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L. Salasnich

Publications and source records attributed to L. Salasnich.

At least 109 records · Page 6Linked to original sources
arXiv2006

Dimensional Effects on Solitonic Matter and Optical Waves with Normal and Anomalous Dispersion

We investigate bright and dark solitons with anomalous or normal dispersion and under transverse harmonic confinement. In matter waves, positive atomic mass implies anomalous dispersion (kinetic spreading) while negative mass gives normal dispersion (kinetic shrinking). We find that, contrary to the strictly one-dimensional case, the axial and transverse profiles of these solitons crucially depend on the strength of the nonlinearity and on their dispersive properties. In particular, we show that, like bright solitons with anomalous dispersion, also dark solitons with normal dispersion disappear at a critical axial density. Our predictions are useful for the study of atomic matter waves in Bose-Einstein condensates and also for optical bullets in inhomogeneous Kerr media.

cond-mat.other↗
arXiv2005

Quantum Phases of Attractive Matter Waves in a Toroidal Trap

Investigating the quantum phase transition in a ring from a uniform attractive Bose-Einstein condensate to a localized bright soliton we find that the soliton undergoes transverse collapse at a critical interaction strength, which depends on the ring dimensions. In addition, we predict the existence of other soliton configurations with many peaks, showing that they have a limited stability domain. Finally, we show that the phase diagram displays several new features when the toroidal trap is set in rotation.

cond-mat.other↗
arXiv2005

$1/f^α$ Noise in Spectral Fluctuations of Quantum Systems

The power law $1/f^α$ in the power spectrum characterizes the fluctuating observables of many complex natural systems. Considering the energy levels of a quantum system as a discrete time series where the energy plays the role of time, the level fluctuations can be characterized by the power spectrum. Using a family of quantum billiards, we analyze the order to chaos transition in terms of this power spectrum. A power law $1/f^α$ is found at all the transition stages, and it is shown that the exponent $α$ is related to the chaotic component of the classical phase space of the quantum system.

cond-mat.stat-mech↗
arXiv2004

Bulk and Collective Properties of a Dilute Fermi Gas in the BCS-BEC Crossover

We investigate the zero-temperature properties of a dilute two-component Fermi gas with attractive interspecies interaction in the BCS-BEC crossover. We build an efficient parametrization of the energy per particle based on Monte Carlo data and asymptotic behavior. This parametrization provides, in turn, analytical expressions for several bulk properties of the system such as the chemical potential, the pressure and the sound velocity. In addition, on the basis of a local polytropic equation of state, we determine the collective modes of the Fermi gas under harmonic confinement in the framework of the hydrodynamic theory. The calculated collective frequencies are compared to experimental data on confined vapors of $^6$Li atoms and with other theoretical predictions.

cond-mat.soft↗
arXiv2004

Transition from 3D to 1D in Bose Gases at Zero Temperature

We investigate the effects of dimensional reduction in Bose gases induced by a strong harmonic confinement in the transverse cylindric radial direction. By using a generalized Lieb-Liniger theory, based on a variational treatment of the transverse width of the Bose gas, we analyze the transition from a 3D Bose-Einstein condensate to the 1D Tonks-Girardeau gas. The sound velocity and the frequency of the lowest compressional mode give a clear signature of the regime involved. We study also the case of negative scattering length deriving the phase diagram of the Bose gas (uniform, single soliton, multi soliton and collapsed) in toroidal confinement.

cond-mat.stat-mech↗
arXiv2004

Dimensional Reduction in Bose-Condensed Alkali-Metal Vapors

We investigate the effects of dimensional reduction in atomic Bose-Einstein condensates (BECs) induced by a strong harmonic confinement in the cylindric radial direction or in the cylindric axial direction. The former case corresponds to a transition from 3D to 1D in cigar-shaped BECs, while the latter case corresponds to a transition from 3D to 2D in disc-shaped BECs. We analyze the first sound velocity in axially-homogeneous cigar-shaped BECs and in radially-homogeneous disc-shaped BECs. We consider also the dimensional reduction in a BEC confined by a harmonic potential both in the radial direction and in the axial direction. By using a variational approach, we calculate monopole and quadrupole collective oscillations of the BEC. We find that the frequencies of these collective oscillations are related to the dimensionality and to the repulsive or attractive inter-atomic interaction.

