Damping Of Collective Modes Research Articles

Low-energy modes of spin-imbalanced Fermi gases in BCS phase

The low-energy modes of a spin-imbalanced superfluid Fermi gas in the Bardeen-Cooper-Schrieffer (BCS) side are studied. The gas is assumed to be sufficiently dilute so that the pairing of atoms can be considered effective only in s-wave between fermions of different internal state. The order parameter at equilibrium is determined by the mean-field approximation, while the properties of the collective modes are calculated within a Gaussian approximation for the fluctuations of the order parameter. In particular we investigate the effects of asymmetry between the populations of the two different components and of temperature on the frequency and damping of collective modes. It is found that the temperature does not much affect the frequency and the damping of the modes, whereas an increase of the imbalance shifts the frequency toward lower values and enhances the damping sensitively. Besides the Bogoliubov-Anderson phonons, we observe modes at zero frequency for finite values of the wave-number. These modes indicate that an instability develops driving the system toward two separate phases, normal and superfluid.

Determination of the interstitial electron density in liquid metals: Basic quantity to calculate the ion collective-mode velocity and related properties

Considering that various investigations identified a correlation between the interstitial electron density in crystalline metals and some ground-state properties, including the compressibility, we propose a procedure to estimate the interstitial electron density in liquid metals starting from the experimental static structure factor. From the calculated electron density, starting from the standard approximation, which describes a liquid metal as made up of a homogeneous classic ion plasma with Coulomb interaction and a homogeneous interacting electron gas, we determine the ion collective mode velocity. The so-derived collective mode velocity is compared to the experimental data and a coherent view in different metallic systems at the melting point is obtained. Some guess about the collective mode damping is also presented because of the connection to the local static fluctuations of the interstitial electron density.

Atom-dimer scattering amplitude for fermionic mixtures with different masses:s-wave andp-wave contributions

We study near a Feshbach resonance, as a function of the mass ratio, the fermion-dimer scattering amplitude in fermionic mixtures of two fermion species. When masses are equal the physical situation is known to be quite simple. We show that, when the mass ratio is increased, the situation becomes much more complex. For the s-wave contribution we obtain an analytical solution in the asymptotic limit of very large mass ratio. In this regime the s-wave scattering amplitude displays a large number of zeros, essentially linked to the known large value of the fermion-dimer scattering length in this regime. We find by an exact numerical calculation that a zero is still present for a mass ratio of 15. For the p-wave contribution we make our study below the mass ratio of 8.17, where a fermion-dimer bound state appears. We find that a strong p-wave resonance is present at low energy, due to a virtual bound state, in the fermion-dimer system, which is a forerunner of the real bound state. This resonance becomes prominent in the mass ratio range around the one corresponding to the $^{40}$K - $^6$Li mixtures, much studied experimentally. This resonance should affect a number of physical properties. These include the equation of state of unbalanced mixtures at very low temperature but also the equation of state of balanced mixtures at moderate or high temperature. The frequency and the damping of collective modes should also provide a convenient way to evidence this resonance. Finally it should be possible to modify the effective mass of one of the fermionic species by making use of an optical lattice. This would allow to study the strong dependence of the resonance as a function of the mass ratio of the two fermionic elements. In particular one could check if the virtual bound state is relevant for the instabilities of these mixtures.

Collective mode damping and viscosity in a 1D unitary Fermi gas

We calculate the damping of the Bogoliubov–Anderson mode in a one-dimensional (1D) two-component attractive Fermi gas for arbitrary coupling strength within a quantum hydrodynamic approach. Using the Bethe-ansatz solution of the 1D BCS-BEC crossover problem, we derive analytic results for the viscosity covering the full range from a Luther–Emery liquid of weakly bound pairs to a Lieb–Liniger gas of strongly bound bosonic dimers. At the unitarity point, the system is a Tonks–Girardeau gas with a universal constant αζ = 0.38 in the viscosity ζ = αζℏ n for T = 0. For the trapped case, we calculate the Q-factor of the breathing mode and show that the damping provides a sensitive measure of temperature in 1D Fermi gases.

