arXiv subjects

Luca Salasnich

Publications and source records attributed to Luca Salasnich.

At least 163 records · Page 9Linked to original sources

arXiv2002

Critical Temperature of an Interacting Bose Gas in a Generic Power-Law Potential

We investigate the critical temperature of an interacting Bose gas confined in a trap described by a generic isotropic power-law potential. We compare the results with respect to the non-interacting case. In particular, we derive an analytical formula for the shift of the critical temperature holding to first order in the scattering length. We show that this shift scales as $N^{n\over 3(n+2)}$, where $N$ is the number of Bosons and $n$ is the exponent of the power-law potential. Moreover, the sign of the shift critically depends on the power-law exponent $n$. Finally, we find that the shift of the critical temperature due to finite-size effects vanishes as $N^{-{2n\over 3(n+2)}}$.

cond-mat.stat-mech↗

arXiv2001

Multi-parameter generalization of nonextensive statistical mechanics

We show that the stochastic interpretation of Tsallis' thermostatistics given recently by Beck [Phys. Rev. Lett {\bf 87}, 180601 (2001)] leads naturally to a multi-parameter generalization. The resulting class of distributions is able to fit experimental results which cannot be reproduced within the Boltzmann's or Tsallis' formalism.

physics.class-ph↗

arXiv2001

Pulsed Quantum Tunneling with Matter Waves

In this report we investigate the macroscopic quantum tunneling of a Bose condensate falling under gravity and scattering on a Gaussian barrier that could model a mirror of far-detuned sheet of light. We analyze the effect of the inter-atomic interaction and that of a transverse confining potential. We show that the quantum tunneling can be quasi-periodic and in this way one could generate coherent Bose condensed atomic pulses. In the second part of the report, we discuss an effective 1D time-dependent non-polynomial nonlinear Schrodinger equation (NPSE), which describes cigar-shaped condensates. NPSE is obtained from the 3D Gross-Pitaevskii equation by using a variational approach. We find that NPSE gives much more accurate results than all other effective 1D equations recently proposed.

cond-mat.soft↗

arXiv2001

BEC in Nonextensive Statistical Mechanics: Some Additional Results

In a recent paper [Int. J. Mod. Phys. B {\bf 14}, 405 (2000)] we discussed the Bose-Einstein condensation (BEC) in the framework of Tsallis's nonextensive statistical mechanics. In particular, we studied an ideal gas of bosons in a confining harmonic potential. In this memoir we generalize our previous analysis by investigating an ideal Bose gas in a generic power-law external potential. We derive analytical formulas for the energy of the system, the BEC transition temperature and the condensed fraction.

cond-mat.stat-mech↗

arXiv2001

Bose-Einstein Condensation in Exotic Trapping Potentials

We discuss thermal and dynamical properties of Bose condensates confined by an external potential. First we analyze the Bose-Einstein transition temperature for an ideal Bose gas in a generic power-law potential and d-dimensional space. Then we investigate the effect of the shape of the trapping potential on the properties of a weakly-interacting Bose condensate. We show that using exotic trapping potentials the condensate can exhibit interesting coherent quantum phenomena, like superfluidity and tunneling. In particular, we consider toroidal and double-well potentials. The theoretical results are compared with recent experiments.

cond-mat.stat-mech↗

arXiv2000

Degenerate Quantum Gases and Bose-Einstein Condensation

After a brief historical introduction to Bose-Einstein condensation and Fermi degeneracy, we discuss theoretical results we have recentely obtained for trapped degenerate quantum gases by means of a thermal field theory approach. In particular, by using Gross-Pitaevskii and Bogoliubov-Popov equations, we consider thermodynamical properties of two Bosonic systems: a gas of Lithium atoms and a gas of Hydrogen atoms. Finally, we investigate finite-temperature density profiles of a dilute Fermi gas of Potassium atoms confined in a harmonic potential.

cond-mat.stat-mech↗

arXiv2000

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 ${D/2}+{D/n}>1$, where $D$ is the space dimension and $n$ is the power-law exponent.

math-ph↗

arXiv2000

WKB corrections to the energy splitting in double well potentials

By using the WKB quantization we deduce an analytical formula for the energy splitting in a double--well potential which is the usual Landau formula with additional quantum corrections. Then we analyze the accuracy of our formula for the double square well potential, the inverted harmonic oscillator and the quartic potential.

nlin.CD↗

arXiv2000

High order WKB prediction of the energy splitting in the symmetric double well potential

The accuracy of the WKB approximation when predicting the energy splitting of bound states in a double well potential is the main subject of this paper. The splitting of almost degenerate energy levels below the top of the barrier results from the tunneling and is thus supposed to be exponentially small. By using the standard WKB quantization we deduce an analytical formula for the energy splitting, which is the usual Landau formula with additional quantum corrections. We also examine the accuracy of our and Landau formula numerically for the case of the symmetric double well quartic potential.

