuss the possible equivalence of ρ_long≠ 0 with off-diagonal long range order and winding paths that occur in the path integral representation of the Bose gas     

High- and low-frequency behaviour of response functions in a Bose liquid: One-loop approximation

The filed-theoretic analysis of Wong and Gould for a Bose fluid is used to study response functions at arbitrary temperatures. Several rigorous identities are derived for density and momentum current response functions in the high- and low-frequency limits. These involve the condensate fraction n₀ and the superfluid density ?_s. By explicit calculations using the one-loop diagrammatic approximation for the proper irreducible functions, these rigorous results are verified at finite temperatures. In particular, the zero-frequency Gavoret-Nozières relation, the high-frequency Wong-Gould f-sum rule, and the impulse approximation at high momentum transfers are all satisfied in this simple microscopic calculation. On the other hand, the superfluid f-sum rule is found not to be satisfied.     

On the low-temperature behavior of condensed Bose systems

A microscopic derivation of theT ²-law for the low-temperature behavior of the condensate depletion in an interacting Bose liquid is given using the knownT=0 low-lying single-particle excitations. TheT ²-term gives no contribution to the orderT ³ in the microscopic proof of Landau'sT ³-law for the specific heat of an interacting Bose liquid.     

Normal phase and superconducting instability in the attractive Hubbard model: a DMFT(NRG) study

We study the normal (nonsuperconducting) phase of the attractive Hubbard model within the dynamical mean field theory (DMFT) using the numerical renormalization group (NRG) as an impurity solver. A wide range of attractive potentials U is considered, from the weak-coupling limit, where superconducting instability is well described by the BCS approximation, to the strong-coupling region, where the superconducting transition is described by Bose condensation of compact Cooper pairs, which are formed at temperatures much exceeding the superconducting transition temperature. We calculate the density of states, the spectral density, and the optical conductivity in the normal phase for this wide range of U, including the disorder effects. We also present the results on superconducting instability of the normal state dependence on the attraction strength U and the degree of disorder. The disorder influence on the critical temperature T _c is rather weak, suggesting in fact the validity of Anderson’s theorem, with the account of the general widening of the conduction band due to disorder.     

Application of potential harmonic expansion method to BEC: Thermodynamic properties of trapped23Na atoms

We adopt the potential harmonics expansion method for anab initio solution of the many-body system in a Bose condensate containing interacting bosons. Unlike commonly adopted mean-field theories, our method is capable of handling two-body correlation properly. We disregard three- and higher-body correlations. This simplification is ideally suited to dilute Bose Einstein condensates, whose number density is required to be so small that the interparticle separation is much larger than the range of two-body interaction to avoid three- and higher-body collisions, leading to the formation of molecules and consequent instability of the condensate. In our method we can incorporate realistic finite range interactions. We calculate energies of low-lying states of a condensate containing²³Na atoms and some thermodynamical properties of the condensate.     

Discussion of thermodynamic features within the PNJL model

We discuss some thermodynamical features of a QCD system within the two-flavor Polyakov loop extended Nambu–Jona-Lasinio(PNJL) model. Several thermodynamical quantities of interest(pressure, energy density,specific heat, speed of sound, etc.) are investigated and discussed in detail with two different forms of Polyakov loop potential. The effective coupling strength G incorporating a quark feedback(quark condensate) through operator product expansion is also discussed, as well as the relationship between color deconfinement and chiral phase crossover.We find that some thermodynamical quantities have quite different behavior for different Polyakov loop potentials.By changing the characteristic temperature T_0 of the pure Yang-Mills field, we find that when T_0 becomes small,color deconfinement might happen earlier than chiral phase crossover, while their relationship can be determined via some thermodynamical quantities. Furthermore, the behavior of the thermodynamical quantities is quite different in the two different forms of Polyakov loop potential studied. Especially, one of the potentials, specific heat, has two peaks, which correspond to color deconfinement and chiral phase crossover respectively. This interesting phenomenon may shed some light on whether the inflection points of the chiral condensate and deconfinement transitions happen at the same temperature or not for lattice QCD and experimental studies.