cond-mat.stat-mech↗
arXiv2003

Modulational Instability and Complex Dynamics of Confined Matter-Wave Solitons

We study the formation of bright solitons in a Bose-Einstein condensate of $^7$Li atoms induced by a sudden change in the sign of the scattering length from positive to negative, as reported in a recent experiment (Nature {\bf 417}, 150 (2002)). The numerical simulations are performed by using the 3D Gross-Pitaevskii equation (GPE) with a dissipative three-body term. We show that a number of bright solitons is produced and this can be interpreted in terms of the modulational instability of the time-dependent macroscopic wave function of the Bose condensate. In particular, we derive a simple formula for the number of solitons that is in good agreement with the numerical results of 3D GPE. By investigating the long time evolution of the soliton train solving the 1D GPE with three-body dissipation we find that adjacent solitons repel each other due to their phase difference. In addition, we find that during the motion of the soliton train in an axial harmonic potential the number of solitonic peaks changes in time and the density of individual peaks shows an intermittent behavior. Such a complex dynamics explains the ``missing solitons'' frequently found in the experiment.

cond-mat.stat-mech↗
arXiv2003

Spectral Statistics of the Triaxial Rigid Rotator: Semiclassical Origin of their Pathological Behavior

In this paper we investigate the local and global spectral properties of the triaxial rigid rotator. We demonstrate that, for a fixed value of the total angular momentum, the energy spectrum can be divided into two sets of energy levels, whose classical analog are librational and rotational motions. By using diagonalization, semiclassical and algebric methods, we show that the energy levels follow the anomalous spectral statistics of the one-dimensional harmonic oscillator.

cond-mat.stat-mech↗
arXiv2002

Bose-condensed Bright Solitons under Transverse Confinement

We investigate the dynamics of Bose-condensed bright solitons made of alkali-metal atoms with negative scattering length and under harmonic confinement in the transverse direction. Contrary to the 1D case, the 3D bright soliton exists only below a critical attractive interaction which depends on the extent of confinement. Such a behavior is also found in multi-soliton condensates with box boundary conditions. We obtain numerical and analytical estimates of the critical strength beyond which the solitons do not exist. By using an effective 1D nonpolynomial nonlinear Schrödinger equation (NPSE), which accurately takes into account the transverse dynamics of cigar-like condensates, we numerically simulate the dynamics of the "soliton train" reported in a recent experiment (Nature {\bf 417} 150 (2002)). Then, analyzing the macroscopic quantum tunneling of the bright soliton on a Gaussian barrier we find that its interference in the tunneling region is strongly suppressed with respect to non-solitonic case; moreover, the tunneling through a barrier breaks the solitonic nature of the matter wave. Finally, we show that the collapse of the soliton is induced by the scattering on the barrier or by the collision with another matter wave when the density reaches a critical value, for which we derive an accurate analytical formula.

cond-mat.stat-mech↗
arXiv2002

Periodic Quantum Tunneling and Parametric Resonance with Cigar-Shaped Bose-Einstein Condensates

We study the tunneling properties of a cigar-shaped Bose-Einstein condensate by using an effective 1D nonpolynomial nonlinear Schrödinger equation (NPSE). First we investigate a mechanism to generate periodic pulses of coherent matter by means of a Bose condensate confined in a potential well with an oscillating height of the energy barrier. We show that is possible to control the periodic emission of matter waves and the tunneling fraction of the Bose condensate. We find that the number of emitted particles strongly increases if the period of oscillation of the height of the energy barrier is in parametric resonance with the period of oscillation of the center of mass of the condensate inside the potential well. Then we use NPSE to analyze the periodic tunneling of a Bose-Einstein condensate in a double-well potential which has an oscillating energy barrier. We show that the dynamics of the Bose condensate critically depends on the frequency of the oscillating energy barrier. The macroscopic quantum self-trapping (MQST) of the condensate can be suppressed under the condition of parametric resonance between the frequency of the energy barrier and the frequency of oscillation through the barrier of the very small fraction of particles which remain untrapped during MQST.

cond-mat.stat-mech↗
arXiv2002

Effective wave-equations for the dynamics of cigar-shaped and disc-shaped Bose condensates

Starting from the 3D Gross-Pitaevskii equation and using a variational approach, we derive an effective 1D wave-equation that describes the axial dynamics of a Bose condensate confined in an external potential with cylindrical symmetry. The trapping potential is harmonic in the transverse direction and generic in the axial one. Our equation, that is a time-dependent non-polynomial nonlinear Schrödinger equation (1D NPSE), can be used to model cigar-shaped condensates, whose dynamics is essentially 1D. We show that 1D NPSE gives much more accurate results than all other effective equations recently proposed. By using 1D NPSE we find analytical solutions for bright and dark solitons, which generalize the ones known in the literature. We deduce also an effective 2D non-polynomial Schrödinger equation (2D NPSE) that models disc-shaped Bose condensates confined in an external trap that is harmonic along the axial direction and generic in the transverse direction. In the limiting cases of weak and strong interaction, our approach gives rise to Schrödinger-like equations with different polynomial nonlinearities.

