601 research outputs found
Ideal Quantum Gases in D-dimensional Space and Power-law Potentials
We investigate ideal quantum gases in D-dimensional space and confined in a
generic external potential by using the semiclassical approximation. In
particular, we derive density of states, density profiles and critical
temperatures for Fermions and Bosons trapped in isotropic power-law potentials.
Form such results, one can easily obtain those of quantum gases in a rigid box
and in a harmonic trap. Finally, we show that the Bose-Einstein condensation
can set up in a confining power-law potential if and only if ,
where is the space dimension and is the power-law exponent.Comment: 18 pages, Latex, to be published in Journal of Mathematical Physic
Instability and Chaos in Spatially Homogeneous Field Theories
Spatially homogeneous field theories are studied in the framework of
dynamical system theory. In particular we consider a model of inflationary
cosmology and a Yang-Mills-Higgs system. We discuss also the role of quantum
chaos and its application to field theories.Comment: 28 pages, 4 figures, to be published in J. Math. Phy
Dynamics of a BEC bright soliton in an expulsive potential
We theoretically investigate the dynamics of a matter-wave soliton created in
a harmonic potential, which is attractive in the transverse direction but
expulsive in the longitudinal direction. This Bose-Einstein-condensate (BEC)
bright soliton made of Li atoms has been observed in a recent experiment
(Science {\bf 296}, 1290 (2002)). We show that the non-polynomial Schr\"odinger
equation, an effective one-dimensional equation we derived from the
three-dimensional Gross-Pitaevskii equation, is able to reproduce the main
experimental features of this BEC soliton in an expulsive potential.Comment: 5 pages, 4 figures (2 of them with colors
Reliable equation of state for composite bosons in the 2D BCS-BEC crossover
We briefly discuss recent experiments on the BCS-BEC crossover with ultracold
alkali-metal atoms both in three-dimensional configurations and two-dimensional
ones. Then we analyze the quantum-field-theory formalism used to describe an
attractive -dimensional Fermi gas taking into account Gaussian fluctuations.
Finally, we apply this formalism to obtain a reliable equation of state of the
2D system at low temperaratures in the BEC regime of the crossover by
performing a meaningful dimensional regularization of the divergent zero-point
energy of collective bosonic excitations.Comment: 4 pages, 2 figures, presented to the Conference SUPERSTRIPES 2015,
June 13-18, 2015 (Ischia, Italy), Proceedings to be published in the Journal
of Superconductivity and Novel Magnetis
Goldstone and Higgs Hydrodynamics in the BCS-BEC Crossover
We discuss the derivation of a low-energy effective field theory of phase
(Goldstone) and amplitude (Higgs) modes of the pairing field from a microscopic
theory of attractive fermions. The coupled equations for Goldstone and Higgs
fields are critically analyzed in the Bardeen-Cooper-Schrieffer (BCS) to
Bose-Einstein condensate (BEC) crossover both in three spatial dimensions and
in two spatial dimensions. The crucial role of pair fluctuations is
investigated, and the beyond-mean-field Gaussian theory of the BCS-BEC
crossover is compared with available experimental data of the two-dimensional
ultracold Fermi superfluid.Comment: 13 pages, 3 figures, to be published in the Special Issue "Control
and Enhancement of Quantum Coherence in Nanostructured Materials" (Eds. A.
Perali and A. Ricci) of the open-access journal Condensed Matte
Self-consistent derivation of the modified Gross-Pitaevskii equation with Lee-Huang-Yang correction
We consider a dilute and ultracold bosonic gas of weakly-interacting atoms.