nlin.CD↗

arXiv2000

Resonances and Chaos in the Collective Oscillations of a Trapped Bose Condensate

We investigate the collective oscillations of a Bose condensate in an anisotropic harmonic trap. We analytically calculate the values of the trap deformation for which the normal modes are in resonance. In presence of low-order resonances, the amplitude dependence of frequencies is strongly enhanced. We also study the transition to chaos of the collective modes as a function of the trap anisotropy.

cond-mat.stat-mech↗

arXiv1999

BEC in Nonextensive Statistical Mechanics

We discuss the Bose-Einstein condensation (BEC) for an ideal gas of bosons in the framework of Tsallis's nonextensive statistical mechanics. We study the corrections to the standard BEC formulas due to a weak nonextensivity of the system. In particular, we consider three cases in the D-dimensional space: the homogeneous gas, the gas in a harmonic trap and the relativistic homogenous gas. The results show that small deviations from the extensive Bose statistics produce remarkably large changes in the BEC transition temperature.

cond-mat.stat-mech↗

arXiv1999

Self-Trapping, Quantum Tunneling and Decay Rates for a Bose Gas with Attractive Nonlocal Interaction

We study the Bose-Einstein condensation for a cloud of $^7$Li atoms with attractive nonlocal (finite-range) interaction in a harmonic trap. In addition to the low-density metastable branch, that is present also in the case of local interaction, a new stable branch appears at higher densities. For a large number of atoms, the size of the cloud in the stable high-density branch is independent of the trap size and the atoms are in a macroscopic quantum self-trapped configuration. We analyze the macroscopic quantum tunneling between the low-density metastable branch and the high-density one by using the istanton technique. Moreover we consider the decay rate of the Bose condensate due to inelastic two- and three-body collisions.

cond-mat.stat-mech↗

arXiv1999

Time-Dependent Variational Approach to Bose-Einstein Condensation

We discuss the mean-field approximation for a trapped weakly-interacting Bose-Einstein condensate (BEC) and its connection with the exact many-body problem by deriving the Gross-Pitaevskii action of the condensate. The mechanics of the BEC in a harmonic potential is studied by using a variational approach with time-dependent Gaussian trial wave-functions. In particular, we analyze the static configurations, the stability and the collective oscillations for both ground-state and vortices.

cond-mat.stat-mech↗

arXiv1999

Chaotic Oscillations in Finite Quantum Systems: Trapped Bose-Einstein Condensates

We discuss the recently achieved Bose-Einstein condensation for alkali-metal atoms in magnetic traps. The theoretically predicted low-energy collective oscillations of the condensate have been experimentally confirmed by laser imaging techniques. We show by using Poincarè sections that at higher energies non-linear effects appear and oscillations become chaotic. PACS 03.75.Fi, 05.30.Jp, 05.45.+b, 32.80.Pj

chao-dyn↗

arXiv1999

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.

math-ph↗

arXiv1998

A CTMC study of collisions between protons and $H_2^+$ molecular ions

We study numerically collisions between protons and $H_2^+$ molecular ions at intermediate impact energies by using the Classical Trajectory Monte Carlo method (CTMC). Total and differential cross sections are computed. The results are compared with: a) the standard one electron--two nucleon scattering, and b) the quantum mechanical treatment of the $ H^{+} - H^{+}_{2} $ scattering.

physics.atom-ph↗

arXiv1998

Statistical Mechanics of a Trapped Bose-Einstein Condensate

Bose-Einstein condensation (BEC) in a gas has now been achieved. Alkali atoms ($^{87}Rb$, $^{23}Na$ and $^{7}Li$) have been cooled to the point of condensation (temperature of 100 nK) using laser cooling and trapping, followed by magnetic trapping and evaporative cooling. This important experimental result has also renewed the interest on theoretical studies of BEC. In this contribution we discuss the statistical mechanics of the trapped BEC at zero temperature. In particular, we study the stability of the condensate by using a variational method with local and non-local interaction between the particles.

quant-ph↗

arXiv1998

Turbulence and Bifurcation in the Motion of an Hydrocyclone

The hydrocyclone is a tool used in different fields but mostly in mining industries to separate minerals. The minerals are put in a liquid or in a stable suspension of a chosen density which must be less than the density of the heavier minerals and greater than that of the lighter minerals. Because of the effect of the walls the flow in a hydrocyclone is the result of a movement of confined swirling (vortex) and recirculating flow, which are generated by the difference of the means. We study turbulence and bifurcation in the motion of the Hydrocyclone by using the Navier-Stokes for the conservation of the mass and of the momentum. These equations are numerically solved with the finite element method (FEM) and the $k-ε$ model. Our FEM results are in quite good agreement with the experimental data. Finally, we introduce a simple 3D family of maps which models very well the behaviour of the trajectories of the light and heavy particles in the Hydrocyclone.

chao-dyn↗