23 research outputs found

### Dilute Bose gas in two dimensions: Density expansions and the Gross-Pitaevskii equation

A dilute two-dimensional (2D) Bose gas at zero temperature is studied by the
method developed earlier by the authors. Low density expansions are derived for
the chemical potential, ground state energy, kinetic and interaction energies.
The expansion parameter is found to be a dimensionless in-medium scattering
amplitude u obeying the equation 1/u+\ln u=-\ln(na^2\pi)-2\gamma, where na^2
and \gamma are the gas parameter and the Euler constant, respectively. It is
shown that the ground state energy is mostly kinetic in the low density limit;
this result does not depend on a specific form of the pairwise interaction
potential, contrary to 3D case. A new form of 2D Gross-Pitaevskii equation is
proposed within our scheme.Comment: 4 pages, REVTeX, no figure

### Effect of a columnar defect on the shape of slow-combustion fronts

We report experimental results for the behavior of slow-combustion fronts in
the presence of a columnar defect with excess or reduced driving, and compare
them with those of mean-field theory. We also compare them with simulation
results for an analogous problem of driven flow of particles with hard-core
repulsion (ASEP) and a single defect bond with a different hopping probability.
The difference in the shape of the front profiles for excess vs. reduced
driving in the defect, clearly demonstrates the existence of a KPZ-type of
nonlinear term in the effective evolution equation for the slow-combustion
fronts. We also find that slow-combustion fronts display a faceted form for
large enough excess driving, and that there is a corresponding increase then in
the average front speed. This increase in the average front speed disappears at
a non-zero excess driving in agreement with the simulated behavior of the ASEP
model.Comment: 7 pages, 7 figure

### Reunion of random walkers with a long range interaction: applications to polymers and quantum mechanics

We use renormalization group to calculate the reunion and survival exponents
of a set of random walkers interacting with a long range $1/r^2$ and a short
range interaction. These exponents are used to study the binding-unbinding
transition of polymers and the behavior of several quantum problems.Comment: Revtex 3.1, 9 pages (two-column format), 3 figures. Published version
(PRE 63, 051103 (2001)). Reference corrections incorporated (PRE 64, 059902
(2001) (E

### Weakly-Interacting Bosons in a Trap within Approximate Second Quantization Approach

The theory of Bogoliubov is generalized for the case of a weakly-interacting
Bose-gas in harmonic trap. A set of nonlinear matrix equations is obtained to
make the diagonalization of Hamiltonian possible. Its perturbative solution is
used for the calculation of the energy and the condensate fraction of the model
system to show the applicability of the method.Comment: 6 pages, two figures .Presented at the International Symposium on
Quantum Fluids and Solids QFS2006 (Kyoto, Japan

### Interference of a Tonks-Girardeau Gas on a Ring

We study the quantum dynamics of a one-dimensional gas of impenetrable bosons
on a ring, and investigate the interference that results when an initially
trapped gas localized on one side of the ring is released, split via an
optical-dipole grating, and recombined on the other side of the ring. Large
visibility interference fringes arise when the wavevector of the optical dipole
grating is larger than the effective Fermi wavevector of the initial gas.Comment: 7 pages, 3 figure

### Momentum flux density, kinetic energy density and their fluctuations for one-dimensional confined gases of non-interacting fermions

We present a Green's function method for the evaluation of the particle
density profile and of the higher moments of the one-body density matrix in a
mesoscopic system of N Fermi particles moving independently in a linear
potential. The usefulness of the method is illustrated by applications to a
Fermi gas confined in a harmonic potential well, for which we evaluate the
momentum flux and kinetic energy densities as well as their quantal mean-square
fluctuations. We also study some properties of the kinetic energy functional
E_{kin}[n(x)] in the same system. Whereas a local approximation to the kinetic
energy density yields a multi-valued function, an exact single-valued
relationship between the density derivative of E_{kin}[n(x)] and the particle
density n(x) is demonstrated and evaluated for various values of the number of
particles in the system.Comment: 10 pages, 5 figure

### WKB analysis for nonlinear Schr\"{o}dinger equations with potential

We justify the WKB analysis for the semiclassical nonlinear Schr\"{o}dinger
equation with a subquadratic potential. This concerns subcritical, critical,
and supercritical cases as far as the geometrical optics method is concerned.
In the supercritical case, this extends a previous result by E. Grenier; we
also have to restrict to nonlinearities which are defocusing and cubic at the
origin, but besides subquadratic potentials, we consider initial phases which
may be unbounded. For this, we construct solutions for some compressible Euler
equations with unbounded source term and unbounded initial velocity.Comment: 25 pages, 11pt, a4. Appendix withdrawn, due to some inconsistencie

### Finite temperature theory of the trapped two dimensional Bose gas

We present a Hartree-Fock-Bogoliubov (HFB) theoretical treatment of the
two-dimensional trapped Bose gas and indicate how semiclassical approximations
to this and other formalisms have lead to confusion. We numerically obtain
results for the fully quantum mechanical HFB theory within the Popov
approximation and show that the presence of the trap stabilizes the condensate
against long wavelength fluctuations. These results are used to show where
phase fluctuations lead to the formation of a quasicondensate.Comment: 4 pages, 3 figure

### Energy dependent scattering and the Gross-Pitaevskii Equation in two dimensional Bose-Einstein condensates

We consider many-body effects on particle scattering in one, two and three
dimensional Bose gases. We show that at zero temperature these effects can be
modelled by the simpler two-body T-matrix evaluated off the energy shell. This
is important in 1D and 2D because the two-body T-matrix vanishes at zero energy
and so mean-field effects on particle energies must be taken into account to
obtain a self-consistent treatment of low energy collisions. Using the
off-shell two-body T-matrix we obtain the energy and density dependence of the
effective interaction in 1D and 2D and the appropriate Gross-Pitaevskii
equations for these dimensions. We present numerical solutions of the
Gross-Pitaevskii equation for a 2D condensate of hard-sphere bosons in a trap.
We find that the interaction strength is much greater in 2D than for a 3D gas
with the same hard-sphere radius. The Thomas-Fermi regime is therefore
approached at lower condensate populations and the energy required to create
vortices is lowered compared to the 3D case.Comment: 22 pages, 6 figure

### Monotonicity of quantum ground state energies: Bosonic atoms and stars

The N-dependence of the non-relativistic bosonic ground state energy is
studied for quantum N-body systems with either Coulomb or Newton interactions.
The Coulomb systems are "bosonic atoms," with their nucleus fixed, and the
Newton systems are "bosonic stars". In either case there exists some third
order polynomial in N such that the ratio of the ground state energy to the
respective polynomial grows monotonically in N. Some applications of these new
monotonicity results are discussed