Static response function for longitudinal and transverse excitations in superfluid helium

Abstract

The sum rule formalism is used to evaluate rigorous bounds for the density and current static response functions in superfluid 4 He at zero temperature.Both lower and upper bounds are considered. The bounds are expressed in terms of ground state properties (density and current correlation functions) and of the interatomic potential. The results for the density static response significantly improve the Feynman approximation and turn out to be close to the experimental (neutron scattering) data. A quantitative prediction for the transverse current response is given. The role of one-phonon and multi-particle excitations in the longitudinal and transverse channels is discussed.

Static Structure Factor and Static Response Function of Superfluid Helium 4: a Comparative Analysis

“…Because of multiphonon scattering, the bounds are relatively different, and may just serve as an internal consistency test that should be passed by all neutron data. Better bounds were later derived by Dalfovo and Stringari [25]:…”

Nonequilibrium and local detection of the normal fraction of a trapped two-dimensional Bose gas

“…The basic idea of our proposal is based on the definition of normal and superfluid fractions of a quantum fluid in terms of its current response to a transverse gauge field in the low-frequency and long-wavelength limit [15,16]. A spatially oscillating artificial gauge field [17][18][19][20] with a spatially localized envelope can be applied to the atomic gas using a suitable combination of laser beams.…”

“…(26) was used to obtain the last identity. An application of the fluctuationdissipation relation (E5) to the susceptibility and the fluctuations of the mass current in liquid He can be found in [16].…”

“…Our proposal to quantitatively assess the superfluidity of the two-dimensional atomic gas is based on the traditional definition of the normal fraction f n in terms of the response to a transverse gauge field coupling to the atomic current operator [15,16]. The Hamiltonian giving the coupling of the matter current to an arbitrary vector potential A(r) is…”

Thomas-Reiche-Kuhn Sum Rule for Electron Transitions in Solids

“…Parallel, the moments of the oscillator strength distributions of the order higher than one which is represented by the TRK sum rule have been calculated [8,11]. This derivation of the sum rules of different kinds appeared useful in the calculation of the particle excitations in the Bose superfluids [12] and also became important for the static response function for longitudinal and transverse excitations in the superfluid helium [13]. A direct application of the TRK sum rule comes into play when the total photoabsorption cross-section σ D (ω) is calculated in the long wavelength approximation The total photoabsorption cross-section (5) integrated over the whole spectrum of frequencies ω gives Taking into account (2), expression (6) -with the accuracy to a constant multiplier -is identical to the left-hand side of Eq.…”