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Starting from the the Boltzmann equation, we study the center of mass oscillation of a harmonically trapped normal Fermi gas in the presence of a one-dimensional periodic potential. We show that for values of the the Fermi energy above the first Bloch band the center of mass motion is strongly damped in the collisional regime due to umklapp processes. This should be contrasted with the behaviour of a superfluid where one instead expects the occurrence of persistent Josephson-like oscillations., Comment: 11 pages, 3 figures, corrected typos

The elastic oscillations of the vortex lattice of a cold Bose gas (Tkachenko modes) are shown to play a crucial role in the saturation of the compressibility sum rule, as a consequence of the hybridization with the longitudinal degrees of freedom. The presence of the vortex lattice is responsible for a ${q}^{2}$ behavior of the static structure factor at small wave vectors $q$, which implies the absence of long range order in 2D configurations at zero temperature. Sum rules are used to calculate the Tkachenko frequency in the presence of harmonic trapping. Results are derived in the Thomas-Fermi regime and compared with experiments as well as with previous theoretical estimates.

Using a scattering length parametrization of the BCS-BEC crossover as well as the local density approximation for the density profile, we calculate the momentum distribution of a harmonically trapped atomic Fermi gas at zero temperature. Various interaction regimes are considered, including the BCS phase, the unitarity limit and the molecular regime. We show that the relevant parameter which characterizes the crossover is given by the dimensionless combination $N^{1/6}a/a_{ho}$, where $N$ is the number of atoms, $a$ is the scattering length and $a_{ho}$ is the oscillator length. The width of the momentum distribution is shown to depend in a crucial way on the value and sign of this parameter. Our predictions can be relevant for experiments on ultracold atomic Fermi gases near a Feshbach resonance., 6 pages, 2 figures. Submitted to Phys. Rev. A. Added references

It is shown that grey soliton dynamics in an one-dimensional trap can be treated as Landau dynamics of a quasi-particle. A soliton of arbitrary amplitude moves in the trapping potential without deformation of its density profile as a particle of mass $2m$. The dynamics in the local density approximation is shown to be consistent with the perturbation theory for dark solitons. Dynamics of a vortex ring in a trap is discussed qualitatively., Comment: REVTEX, 4 pages, submitted

We investigate theoretically and experimentally the center-of-mass motion of an ideal Fermi gas in a combined periodic and harmonic potential. We find a crossover from a conducting to an insulating regime as the Fermi energy moves from the first Bloch band into the bandgap of the lattice. The conducting regime is characterized by an oscillation of the cloud about the potential minimum, while in the insulating case the center of mass remains on one side of the potential., Comment: 4 pages, 4 figures

Quasi-one-dimensional two-component Fermi gases with effectively attractive and repulsive interactions are characterized for arbitrary interaction strength. The ground-state properties of the gas confined in highly elongated harmonic traps are determined within the local density approximation. For strong attractive effective interactions the existence of a molecular Tonks-Girardeau gas is predicted. The frequency of the lowest breathing mode is calculated as a function of the coupling strength for both attractive and repulsive interactions.

We study the effect of a one-dimensional periodic potential on the dynamic structure factor of an interacting Bose-Einstein condensate at zero temperature. We show that, due to phononic correlations, the excitation strength toward the first band develops a typical oscillating behavior as a function of the momentum transfer, and vanishes at even multiples of the Bragg momentum. The effects of interactions on the static structure factor are found to be significantly amplified by the presence of the optical potential. Our predictions can be tested in stimulated photon scattering experiments.

The quantum description of a Bose-Einstein condensates in double-well traps connected by a Josephson junction is discussed. The quantization in terms of the number and phase canonically-conjugated operators gives correct energy levels, but results in finite phase fluctuations in the absence of interaction. This seems to contradict the perfect coherence of a system of non-interacting particles. The problem can be solved by calculating the observables that characterize the coherence properties of a system, as, for example, the momentum distribution. It occurs that the visibility of interference fringes depends both on the fluctuations of the phase and the number of atoms. The visibility is calculated in the limit of small interaction and the results exhibit the correct behavior.

