arXiv subjects

L. P. Pitaevskii

Publications and source records attributed to L. P. Pitaevskii.

46 records · Page 3Linked to original sources

arXiv1999

Dynamic structure factor and momentum distribution of a trapped Bose gas

The dynamic structure factor of a trapped Bose-Einstein condensed gas is investigated at zero temperature in the framework of Bogoliubov theory. Different values of momentum transfer are considered, ranging from the phonon to the single-particle regime. Various approximated schemes are discussed, including the local density approximation, where the system is locally described as a uniform gas, and the impulse approximation, where the response is fixed by the momentum distribution of the condensate. A comprehensive approach, based on the eikonal expansion, is presented. The predictions of theory are successfully compared with the results of recent two-photon Bragg scattering experiments, both at low and high momentum transfer. Relevant features of the dynamic structure factor are also discussed using the formalism of sum rules and the concept of scaling. Particular emphasis is given to the regime of high momentum transfer, where the dynamic structure factor is sensitive to the behaviour of the order parameter in momentum space, and some instructive examples showing the consequence of long-range coherence are presented.

cond-mat↗

arXiv1999

Temperature-induced resonances and Landau damping of collective modes in Bose-Einstein condensed gases in spherical traps

Interaction between collective monopole oscillations of a trapped Bose-Einstein condensate and thermal excitations is investigated by means of perturbation theory. We assume spherical symmetry to calculate the matrix elements by solving the linearized Gross-Pitaevskii equations. We use them to study the resonances of the condensate induced by temperature when an external perturbation of the trapping frequency is applied and to calculate the Landau damping of the oscillations.

cond-mat↗

arXiv1998

Theory of Bose-Einstein condensation in trapped gases

The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.

cond-mat↗

arXiv1997

Anomalous fluctuations of the condensate in interacting Bose gases

We find that the fluctuations of the condensate in a weakly interacting Bose gas confined in a box of volume $V$ follow the law $<δN_0^2>\sim V^{4/3}$. This anomalous behaviour arises from the occurrence of infrared divergencies due to phonon excitations and holds also for strongly correlated Bose superfluids. The analysis is extended to an interacting Bose gas confined in a harmonic trap where the fluctuations are found to exhibit a similar anomaly.

cond-mat↗

arXiv1997

Frequency shift and mode coupling in the nonlinear dynamics of a Bose condensed gas

We investigate the behavior of large amplitude oscillations of a trapped Bose-condensed gas of alkali atoms at zero temperature, by solving the equations of hydrodynamics for collective modes. Due to the atom-atom interaction, the equations of motion are nonlinear and give rise to significant frequency shift and mode coupling. We provide analytic expressions for the frequency shift, pointing out the crucial role played by the anisotropy of the confining potential. For special values of the anisotropy parameter the mode coupling is particularly strong and the frequency shift becomes large, revealing a peculiar behavior of the Bose-condensed gas. Consequences on the theory of collapse and revival of collective excitations are also discussed.

cond-mat↗

arXiv1997

Landau damping in dilute Bose gases

Landau damping in weakly interacting Bose gases is investigated by means of perturbation theory. Our approach points out the crucial role played by Bose-Einstein condensation and yields an explicit expression for the decay rate of elementary excitations in both uniform and non uniform gases. Systematic results are derived for the phonon width in homogeneous gases interacting with repulsive forces. Special attention is given to the low and high temperature regimes.

cond-mat↗

arXiv1997

Thermodynamics of a trapped Bose-condensed gas

We investigate the thermodynamic behaviour of a Bose gas interacting with repulsive forces and confined in a harmonic anisotropic trap. We develop the formalism of mean field theory for non uniform systems at finite temperature, based on the generalization of Bogoliubov theory for uniform gases. By employing the WKB semiclassical approximation for the excited states we derive systematic results for the temperature dependence of various thermodynamic quantities: condensate fraction, density profiles, thermal energy, specific heat and moment of inertia. Our analysis points out important differences with respect to the thermodynamic behaviour of uniform Bose gases. This is mainly the consequence of a major role played by single particle states at the boundary of the condensate. We find that the thermal depletion of the condensate is strongly enhanced by the presence of repulsive interactions and that the critical temperature is decreased with respect to the predictions of the non-interacting model. Our work points out an important scaling behaviour exhinited by the system in large $N$ limit. Scaling permits to express all the relevant thermodynamic quantities in terms of only two parameters: the reduced temperature $t=T/T_c^0$ and the ratio between the $T=0$ value of the chemical potential and the critical temperature $T_c^0$ for Bose-Einstein condensation. Comparisons with first experimental results and ab-initio calculations are presented.

cond-mat↗

arXiv1997

Phenomenological Theory of Mode Collapse-revival in Confined Bose Gas

A phenomenological theory of mode collapse-revival for a system with a weak nonlinearity is presented. The theory takes into account fluctuations of the number n of quanta of oscillations. The collapse time $τ_c ^{-1}$ for a mode of frequency $ω_0$ turns out to be $ω_0(\sqrt{n/2}\hbar ω_0 \mid ν\mid)$, where νis a coefficient in a nonlinear correction to the mode frequency with respect to the oscillation energy E. For a Bose gas in a harmonic trap $τ_c$ is order of $ω_0^{-1}\sqrt{μN/E\hbar ω_0}$. This value is order of 250 ms. for typical experimental conditions. The coefficient νis calculated for the breathing mode in an isotropic trap.

cond-mat↗

arXiv1996

Breathing Modes and Hidden Symmetry of Trapped Atoms in 2D

Atoms confined in a harmonic potential show universal oscillations in 2D. We point out the connection of these ''breathing'' modes to the presence of a hidden symmetry. The underlying symmetry SO(2,1), i.e. the two dimensional Lorentz group, allows pulsating solutions to be constructed for the interacting quantum system and for the corresponding nonlinear Gross-Pitaevskii equation. We point out how this symmetry can be used as a probe for recently proposed experiments of trapped atoms in 2D.

cond-mat↗

arXiv1996

Dynamics of Collapse of a Confined Bose Gas

Rigorous results on the nonlinear dynamics of a dilute Bose gas with a negative scattering length in an harmonic magnetic trap are presented and sufficient conditions for the collapse of the system are formulated. By using the virial theorem for the Gross-Pitaevskii equations in an external field we analyze the temporal evolution of the mean square radius of the gas cloud. In the 2D case the quantity undergoes harmonic oscillation with frequency $2ω_0$ It implies that for a negative value of energy of the system, the gas cloud will collapse after a finite time interval. For positive energy the cloud collapses if the initial conditions correspond to a large enough amplitude of oscillations. Stable oscillations with a small amplitude are possible. In the 3D case the system also collapsed after a finite time for a state with negative energy. A stringent condition for the collapse is also derived.

cond-mat↗