Integral functions of the Bose gas

The asymptotic behaviour of generalised Bose-Einstein integral functions at small values of the chemical potential is shown to depend crucially on the behaviour, close to zero, of the spectral measure induced on R ⁺ by the single particle Hamiltonian, at fixed inverse temperature.     

Gauge invariance and structure of the correlation functions of an imperfect Bose gas

Acta physica Academiae Scientiarum Hungaricae -     

Continuity of state functions of the Bose gas

In this paper we show that some state functions of the Bose gas, especially the entropy, depend continuously on the energy levels for the free Hamiltonian and on perturbations of the free Hamiltonian by operators of degree 0. The method used here is to introduce an appropriate topology on the density matrices and on the perturbations of the free Hamiltonian.     

Correlation functions of the one-dimensional attractive Bose gas

The zero-temperature correlation functions of the one-dimensional attractive Bose gas with a delta-function interaction are calculated analytically for any value of the interaction parameter and number of particles, directly from the integrability of the model. We point out a number of interesting features, including zero recoil energy for a large number of particles, analogous to the M?ssbauer effect.     

Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas

The Lieb–Liniger model is a prototypical integrable model and has been turned into the benchmark physics in theoretical and numerical investigations of low-dimensional quantum systems. In this note, we present various methods for calculating local and nonlocal M-particle correlation functions, momentum distribution, and static structure factor. In particular, using the Bethe ansatz wave function of the strong coupling Lieb–Liniger model, we analytically calculate the two-point correlation function, the large moment tail of the momentum distribution, and the static structure factor of the model in terms of the fractional statistical parameter α = 1-2/γ, where γ is the dimensionless interaction strength. We also discuss the Tan's adiabatic relation and other universal relations for the strongly repulsive Lieb–Liniger model in terms of the fractional statistical parameter.     

A renormalization group analysis of correlation functions for the dipole gas

We develop a renormalization group method for analyzing the generating functional for charge correlations of a dilute classical dipole gas. It is based on and extends the renormalization group analysis introduced by Brydges and Yau for the dipole gas partition function. Our method leads to systematic formulas for the large-distance behavior of correlation functions of all orders. We prove that in any dimensiond2, at any value>0 of the inverse temperature, and at sufficiently small activityz, the correlation functions exhibit at large distances the same behavior as for a vacuum (z=0), but with a new dielectric constant 1+ over which we have good control. The results proved here extend existing results on the two-point correlations to all higher correlations, and constitute a general confirmation of the fact that dipoles do not screen.     

Correlation functions of the one-dimensional Bose gas in the repulsive case

The one dimensional Bose gas is considered in the repulsive case. The ground state of the system is the Dirac sea with a finite density. The correlation function of the currents is presented in the form of the series, then ^th term being the contribution ofn vacuum particles. In the strong coupling limitc then ^th term decreases asc ^–n . In the weak coupling limitc 0 the series is also essentially simplified. The decomposition gives the uniform approximation in the distance between the currents. The arguments in favour of convergence of the series are given.     

Critical indices for the charged Bose gas

A self-consistent version of the static random phase approximation leads to a quasi-particle energy satisfying ?(k)=Ak^v for small k, where v ≈ 1.8. The critical indices are those of an ideal Bose gas with this spectrum.     

A grand-canonical approach to the disordered Bose gas

We study the problem of disordered interacting bosons within grand-canonical thermodynamics and Bogoliubov theory. We compute the fractions of condensed and non-condensed particles and corrections to the compressibility and the speed of sound due to interaction and disorder. There are two small parameters, the disorder strength compared to the chemical potential and the dilute-gas parameter.     

Convolution identities for quasiprobabilities for Bose functions

We present identities relating the equations of motion of various quasiprobabilities for quantum oscillators. These identities turn out useful for checking the consistency of approximations made in constructing the equations of motion with the basic Bose commutator. Moreover, our identities allow to identify the quasiprobability distributions which have the easiest-to-solve equations of motion.     

