Controlling integrability in a quasi-1D atom-dimer mixture

We analytically study the atom-dimer scattering problem in the near-integrable limit when the oscillator length l_0 of the transverse confinement is smaller than the dimer size, ~l_0^2/|a|, where a<0 is the interatomic scattering length. The leading contributions to the atom-diatom reflection and break-up probabilities are proportional to a^6 in the bosonic case and to a^8 for the up-(up-down) scattering in a two-component fermionic mixture. We show that by tuning a and l_0 one can control the "degree of integrability" in a quasi-1D atom-dimer mixture in an extremely wide range leaving thermodynamic quantities unchanged. We find that the relaxation to deeply bound states in the fermionic (bosonic) case is slower (faster) than transitions between different Bethe ansatz states. We propose a realistic experiment for detailed studies of the crossover from integrable to nonintegrable dynamics.Comment: 12 pages, 1 figur

Atom-dimer scattering and long-lived trimers in fermionic mixtures

We consider a heteronuclear fermionic mixture on the molecular side of an interspecies Feshbach resonance and discuss atom-dimer scattering properties in uniform space and in the presence of an external confining potential, restricting the system to a quasi-2D geometry. We find that there is a peculiar atom-dimer p-wave resonance which can be tuned by changing the frequency of the confinement. Our results have implications for the ongoing experiments on Lithium-Potassium mixtures, where this mechanism allows for switching the p-wave interaction between a K atom and Li-K dimer from attractive to repulsive, and forming a weakly bound trimer with unit angular momentum. We show that such trimers are long-lived and the atom-dimer resonance does not enhance inelastic relaxation in the mixture, making it an outstanding candidate for studies of p-wave resonance effects in a many-body system.Comment: 4 pages, 2 figures, published versio

Two atoms in an anisotropic harmonic trap

We consider the system of two interacting atoms confined in axially symmetric harmonic trap. Within the pseudopotential approximation, we solve the Schroedinger equation exactly, discussing the limits of quasi-one and quasi-two-dimensional geometries. Finally, we discuss the application of an energy-dependent pseudopotential, which allows to extend the validity of our results to the case of tight traps and large scattering lengths.Comment: RevTeX 4 pages, 2 figure

Feshbach resonances in a quasi-2D atomic gas

Strongly confining an ultracold atomic gas in one direction to create a quasi-2D system alters the scattering properties of this gas. We investigate the effects of confinement on Feshbach scattering resonances and show that strong confinement results in a shift in the position of the Feshbach resonance as a function of the magnetic field. This shift, as well as the change of the width of the resonance, are computed. We find that the resonance is strongly damped in the thermal gas, but in the condensate the resonance remains sharp due to many-body effects. We introduce a 2D model system, suited for the study of resonant superfluidity, and having the same scattering properties as the tightly confined real system near a Feshbach resonance. Exact relations are derived between measurable quantities and the model parameters.Comment: 8 pages, 2 figure

Worldsheet Matter Superfields on Half-Shell

In this paper we discuss some of the effects of using "unidexterous" worldsheet superfields, which satisfy worldsheet differential constraints and so are partly on-shell, i.e., on half-shell. Most notably, this results in a stratification of the field space that reminds of "brane-world" geometries. Linear dependence on such superfields provides a worldsheet generalization of the super-Zeeman effect. In turn, non-linear dependence yields additional left-right asymmetric dynamical constraints on the propagating fields, again in a stratified fashion.Comment: 15 pages, 2 figures; minor algebraic correction

The Schwarzschild black hole as a point particle

The description of a point mass in general relativity (GR) is given in the framework of the field formulation of GR where all the dynamical fields, including the gravitational field, are considered in a fixed background spacetime. With the use of stationary (not static) coordinates non-singular at the horizon, the Schwarzschild solution is presented as a point-like field configuration in a whole background Minkowski space. The requirement of a stable $\eta$-causality stated recently in [J.B.Pitts and W.C.Schieve, Found. Phys., v. 34, 211 (2004)] is used essentially as a criterion for testing configurations.Comment: LATEX, 8 pages, no figure