The hydrodynamic equations of superfluids for a weakly interacting Bose gas are generalized to include the effects of periodic optical potentials produced by stationary laser beams. The new equations are characterized by a renormalized interaction coupling constant and by an effective mass accounting for the inertia of the system along the laser direction. For large laser intensities the effective mass is directly related to the tunneling rate between two consecutive wells. The predictions for the frequencies of the collective modes of a condensate confined by a magnetic harmonic trap are discussed for both 1D and 2D optical lattices and compared with recent experimental data., Comment: 4 pages, 2 postscript figures

The quantum and thermal fluctuations of the phase are investigated in a cold Bose gas confined by a double well trap. The coherence of the system is discussed in terms of the visibility of interference fringes in both momentum and coordinate space. The visibility is calculated at zero as well as at finite temperature. The thermal fluctuations are shown to affect significantly the transition from the coherent to the incoherent regime even at very low temperatures. The coherence of an array of multiple condensates is also discussed., 4 pages, 2 postscript figures

We consider the criterion for Bose condensation for particles in a harmonic trap. For a fixed angular momentum, the lowest energy state for a cloud of bosons with attractive interactions is the ground state of the cloud with all the angular momentum in the center-of-mass motion, and the one-particle reduced density matrix generally does not have a single large eigenvalue, but a number of them, suggesting that the state is an example of a fragmented condensate (Wilkin, Gunn, and Smith, Phys. Rev. Lett. 80, 2265 (1998)). We show that a convenient way to describe correlations in the system is by defining an internal one-particle reduced density matrix, in which the center-of-mass motion is eliminated, and that this has a single eigenvalue equal to the number of particles for the problem considered here. Our considerations indicate that care is necessary in formulating a criterion for Bose-Einstein condensation., Comment: 2 pages, RevTex, Submitted to Phys. Rev. A

We propose an experiment, based on two consecutive Bragg pulses, to measure the momentum distribution of quasiparticle excitations in a trapped Bose gas at low temperature. With the first pulse one generates a bunch of excitations carrying momentum $q$, whose Doppler line is measured by the second pulse. We show that this experiment can provide direct access to the amplitudes $u_{q}$ and $v_{q}$ characterizing the Bogoliubov transformations from particles to quasiparticles. We simulate the behavior of the nonuniform gas by numerically solving the time dependent Gross-Pitaevskii equation., 12 pages, 4 figures included

We propose a method to reach conditions of high degeneracy in a trapped Fermi gas, based on the adiabatic transfer of atoms from a magnetic to a tighter optical trap. The transformation yields a large increase of the Fermi energy, without a significant change of the temperature. The large enhancement of the central density emphasizes the role of the interactions and makes the system much closer to the BCS transition. An estimate of the time needed to achieve the conditions of adiabaticity is also given., Comment: 4 pages, RevTex, 5 eps figures

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., 29 pages, 12 figures

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., revtex, 9 pages, 5 figures

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., 47 pages, RevTeX, figures are available on request, please write to giorgini@alpha.science.unitn.it

We investigate the dynamic behavior of a Bose-condensed gas of alkali atoms interacting with repulsive forces and confined in a magnetic trap at zero temperature. Using the Thomas-Fermi approximation, we rewrite the Gross-Pitaevskii equation in the form of the hydrodynamic equations of superfluids. We present solutions describing large amplitude oscillations of the atomic cloud as well as the expansion of the gas after switching off the trap. We compare our theoretical predictions with the recent experimental data obtained at Jila and MIT., 5 pages, REVTeX, 4 postscript figures, available also at http://anubis.science.unitn.it/~dalfovo/papers/papers.html

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 $2\omega _0$ 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., Comment: 10 pages, REVTEX, 2 figures (available upon request)

We study the scattering of atoms, rotons and phonons at the free surface of $^4$He at normal incidence and calculate the evaporation, condensation and reflection probabilities. Assuming elastic one-to-one processes and using general properties of the scattering matrix, such as unitarity and time reversal, we argue that all nonzero probabilities can be written in terms of a single energy-dependent parameter. Quantitative predictions are obtained using linearized time dependent density functional theory., Comment: 12 pages, REVTeX, 2 postscript figures, available also at http://anubis.science.unitn.it/~dalfovo/papers/papers.html

