Related papers: The scattering length at positive temperature
We present an exact procedure that allows one to calculate the scattering lenth for any potential expressed as an algebraic sum of inverse powers of the interatomic distance. We apply it to (12, $s$) Lennard-Jones potentials, with different…
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…
We consider a dilute Bose gas in the thermodynamic limit and prove a lower bound on the free energy for low temperatures which is in agreement with the conjecture of Lee-Huang-Yang on the excitation spectrum of the system. Combining…
Scattering processes are a fundamental way of experimentally probing distributions and properties of systems in several areas of physics. Considering two-body scattering at low energies, when the de Broglie wavelength is larger than the…
The specific heat for an ideal Bose gas confined in semi-infinite multifilament cables is analyzed. We start with a Bose gas inside a semi-infinite tube of impenetrable walls and finite rectangular cross section. The internal filament…
The equation of state of dilute Bose gases, in which the energy only depends on the $s$-wave scattering length, is rather unknown beyond the universal limit. We have carried out a bunch of diffusion Monte Carlo calculations up to gas…
We prove an upper bound on the free energy of a two-dimensional homogeneous Bose gas in the thermodynamic limit. We show that for $a^2 \rho \ll 1$ and $\beta \rho \gtrsim 1$ the free energy per unit volume differs from the one of the…
We compute the critical temperature of Bose-Einstein condensation in dilute three-dimensional homogeneous Bose gases. Our method involves the models of spatial permutations and it should be exact to lowest order in the scattering length of…
We produce the discontinuity in the specific heat of a homogeneous, dilute, and weakly interacting Bose gas in a short-wavelength range with a simple statistical method. The magnitude of the discontinuity at the phase transition temperature…
We have previously studied properties of a one-dimensional potential with $N$ equally spaced identical barriers in a (fixed) finite interval for both finite and infinite $N$. It was observed that scattering and spectral properties depend…
The Lieb-Liniger equation of state accurately describes the zero-temperature universal properties of a dilute one-dimensional Bose gas in terms of the s-wave scattering length. For weakly-interacting bosons we derive non-universal…
Let $\alpha\in(0,2)$ and $X_t$ be a symmetric $\alpha$-stable process. We define the scattering length $\Gamma(v)$ of the positive potential $v$ and prove several of its basic properties. We use the scattering length to findestimates for…
We review recent advances in the theory of the three-dimensional dilute homogeneous Bose gas at zero and finite temperature. Effective field theory methods are used to formulate a systematic perturbative framework that can be used to…
The use of scattering length of particle-target interaction due to real- valued potential to study the bound states of the particle-target system is well known in nuclear and atomic physics. In view of the current interest in using…
We analyze the scattering problem of identical bosonic particles confined on a spherical surface. At low scattering energies and for a radius much larger than the healing length, we express the contact interaction strength in terms of the…
We review our version of the classical field approximation to the dynamics of a finite temperature Bose gas. In the case of a periodic box potential, we investigate the role of the high momentum cut-off, essential in the method. In…
We consider a homogeneous Bose gas in the Gross-Pitaevskii limit at temperatures that are comparable to the critical temperature for Bose-Einstein condensation in the ideal gas. Our main result is an upper bound for the grand canonical free…
We consider a two-dimensional Bose gas in the dilute regime where $\rho a^2$ is small. For temperatures below the Berezinskii-Kosterlitz-Thouless critical temperature, we derive an explicit upper bound for the free energy density using…
Bose-Einstein condensation in a Bose gas is studied analytically, in any positive dimensionality ($d>0$) for identical bosons with any energy-momentum positive-exponent ($s>0$) plus an energy gap $\Delta$ between the ground state energy…
We present a scheme of analytical calculations determining the critical temperature and the number of condensed atoms of ideal gas Bose-Einstein condensation in external potentials with 1D, 2D or 3D periodicity. In particular we show that…