A nonideal Bose gas at finite temperatures

The present paper, based on an obvious generalization of the formalism of Belyaev [1,5], supplements the work of Belyaev [2] for the case T 0. The temperature dependence of the quasiparticle excitation and damping spectrum, the ground state energy, and the thermodynamic quantities is determined to second order in the gas-density parameter using the constant amplitude approximation. In the limiting case of free particles, the results are obtained for an ideal gas with T < T₀, where T₀ is the condensation temperature of the ideal Bose gas.In conclusion I wish to thank B. T. Geilikman, under whose supervision this work was performed.     

A nonideal Bose gas at high temperatures

Thermodynamic Green's functions are used to examine the properties of a Bose gas whose particles repel one another, not necessarily weakly, for finite temperatures T > T₀, in which T₀ is the phase-transition point and T/n^2/3 1. The excitation spectrum is deduced, together with the temperature dependence of the renormalized chemical potential and mass of the excitations.     

Relaxation of the ideal Bose gas

For the ideal Bose gas we study the approach to equilibrium. Above the critical temperature we prove exponential behaviour, with a relaxation time of the order (T-T _c)^-2 around T _c. For T _c we find the t ^-1 law for the two-point function.     

Existence of Green's functions for dilute Bose gases

Some properties of finite volume Green's functions are obtained, and the infinite volume limit is shown to exist for the multi-time Green's functions of a dilute Bose gas, constructed with the operators of the quasi-local algebra (see Theorem IV.5).     

Scaling behaviour in the Bose gas

The scaling behaviour of fluctuations of the Bose field (f) in the ergodic infinite volume equilibrium states of ad-dimensional Bose gas at temperatureT and density , can be classified in terms of the testfunctionsf. In the low density regime, the space of testfunctions splits up in two subspaces, leading to two different types of non-commuting macroscopic field fluctuation observables. Testfunctionsf with Fourier transform yield normal fluctuation observables. The local fluctuations of the field operators (f) must be scaled subnormally (i.e. with a negative scaling index) if the testfunctionf has . The macroscopic fluctuations of these fields can then again be described by a Bose field. The situation changes when the density of the gas exceeds the critical density. The field operators which have normal fluctuations in the low density regime need to be scaled abnormally in the high density regime, yielding classical macroscopic fluctuation observables. Another difference with the low density regime is that the space of testfunctions with splits up in two subspaces when the critical density is reached: for a first subspace the algebraic character of the macroscopic field fluctuation observables in also classical because it is necessary to scale the fluctuations of the field operators normally, while for the remaining subclass, the same negative scaling index is required as in the low density regime and hence also the algebraic character of these macroscopic fluctuations is again CCR.     

Scaling in the ideal Bose gas

We have made a detailed study of scaling in the ideal Bose gas in order to resolve the apparent inconsistencies that occur in the scaling laws when the dimensionality of the system is greater than four. We have found that there are not one, but two critical exponents associated with the specific heat singularity that appear in the scaling laws. We have proposed a modification of the scaling laws which is correct in any dimension.     

The ground state of the Bose gas

The mathematical formalism describing the Bose gas at zero temperature is analysed with the aid of methods that have recently been successful in relativistic quantum field theory. First the spectrum conditions for an infinitely extended system are given and the algebra of observables and the algebra of field operators are defined. General properties of states over these algebras are discussed and theorems are given which connect the linked cluster property, translation invariance and the purity of the states. It is proved that pure states over the algebra of observables have the property of factorisable off-diagonal long range order. The class of quasi free states is defined and of these states those which are translation invariant and possess the linked cluster property are analysed. It is shown that this class of states contains a subclass of pure states of the Bogoliubov type and a subclass of states which are mixtures of non-translationally invariant pure states. The applications of these quasi free states to the interacting Bose gas are summarized.