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Short-wave excitations in non-local Gross-Pitaevskii

A. P. Ivashin, Yuri M. Poluektov

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

We show that a non-local form of the Gross-Pitaevskii equation describes not only long-wave excitations, but also the short-wave ones in Bose-condensate systems. At certain parameter values, the excitation spectrum mimics the Landau spectrum of quasi-particle excitations in superfluid helium with roton minimum. The excitation wavelength, at which the roton minimum exists, is close to the inter-particle interaction range. We determine how the roton gap and the eective roton mass depend on the interaction potential parameters, and show that the existence domain of the spectrum with a roton minimum is reduced if one accounts for an inter-particle attraction.

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Short-wave excitations in non-local Gross-Pitaevskii model

A. P. Ivashin, Yuri M. Poluektov

Abstract We show that a non-local form of the Gross-Pitaevskii equation describes not only long-wave excitations, but also the short-wave ones in Bose-condensate systems. At certain parameter values, the excitation spectrum mimics the Landau spectrum of quasi-particle excitations in superfluid helium with roton minimum. The excitation wavelength, at which the roton minimum exists, is close to the inter-particle interaction range. We determine how the roton gap and the effective roton mass depend on the interaction potential parameters, and show that the existence domain of the spectrum with a roton minimum is reduced if one accounts for an inter-particle attraction.

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Spectrum on elementary excitations in superfluid Bose--Fermi systems

Ernst A. Pashitskii

The spectrum of elementary excitations in the system of interacting Bose- and Fermi-particles was obtained at a temperature of absolute zero (Dose- condensation being taken into account by means of the Bogolyabov canonic transformations. In terms of a model of permeable spheres'' with finite repulsion it(is shown that the boson spectrum omega (p) in a definite region of parameter has the minimum at p = 0. By selecting parameters one succeeds in obtaining a quite satisfactory quantitative agreement of the theoretical and experimental spectra for superfluid helium. In the case when the Fermi energy is considerably higher than the bosorins maximum energy, a gap characterizing bond energy of the copper pairs can appear in the fermion speetrum due to exchange of virtual supercondensate'' bosons. If in this case the interaction between fermions at infinity is of attraction character, then under certain conditions sustained longitudinal collective excitations of Pose-type with a finite gap'' in the energy spectrum may exist in the superfluid fermion subsystem. Possibility of appearance of similar excitations in superfluid nuclear matter of neutron stars (pulsars) due to gravitational interaction between nucleons is discussed. (auth)

•Sep 1, 1973•0 citations
We show that a non-local form of the Gross-Pitaevskii equation describes not only long-wave excitations, but also the short-wave ones in Bose-condensate systems. At certain parameter values, the excitation spectrum mimics the Landau spectrum of quasi-particle excitations in superfluid helium with roton minimum. The excitation wavelength, at which the roton minimum exists, is close to the inter-particle interaction range. We determine how the roton gap and the eective roton mass depend on the interaction potential parameters, and show that the existence domain of the spectrum with a roton minimum is reduced if one accounts for an inter-particle attraction.
Abstract We show that a non-local form of the Gross-Pitaevskii equation describes not only long-wave excitations, but also the short-wave ones in Bose-condensate systems. At certain parameter values, the excitation spectrum mimics the Landau spectrum of quasi-particle excitations in superfluid helium with roton minimum. The excitation wavelength, at which the roton minimum exists, is close to the inter-particle interaction range. We determine how the roton gap and the effective roton mass depend on the interaction potential parameters, and show that the existence domain of the spectrum with a roton minimum is reduced if one accounts for an inter-particle attraction.
In three dimensions, noninteracting bosons undergo Bose-Einstein condensation at a critical temperature, T(c), which is slightly shifted by ΔT(c), if the particles interact. We calculate the excitation spectrum of interacting Bose systems, (4)He and (87)Rb, and show that a roton minimum emerges in the spectrum above a threshold value of the gas parameter. We provide a general theoretical argument for why the roton minimum and the maximal upward critical temperature shift are related. We also suggest two experimental avenues to observe rotons in condensates. These results, based upon a path-integral Monte Carlo approach, provide a microscopic explanation of the shift in the critical temperature and also show that a roton minimum does emerge in the excitation spectrum of particles with a structureless, short-range, two-body interaction.
We consider the Gross-Pitaevskii(GP) model of a Bose-Einstein Condensate(BEC) for single-component and multi-component BEC. The pseudopotential for s-wave scattering between atoms is taken to be of width of the order of the s-wave scattering length. Such an interaction giving rise to a roton minimum in the spectrum of elementary excitations of a single component BEC is well known. We study this roton minimum for a multi-component BECs. We show that for a fixed inter-species scattering length, roton mode can be softened by increasing the number of distinct components of a multi-component BEC.
The Gross-Pitaevskii equation is a widely used model in physics, in particular in the context of Bose-Einstein condensates. However, it only takes into account local interactions between particles. This paper demonstrates the validity of using a nonlocal formulation as a generalization of the local model. In particular, the paper demonstrates that the solution of the nonlocal model approaches in norm the solution of the local model as the nonlocal model approaches the local model. The nonlocality and potential used for the Gross-Pitaevskii equation are quite general, thus this paper shows that one can easily add nonlocal effects to interesting classes of Bose-Einstein condensate models. Based on a particular choice of potential for the nonlocal Gross-Pitaevskii equation, we establish the orbital stability of a class of parameter-dependent solutions to the nonlocal problem for certain parameter regimes. Numerical results corroborate the analytical stability results and lead to predictions about the stability of the class of solutions for parameter values outside of the purview of the theory established in this paper.
Dipolar Bose-Einstein condensates (dBECs) exhibit a plethora of physics phenomena, from supersolidity to the rotonlike minimum in the elementary excitation spectrum. In this work we first demonstrate the existence of axis-symmetric solitary waves in (quasi-)two-dimensional dBECs: these localized excitations are characterized by quantized vortex dipoles that continuously transit to vortex-free density depletions. We then show how the presence of the roton minimum fundamentally alters the fate of such solutions when approaching Landau's critical speed: when propagating along the polarization direction where the roton minimum occurs, the solitary wave transits into roton excitations rather than into phonons as for standard contact-interaction BECs. This finding suggests that Feynman's hypothesis, conjectured for 3D superfluid liquid helium regarding the creation of rotons as fading vortex excitations, is valid in the context of 2D dBECs.
The spectrum of elementary excitations in the system of interacting Bose- and Fermi-particles was obtained at a temperature of absolute zero (Dose- condensation being taken into account by means of the Bogolyabov canonic transformations. In terms of a model of permeable spheres'' with finite repulsion it(is shown that the boson spectrum omega (p) in a definite region of parameter has the minimum at p = 0. By selecting parameters one succeeds in obtaining a quite satisfactory quantitative agreement of the theoretical and experimental spectra for superfluid helium. In the case when the Fermi energy is considerably higher than the bosorins maximum energy, a gap characterizing bond energy of the copper pairs can appear in the fermion speetrum due to exchange of virtual supercondensate'' bosons. If in this case the interaction between fermions at infinity is of attraction character, then under certain conditions sustained longitudinal collective excitations of Pose-type with a finite gap'' in the energy spectrum may exist in the superfluid fermion subsystem. Possibility of appearance of similar excitations in superfluid nuclear matter of neutron stars (pulsars) due to gravitational interaction between nucleons is discussed. (auth)