A detailed study of the dispersion law of surface excitations in liquid \hef at zero temperature is presented, with special emphasis to the short wave length region. The hybridization mechanism between surface and bulk modes is discussed on a general basis, investigating the scattering of slow rotons from the surface. An accurate density functional, accounting for backflow effects, is then used to determine the dispersion of both bulk and surface excitations. The numerical results are close to the experimental data obtained on thick films and explicitly reveal the occurrence of important hybridization effects between ripplons and rotons., Comment: 23 pages, REVTEX 3.0, 11 figures upon request, UTF-326/94

Rigorous relations of nonequilibrium statistical physics are discussed. An arbitrary system brought into a strongly nonequilibrium state by an external time-dependent impact is considered. Based on the Hamiltonian formalism of classical mechanics, the Bochkov–Kuzovlev equality, the Jarzynski equality, and Crooks reversal relations valid for fluctuations in the work done on a system are derived. Verification of these equalities in mechanical experiments with a torsion pendulum and biological objects (folded ribonucleic acids) is described.

A natural generalization of the Heisenberg uncertainty principle inequality holding for non hermitian operators is presented and applied to the fractional quantum Hall effect (FQHE). This inequality was used in a previous paper to prove the absence of long range order in the ground state of several 1D systems with continuous group symmetries. In this letter we use it to rule out the occurrence of Bose-Einstein condensation in the bosonic representation of the FQHE wave function proposed by Girvin and MacDonald. We show that the absence of off-diagonal long range order in this 2D problem is directly connected with the $q^2$ behavior of the static structure function $S(q)$ at small momenta., 10 pages, plain TeX, UTF-09-92

We present a microscopic description of edge excitations in the quantum Hall effect which is analogous to Feynman's theory of superfluids. Analytic expressions for the excitation energies are derived in finite dots. Our predictions are in excellent agreement with the results of a recent numerical diagonalization. In the large $N$ limit the dispersion law is proportional to $qlog{1\over q}$. For short range interactions the energy instead behaves as $q^3$. The same results are also derived using hydrodynamic theory of incompressible liquids., Comment: 10 pages, 2 figures upon request, UTF-311-11/93

A short popular review of theoretical and experimental results about properties of ultracold Fermi gases in vicinity of the Feshbach resonance is presented. The paper is based on the authors talk on the meeting of the Physical Department of the Russian Academy of Sciences dedicated to 100th anniversary of the birth of L. D. Landau (Moscow, January 22, 2008). A version of this article has been published in Physics - Uspekhi v. 51 p. 603 (2008).

Arguments are advanced to show that bubbles with a charge e/2 cannot exist in liquid helium.

The properties of Bose–Einstein condensates in an external potential produced by a laser light field are discussed. Considered are the condensates embedded in periodic lattices produced by standing laser waves and the condensates confined within 'optical traps' near the focus of a traveling wave. Observations of the Mott transition in a periodic lattice are described, as are experiments on atoms near the Feshbach resonance and experiments on the condensates in a double potential well, which permit investigating the tunnel dynamics of condensate phases.

We study the properties of magnetically trapped atomic Bose gases with both negative and positive scattering lengths. We present theoretical results for the temperature dependence of the condensate fraction and for other quantities characterizing the thermodynamics of the trapped gas. We investigate the structure of the elementary excitations, including quantized vortices. We explore the behavior of the condensate wave function near the boundary with possible application to Josephson-type effects.

We discuss general properties of the scattering matrix for quantum evaporation from liquid helium. We consider the scattering of atoms, rotons and phonons at the surface of the superfluid atT=0 and the corresponding probabilities of reflection, evaporation and condensation. We show that nontrivial and useful results can be derived from unitarity and time reversal symmetry of the scattering matrix in the case of one-to-one processes.

We discuss various properties of the ground state of a Bose-condensed dilute gas confined by an external potential. We devote particular attention to the role played by the interaction in determining the kinetic energy of the system and the aspect ratio of the velocity distribution. The structure of the wave function near the classical turning point is discussed and the drawback of the Thomas-Fermi approximation is explicitly pointed out. We consider also states with quantized vorticity and calculate the critical angular velocity for the production of vortices. The presence of vortex states is found to increases the stability of the condensate in the case of attractive interactions.