Related papers: Virial theorems for trapped cold atoms
We consider homogeneous abelian vector fields in an expanding universe. We find a mechanical analogy in which the system behaves as a particle moving in three dimensions under the action of a central potential. In the case of bounded and…
We consider N atoms trapped in an isotropic harmonic potential, with s-wave interactions of infinite scattering length. In the zero-range limit, we obtain several exact analytical results: mapping between the trapped problem and the…
In an earlier work we showed that the gravitational interaction could be reproduced as a retarded dispersion interaction (Casimir interaction) between particles composed of hypothetical particles having harmonic oscillator interactions.…
A continuum version of the virial theorem is derived for a radiating self-gravitating accretion disc around a compact object. The central object is point-like, but we can avoid the regularization of its gravitational potential. This is…
In this paper, we develop a large-$N$ field theory for a system of $N$ classical particles in one dimension at thermal equilibrium. The particles are confined by an arbitrary external potential, $V_\text{ex} (x)$, and repel each other via a…
We formulate the finite-temperature perturbation theory of interacting scalar fields under external rotation. Because of the translational non-invariance in the radial direction, Green's functions are described using the Fourier-Bessel…
We study charged particles in three dimensions interacting via a short-range potential in addition to the Coulomb potential. When the Bohr radius and the scattering length are much larger than the potential range, low-energy physics of the…
We construct the invisible quantum barrier which represents the phenomenon of quantum reflection using the available data. We use the Abel equation to invert the data. The resulting invisible quantum barrier is double-valued in both axes.…
Using the grand canonical ensemble and the virial theorem, we show that the Gibbs thermodynamic potential of the non-relativistic system of charged particles is uniquely defined by single-particle Green functions of electrons and nuclei.…
Cold atoms are traditionally trapped by the dipole force in periodically spaced potential wells induced by the standing laser field. We derive here a theory beyond the conventional dipole approximation which provides field/atom coupling…
The scaling property of the thermodynamic free energy ($\Phi$) of a system at global equilibrium has been examined using a real-time method known as the virial theorem. We demonstrate these scaling properties through a derived relation…
We consider the cold bosonic ensemble trapped by a helical interference pattern in the optical \textit{loop} scheme. This rotating helical potential is produced by the two slightly detuned counter propagating Laguerre-Gaussian laser beams…
We consider a model of quantum-mechanical particles interacting via point interactions of infinite scattering length. In the case of fermions we prove a Lieb-Thirring inequality for the energy, i.e., we show that the energy is bounded from…
In the relativistic uniform model for continuous medium the integral theorem of generalized virial is derived, in which generalized momenta are used as particles momenta. This allows us to find exact formulas for the radial component of the…
In the semi-classical limit, the quantum mechanics of a stationary beam of counter-streaming relativistic electrons and ions is described by a nonlinear system of finite-temperature Thomas-Fermi equations. In the high temperature / low…
The propagation invariance of Bessel beams as well as their transversal structure are used to perform a comparative analysis of their effect on cold atoms for four different configurations and combinations thereof. We show that, even at…
We construct the invisible quantum barrier which represents the phenomenon of quantum reflection using the available data. We use the Abel equation to invert the data. The resulting invisible quantum barrier is double-valued in both axes.…
In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic Newton equation with an external potential $V$, $V\in C^2$. Using known results,…
In this course we give a selfcontained introduction to the quantum field theory for trapped atomic gases, using functional methods throughout. We consider both equilibrium and nonequilibrium phenomena. In the equilibrium case, we first…
We have analytically explored the quantum phenomenon of particle scattering by harmonically trapped Bose and Fermi gases with the short ranged (Fermi-Huang $\delta^3_p$ [1]) interactions among the incident particle and the scatterers. We…