219 research outputs found

### Coupled-channel pseudo-potential description of the Feshbach resonance in two dimensions

We derive pseudo-potentials that describe the scattering between two
particles in two spatial dimensions for any partial wave m, whose scattering
strength is parameterized in terms of the m-dependent phase shift. Using our
m=0 pseudo-potential, we develop a coupled channel model with 2D zero-range
interactions, which describes the two-body physics across a Feshbach resonance.
Our model predicts the scattering length, the binding energy and the "closed
channel molecular fraction" of two particles; these observables can be measured
in experiments on ultracold quasi-2D atomic Bose and Fermi gases with
present-day technology.Comment: 4 pages, 3 figure

### Theory of spinor Fermi and Bose gases in tight atom waveguides

Divergence-free pseudopotentials for spatially even and odd-wave interactions
in spinor Fermi gases in tight atom waveguides are derived. The Fermi-Bose
mapping method is used to relate the effectively one-dimensional fermionic
many-body problem to that of a spinor Bose gas. Depending on the relative
magnitudes of the even and odd-wave interactions, the N-atom ground state may
have total spin S=0, S=N/2, and possibly also intermediate values, the case
S=N/2 applying near a p-wave Feshbach resonance, where the N-fermion ground
state is space-antisymmetric and spin-symmetric. In this case the fermionic
ground state maps to the spinless bosonic Lieb-Liniger gas. An external
magnetic field with a longitudinal gradient causes a Stern-Gerlach spatial
separation of the corresponding trapped Fermi gas with respect to various
values of $S_z$.Comment: 4+ pages, 1 figure, revtex4. Submitted to PRA. Minor corrections of
typos and notatio

### Geometry of quantum observables and thermodynamics of small systems

The concept of ergodicity---the convergence of the temporal averages of
observables to their ensemble averages---is the cornerstone of thermodynamics.
The transition from a predictable, integrable behavior to ergodicity is one of
the most difficult physical phenomena to treat; the celebrated KAM theorem is
the prime example. This Letter is founded on the observation that for many
classical and quantum observables, the sum of the ensemble variance of the
temporal average and the ensemble average of temporal variance remains constant
across the integrability-ergodicity transition.
We show that this property induces a particular geometry of quantum
observables---Frobenius (also known as Hilbert-Schmidt) one---that naturally
encodes all the phenomena associated with the emergence of ergodicity: the
Eigenstate Thermalization effect, the decrease in the inverse participation
ratio, and the disappearance of the integrals of motion. As an application, we
use this geometry to solve a known problem of optimization of the set of
conserved quantities---regardless of whether it comes from symmetries or from
finite-size effects---to be incorporated in an extended thermodynamical theory
of integrable, near-integrable, or mesoscopic systems

### Atom-Atom Scattering Under Cylindrical Harmonic Confinement: Numerical and Analytical Studies of the Confinement Induced Resonance

In a recent article [M. Olshanii, Phys. Rev. Lett. {\bf 81}, 938 (1998)], an
analytic solution of atom-atom scattering with a delta-function pseudopotential
interaction in the presence of transverse harmonic confinement yielded an
effective coupling constant that diverged at a `confinement induced resonance.'
In the present work, we report numerical results that corroborate this
resonance for more realistic model potentials. In addition, we extend the
previous theoretical discussion to include two-atom bound states in the
presence of transverse confinement, for which we also report numerical results
hereComment: New version with major revisions. We now provide a detailed physical
interpretation of the confinement-induced resonance in tight atomic
waveguide

### The dynamics of digits: Calculating pi with Galperin's billiards

In Galperin billiards, two balls colliding with a hard wall form an analog
calculator for the digits of the number $\pi$. This classical, one-dimensional
three-body system (counting the hard wall) calculates the digits of $\pi$ in a
base determined by the ratio of the masses of the two particles. This base can
be any integer, but it can also be an irrational number, or even the base can
be $\pi$ itself. This article reviews previous results for Galperin billiards
and then pushes these results farther. We provide a complete explicit solution
for the balls' positions and velocities as a function of the collision number
and time. We demonstrate that Galperin billiard can be mapped onto a
two-particle Calogero-type model. We identify a second dynamical invariant for
any mass ratio that provides integrability for the system, and for a sequence
of specific mass ratios we identify a third dynamical invariant that
establishes superintegrability. Integrability allows us to derive some new
exact results for trajectories, and we apply these solutions to analyze the
systematic errors that occur in calculating the digits of $\pi$ with Galperin
billiards, including curious cases with irrational number bases.Comment: 30 pages, 13 figure

### Three-dimensional Gross-Pitaevskii solitary waves in optical lattices: stabilization using the artificial quartic kinetic energy induced by lattice shaking

In this Letter, we show that a three-dimensional Bose-Einstein solitary wave
can become stable if the dispersion law is changed from quadratic to quartic.
We suggest a way to realize the quartic dispersion, using shaken optical
lattices. Estimates show that the resulting solitary waves can occupy as little
as $\sim 1/20$-th of the Brillouin zone in each of the three directions and
contain as many as $N = 10^{3}$ atoms, thus representing a \textit{fully
mobile} macroscopic three-dimensional object.Comment: 8 pages, 1 figure, accepted in Phys. Lett.

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