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

Abstract

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.PACS (

Volume element structure and roton-maxon-phonon excitations in superfluid helium beyond the Gross-Pitaevskii approximation

“…To derive the energy spectrum of excitations one can use three alternative approaches. The first one is based on the perturbation theory [16], second is the standard Bogoliubov transform [30], and third is about analyzing small perturbations of the equation of motion for the field operator -as shown in [18] by the example of the semitransparent sphere model. In our case one can check that all three approaches yield the same spectrum in the leading approximation.…”

“…Being predicted almost a century ago, it was used by London and Tisza [12] to explain the superfluidity of liquid helium discovered by Kapitsa and Allen [13]. The existence of BEC in the superfluid phase has been confirmed by inelastic neutron scattering [14,15], thus, the influence of BEC upon the properties of liquid helium is under current study as well [16][17][18].…”

“…Here we describe the structure of the volume element of superfluid helium as well as the phenomenological consequences which follow. Among the derived effects is the famous Landau roton spectrum for which full theoretical explanation is still pending despite the numerous efforts made towards its understanding [9,10,[16][17][18][19][20]. As a matter of fact, even usage of the term "roton" itself is often a purely historical one since the explanation of the Landau spectrum in helium does not necessarily have to be based on rotating degrees of freedom of helium atoms [9,18].…”

“…Among the derived effects is the famous Landau roton spectrum for which full theoretical explanation is still pending despite the numerous efforts made towards its understanding [9,10,[16][17][18][19][20]. As a matter of fact, even usage of the term "roton" itself is often a purely historical one since the explanation of the Landau spectrum in helium does not necessarily have to be based on rotating degrees of freedom of helium atoms [9,18]. Indeed, here we show that it is possible to formulate a theory without their explicit involvement -yet obtain a remarkable agreement with experiment.…”

Non-local interactions in a BEC: an analogue gravity perspective

“…There is a symmetry based recent analysis of nonlocality in GP equation in [17]. With the help of nonlocal nonlinearities, roton minimum in the dispersion relation has been predicted which is a typical characteristic of superfluids [18][19][20]. An interesting work [21] considers non-locality in the interactions in the presence of a particular periodic global potential to show that, although the GP free energy and the corresponding solutions show asymptotic correspondence as one moves from the nonlocal to the local limit, but, the asymptotic correspondence in the stability of the solutions is not present [22].…”