Landau damping of collective modes in a harmonically trapped Bose–Einstein condensate

This paper proposes a method for calculating the Landau damping of a low-energy collective mode in a harmonically trapped Bose–Einstein condensate. Based on the divergence-free analytical solutions for ground-state wavefunction of the condensate and eigenvalues and eigenfunctions for thermally excited quasiparticles, obtained beyond Thomas–Fermi approximation, this paper calculates the coupling matrix elements describing the interaction between the collective mode and the quasiparticles. With these analytical results this paper evaluates the Landau damping rate of a monopole mode in a spherical trap and discusses its dependence on temperature, particle number and trapping frequency of the system.

Frequency and damping of hydrodynamic modes in a trapped Bose-condensed gas

Recently it was shown that the Landau-Khalatnikov two-fluid hydrodynamics describes the collision-dominated region of a trapped Bose condensate interacting with a thermal cloud. We use these equations to discuss the low frequency hydrodynamic collective modes in a trapped Bose gas at finite temperatures. We derive a variational expressions based on these equations for both the frequency and damping of collective modes. A new feature is our use of frequency-dependent transport coefficients, which produce a natural cutoff by eliminating the collisionless low-density tail of the thermal cloud. Above the superfluid transition, our expression for the damping in trapped inhomogeneous gases is analogous to the result first obtained by Landau and Lifshitz for uniform classical fluids. We also use the moment method to discuss the crossover from the collisionless to the hydrodynamic region. Recent data for the monopole-quadrupole mode in the hydrodynamic region of a trapped gas of metastable $^4$He is discussed. We also present calculations for the damping of the analogous $m=0$ monopole-quadrupole condensate mode in the superfluid phase.

Recent studies in heavy ion induced fission reactions

Nuclear fission process involves large scale shape changes of the nucleus, while it evolves from a nearly spherical configuration to two separated fission fragments. The dynamics of these shape changes in the nuclear many body system is governed by a strong interplay of the collective and single particle degrees of freedom. With the availability of heavy ion accelerators, there has been an impetus to study the nuclear dynamics through the investigations of nucleus-nucleus collisions involving fusion and fission process. From the various investigations carried out in the past years, it is now well recognized that there is large scale damping of collective modes in heavy ion induced fission reactions, which in other words implies that nuclear motion is highly viscous. In recent years, there have been many experimental observations in heavy ion induced fission reactions at medium bombarding energies, which suggest possible occurrence of various non-equilibrium modes of fission such as quasi-fission, fast fission and pre-equilibrium fission, where some of the internal degrees of freedom of the nucleus is not fully equilibrated. We have carried out extensive investigations on the fission fragment angular distributions at near barrier bombarding energies using heavy fissile targets. The measured fragment anisotropies when compared with the standard saddle point model (SSPM) calculations show that for projectile-target systems having zero or low ground state spins, the angular anisotropy exhibits a peak-like behaviour at the sub barrier energies, which cannot be explained by the SSPM calculations. For projectiles or targets with large ground state spins, the anomalous peaking gets washed out due to smearing of the K-distribution by the intrinsic entrance channel spins. Recently studies have been carried out on the spin distributions of fission fragments through the gamma ray multiplicity measurements. The fission fragments acquire spin mainly from two sources: (i) due to rigid rotation of the nascent fragments at scission and (ii) due to statistical excitation of the spin bearing collective modes in the fissioning nucleus. One of the collective modes — the tilting mode depends on the K quantum number and is responsible for the emission angle dependence of fragment spin. In our studies, we have shown conclusively that the collective statistical spin modes get strongly suppressed for high K values corresponding to large rotational frequencies along the fission axis. These results bring out the importance of the dynamical effects in the heavy ion induced fusion-fission reactions. The present article will review the work carried out on the above aspects in heavy ion fission reactions as well as on the fission time scales, and some of the recent studies on the mass-energy correlations of fission fragments at near-barrier bombarding energies.

Dynamics of Fluctuating Bose–Einstein Condensates

We present a generalized Gross–Pitaevskii equation that describes the dissipative dynamics of a trapped partially Bose-condensed gas. It takes the form of a complex nonlinear Schrodinger equation with noise. We consider an approximation to this Langevin field equation that preserves the correct equilibrium for both the condensed and the noncondensed parts of the gas. We then use this formalism to describe the reversible formation of a one-dimensional Bose condensate, and compare with recent experiments. In addition, we determine the frequencies and the damping of collective modes in this case.