cond-mat.soft↗
arXiv2001

Pathological Behavior in the Spectral Statistics of the Asymmetric Rotor Model

The aim of this work is to study the spectral statistics of the asymmetric rotor model (triaxial rigid rotator). The asymmetric top is classically integrable and, according to the Berry-Tabor theory, its spectral statistics should be Poissonian. Surprisingly, our numerical results show that the nearest neighbor spacing distribution $P(s)$ and the spectral rigidity $Δ_3(L)$ do not follow Poisson statistics. In particular, $P(s)$ shows a sharp peak at $s=1$ while $Δ_3(L)$ for small values of $L$ follows the Poissonian predictions and asymptotically it shows large fluctuations around its mean value. Finally, we analyze the information entropy, which shows a dissolution of quantum numbers by breaking the axial symmetry of the rigid rotator.

cond-mat.stat-mech↗
arXiv2001

Anomalous Spectral Statistics of the Asymmetric Rotor Model

We investigate the spectral statistics of the asymmetric rotor model (triaxial rigid rotator). The asymmetric top is classically integrable and, according to the Berry-Tabor theory, its spectral statistics should be Poissonian. Surprisingly, our numerical results show that the nearest neighbor spacing distribution $P(s)$ and the spectral rigidity $Δ_3(L)$ do not follow Poisson statistics.

nucl-th↗
arXiv2001

Pulsed Macroscopic Quantum Tunneling of Falling Bose Condensates

We investigate macroscopic quantum tunneling of a Bose condensate and how it is affected by the interatomic interaction. We study the dynamics of a condensate falling under gravity and scattering on a Gaussian potential barrier that models a mirror formed by a far-detuned sheet of light. We observe bouncing, interference and quantum tunneling of the condensate. We find that the tunneling rate is very sensitive to the interatomic interaction and to the shape of the condensate. Under many conditions the tunneling rate is strongly enhanced by the interaction as achieved, for instance, by increasing the number of condensed particles. In a quasi 1D situation the tunneling pulse displays two peaks. The quantum tunneling can be quasi-periodic and in this way one could generate coherent Bose condensed atomic pulses.

cond-mat.stat-mech↗
arXiv2000

Shell Effects and Phase Separation in a Trapped Multi-Component Fermi System

Shell effects in the coordinate space can be seen with degenerate Fermi vapors in non-uniform trapping potentials. In particular, below the Fermi temperature, the density profile of a Fermi gas in a confining harmonic potential is characterized by several local maxima. This effect is enhanced for "magic numbers" of particles and in quasi-1D (cigar-shaped) configurations. In the case of a multi-component Fermi vapor, the separation of Fermi components in different spatial shells (phase-separation) depends on temperature, number of particles and scattering length. We derive analytical formulas, based on bifurcation theory, for the critical density of Fermions and the critical chemical potential, which give rise to the phase-separation.

cond-mat.stat-mech↗
arXiv2000

Energy Level Quasi-Crossings: Accidental Degeneracies or Signature of Quantum Chaos?

In the field of quantum chaos, the study of energy levels plays an important role. The aim of this review paper is to critically discuss some of the main contributions regarding the connection between classical dynamics, semi-classical quantization and spectral statistics of energy levels. In particular, we analyze in detail degeneracies and quasi-crossings in the eigenvalues of quantum Hamiltonians which are classically non-integrable. Summary: 1. Introduction; 2. Quasi-Crossing and Chaos; 3. Molecular Spectroscopy; 4. Nuclear Models; 4.1 Zirnbauer-Verbaashot-Weidenmuller Model; 4.2 Lipkin-Meshow-Glick Model; 5. Particle Physics and Field Theory; 6. Conclusions.

cond-mat.mtrl-sci↗
arXiv2000

Thermodynamics of Multi-Component Fermi Vapors

We study the thermodynamical properties of Fermi vapors confined in a harmonic external potential. In the case of the ideal Fermi gas, we compare exact density profiles with their semiclassical approximation in the conditions of recent experiments. Then, we consider the phase-separation of a multi-component Fermi vapor. In particular, we analyze the phase-separation as a function of temperature, number of particles and scattering length. Finally, we discuss the effect of rotation on the stability and thermodynamics of the trapped vapors.

cond-mat.stat-mech↗