Within the framework of quantum field theory we derive a zero-temperature
modified Gross-Pitaevskii equation with beyond-mean-field corrections due to
quantum depletion and anomalous density. This result is obtained from the
stationary equation of the Bose-Einstein order parameter coupled to the
Bogoliubov-de Gennes equations of the out-of-condensate field operator. We show
that, in the presence of a generic external trapping potential, the key steps
to get the modified Gross-Pitaevskii equation are the semiclassical
approximation for the Bogoliubov-de Gennes equations, a slowly-varying order
parameter, and a small quantum depletion. In the uniform case, from the
modified Gross-Pitaevskii equation we get the familiar equation of state with
Lee-Huang-Yang correction.Comment: 7 pages, invited contribution for the special issue "Optical
Properties of Confined Quantum Systems" of the journal Applied Sciences,
included the effect of anomalous densit
Non-Universal Equation of State of the Two-Dimensional Bose Gas
For a dilute two-dimensional Bose gas the universal equation of state has a
logarithmic dependence on the s-wave scattering length. Here we derive
non-universal corrections to this equation of state taking account finite-range
effects of the inter-atomic potential. Our beyond-mean-field analytical results
are obtained performing dimensional regularization of divergent zero-point
quantum fluctuations within the finite-temperature formalism of functional
integration. In particular, we find that in the grand canonical ensemble the
pressure has a nonpolynomial dependence on the finite- range parameter and it
is a highly nontrivial function of chemical potential and temperature.Comment: 5 pages, to be published in Phys. Rev. Let
Bright solitons in ultracold atoms
We review old and recent experimental and theoretical results on bright
solitons in Bose-Einstein condensates made of alkali-metal atoms and under
external optical confinement. First we deduce the three-dimensional
Gross-Pitaevskii equation (3D GPE) from the Dirac-Frenkel action of interacting
identical bosons within a time-dependent Hartree approximation. Then we discuss
the dimensional reduction of the GPE from 3D to 1D, deriving the 1D GPE and
also the 1D nonpolynomial Schr\"odinger equation (1D NPSE). Finally, we analyze
the bright solition solutions of both 1D GPE and 1D NPSE and compare these
theoretical predictions with the available experimental data.Comment: 12 pages, 4 figures, tutorial talk at the VI International School and
Conference on Photonics "Photonica 2017", 28 August - 1 September 2017,
Belgrade, Serbia; new version: added one figure and some references,
corrected typo
Collapse of triaxial bright solitons in atomic Bose-Einstein condensates
We study triaxial bright solitons made of attractive Bose-condensed atoms
characterized by the absence of confinement in the longitudinal axial direction
but trapped by an anisotropic harmonic potential in the transverse plane. By
numerically solving the three-dimensional Gross-Pitaevskii equation we
investigate the effect of the transverse trap anisotropy on the critical
interaction strength above which there is the collapse of the condensate. The
comparison with previous predictions [Phys. Rev. A {\bf 66}, 043619 (2002)]
shows significant differences for large anisotropies.Comment: Accepted for the publication in Phys. Lett.
Matter-wave vortices in cigar-shaped and toroidal waveguides
We study vortical states in a Bose-Einstein condensate (BEC) filling a
cigar-shaped trap. An effective one-dimensional (1D) nonpolynomial Schroedinger
equation (NPSE) is derived in this setting, for the models with both repulsive
and attractive inter-atomic interactions. Analytical formulas for the density
profiles are obtained from the NPSE in the case of self-repulsion within the
Thomas-Fermi approximation, and in the case of the self-attraction as exact
solutions (bright solitons). A crucially important ingredient of the analysis
is the comparison of these predictions with direct numerical solutions for the
vortex states in the underlying 3D Gross-Pitaevskii equation (GPE). The
comparison demonstrates that the NPSE provides for a very accurate
approximation, in all the cases, including the prediction of the stability of
the bright solitons and collapse threshold for them. In addition to the
straight cigar-shaped trap, we also consider a torus-shaped configuration. In
that case, we find a threshold for the transition from the axially uniform
state, with the transverse intrinsic vorticity, to a symmetry-breaking pattern,
due to the instability in the self-attractive BEC filling the circular trap.Comment: 6 pages, Physical Review A, in pres
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