Collisional relaxation in diffuse clouds of trapped bosons

The damping of collective modes and the relaxation of temperature anisotropies in a trapped Bose gas is determined at temperatures above the Bose-Einstein condensation temperature in the collisionless regime. We demonstrate for both cases how the effects of collisions may be treated perturbatively and calculate relaxation rates based on a variational principle. Our results are compared with experiment and with previous theoretical calculations.

Linear response, dynamical friction and the fluctuation dissipation theorem in stellar dynamics

ABSTRA C T We apply linear response theory to a general, inhomogeneous, stationary stellar system, with particular emphasis on dissipative processes analogous to Landau damping. Assuming only that the response is causal, we show that the irreversible work done by an external perturber is described by the anti-Hermitian part of a linear response operator, and damping of collective modes is described by the anti-Hermitian part of a related polarization operator. We derive an exact formal expression for the response operator, which is the classical analogue of a wellknown result in quantum statistical physics. When the self-gravity of the response can be ignored, and the Hamiltonian corresponding to the ensemble-averaged gravitational potential is integrable, the expressions for the mode energy, damping rate and polarization operator reduce to well-known formulae derived from perturbation theory in action-angle variables. In this approximation, dissipation occurs only via resonant interaction with stellar orbits or collective modes. For stellar systems in thermal equilibrium, the anti-Hermitian part of the response operator is directly related to the correlation function of the fluctuations. Thus dissipative properties of the system are completely determined by the spectrum of density fluctuations ‐ the fluctuation dissipation theorem. In particular, we express the coefficient of dynamical friction for an orbiting test particle in terms of the fluctuation spectrum; this reduces to the known Chandrasekhar formula in the restrictive case of an infinite homogeneous system with a Maxwellian velocity distribution.

TRAPPED BOSE GAS: MEAN-FIELD APPROXIMATION AND BEYOND

The recent realization of Bose-Einstein condensation in atomic gases opens new possibilities for observation of macroscopic quantum phenomena. There are two important features of the system - weak interaction and significant spatial inhomogeneity. Because of this inhomogeneity a non-trivial "zeroth-order" theory exists, compared to the "first-order" Bogolubov theory. This theory is based on the mean-field Gross-Pitaevskii equation for the condensate ψ-function. The equation is classical in its essence but contains the ℏ constant explicitly. Phenomena such as collective modes, interference, tunneling, Josephson-like current and quantized vortex lines can be described using this equation. The study of deviations from the zeroth-order theory arising from zero-point and thermal fluctuations is also of great interest. Thermal fluctuations are described by elementary excitations which define the thermodynamic behaviour of the system and result in Landau-type damping of collective modes. Fluctuations of the phase of the condensate wave function restrict the monochromaticity of the Josephson current. Fluctuations of the numbers of quanta result in the quantum collapse-revival of the collective oscillations. This phenomenon is considered in some details. Collapse time for the JILA experimental conditions turns out to be of the order of seconds.

Dielectric formalism and damping of collective modes in trapped Bose-Einstein condensed gases

We present the general dielectric formalism for Bose-Einstein condensed systems in external potential at finite temperatures. On the basis of a model arising within this framework as a first approximation in an intermediate temperature region for large condensate we calculate the damping of low-energy excitations in the collisionless regime.

Dispersion corrections to the collective mode spectrum in axial and planar phases of superfluid He3

Using the path integration technique developed by Brusov and Popov earlier, we have calculated for the first time the dispersion corrections to the collective mode spectrum in A- and 2D- phases of superfluidHe3 for arbitrary directions of the collective excitation momentumk, taking the damping of collective modes into account. In axial-phase clapping (cl) mode remains six fold degenerate fork ∥l, while for other directions a three fold splitting takes place, which reaches a maximum fork ⊥l. The pairbreaking modes remain degenerate even taking the dispersion induced corrections into account. In the planar phase the degeneracy of clapping (cl) and quasi-Goldstone (qGd) modes depends on the direction of the collective mode momentumk with respect to the external magnetic fieldH: the mode degeneracy remains the same as in the case of zero momentumk fork ∥H only, and for any other directions two fold splitting of these modes takes place. The dispersion induced splitting of collective modes could be observed (at least in the A-phase) in sound absorption experiments.

Microscopic analysis of two-body correlations in light nuclei

Within a nonperturbative dynamical two-body approach — based on coupled equations of motion for the one-body density matrix and the two-body correlation function — we study the distribution of occupation numbers in a correlated system close to the groundstate, the relaxation of singleparticle excitations and the damping of collective modes. For this purpose the nonlinear equations of motion are solved numerically within a finite oscillator basis for the first time adopting shortrange repulsive and long-range attractive two-body forces. We find in all cases that the formation of long- and short-range correlations and their mixing is related to the long- and short-range part of the nucleon-nucleon interaction which dominate the resummation of loop or ladder diagrams, respectively. However, the proper description of relaxation or damping phenomena is found to require both types of diagrams as well as the mixed terms simultaneously.

Open quantum systems and the damping of collective modes in deep inelastic collisions

In the framework of the Lindblad theory for open quantum systems the following results are obtained: A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the corresponding master equations, a generalization of the Hasse pure-state condition, and a generalized Schrödinger-type nonlinear equation for an open system. Also, the Schrödinger, Heisenberg, and Weyl-Wigner-Moyal representations of the Lindblad equation are given explicitly. On the basis of these representations it is shown that various master equations for the damped quantum oscillator used in the literature for the description of the damped collective modes in deep inelastic collisions (DIC) are particular cases of the Lindblad equaton and that the majority of these equations are not satisfying the constraints on quantum mechanical diffusion coefficients. The solutions of the differential equations for the variances are put in a new synthetic form, suggested by a direct computation of the variances from the time dependent Weyl operators. The solution of the Lindblad equation in the Weyl-Wigner-Moyal representation is of Gaussian type if the initial form of the Wigner function is taken to be a Gaussian corresponding to a coherent wavefunction.

Open Quantum Systems and the Damping of Collective Modes in Deep Inelastic Collisions.: S. Săndulescu. Joint Institute for Nuclear Research, Dubna, USSR; and H. Scutaru. Central Institute of Physics, Bucharest, Rumania

Open Quantum Systems and the Damping of Collective Modes in Deep Inelastic Collisions.: S. Săndulescu. Joint Institute for Nuclear Research, Dubna, USSR; and H. Scutaru. Central Institute of Physics, Bucharest, Rumania

Damping of giant resonances in a stochastic two-level model

We derive a theory for small amplitude motion about states in thermal equilibrium. This motion couples mean-field oscillations and occupation number relaxations. The theory contains the effects of two-body collisions treated beyond the Markov approximation. The damping of collective modes is studied in a stochastic two-level model. The widths of giant resonances in finite nuclei are estimated using sum rules.

Damping of collective modes in DIC: Quantal versus statistical fluctuations

A model is developed to describe the transformation of relative kinetic energy into intrinsic excitation energy in DIC. Energy dissipation is viewed as an indirect process, in which collective vibrational modes are first excited coherently and then damped due to the coupling to the remaining non-collective degrees of freedom. Both collective and intrinsic degrees of freedom are included explicitly, and the coupling between them is treated in a random-matrix model. Under certain assumptions it is shown that, in the weak-coupling limit, the collective probability distribution in phase space obeys a Fokker-Planek equation. This transport equation is used to derive equations of motion for the expectation values of some “macroscopic” quantities characterizing the process. Some numerical results are presented and a qualitative comparison with the Copenhagen model is attached.

Damping of low-lying collective modes in TbVO4near the structural phase transition

The damping of collective modes in TbVO4 near the structural phase transition is calculated with the use of a perturbation method applied to a pseudospin-phonon model. A pseudofermion representation is utilised for the pseudospin operator in order to take into account an intrinsic effect of fluctuation field caused by surrounding pseudospins on a given pseudospin. It is shown that the spectrum of singlet pair excitations splits into a pair of spin waves by the fluctuation field and at the same time it gives the damping of the collective modes of the order of the experimental values. The damping of both the acoustic phonon and the central doublet excitation are also derived by using relationships which hold exactly between pseudospin and phonon Green functions.

Nonlinear waves and solitons in superconductors near critical temperature

Abstract A dynamical scheme permitting consideration of nonlinear ac properties of superconductors in the range of wave vectors and frequencies Dk 2 ⪡ ω ⪡ Δ ⪡ T near T c is proposed. D is the diffusion constant and Δ the energy gap. Possible existence of nonlinear and solitary branch-imbalance waves and nonlinear damping of collective mode are discussed. The same method is applied to the study of phase slip centers and quantized resistance states in superconducting channels.