Spectrum Of Elementary Excitations Research Articles

Nonideal Bose Gas at Nonzero Temperatures

An extension to nonzero temperatures of the Hugenholtz-Pines procedure for the degenerate Bose gas is provided. It is shown that under certain conditions the elementary excitation spectrum must approach zero for zero momentum, at nonzero, as well as at zero temperatures. The apparent discrepancy of this result with the particular case of a charged boson gas with a uniform positive background is discussed. Finally, a suggestion is made for modifying the Bogoliubov approximation, which is particularly relevant at nonzero temperatures.

Energy Spectrum of Elementary Excitations in Helium II

The contribution of phonon-phonon interactlon to the energy of elementary excitations in liquid He/sub 4/ is evaluated in the approximation of the Brillouin-Wigner second order energy. The three-particle distribution function p(1,2,3) occurring in the interaction matrix elements is approximated by the Kirkwood superposition form and also by the convolution'' form. A generai criterion is developed to test the accuracy of possible approximations for p(1,2,3). The criterion has the form of a functional X in p(1,2,3) which vanishes if p(1,2,3) is generated by the correct ground state solution of the Schrodinger equation. If an approximate form is used the corresponding functional X/sub a/ does not vanish and thus provides a measure of accuracy. The power of this criterion resides in the fact that X/sub a/ is a function of three variabies, the magnitudes of two wave vectors and the cosine of the angle between them. The computed dispersion curves are compared with the experimental curve constructed by Henshaw and Woods from the inelastic single scattering of slow neutrons in liquid helium (auth)

Elementary Excitations in Liquid Helium

An analysis of some recent experimental and theoretical investigations of the elementary excitation spectrum of liquid He II is carried out. The spectrum of density fluctuations, which is measured in an inelastic neutron scattering experiment, is shown to consist of two distinct parts: direct excitation of single quasi-particles from the condensed zero-momentum state; and excitation of more complex configurations arising from the interaction of two, three, or more quasi-particles. With the aid of general sum-rule arguments it is demonstrated that: (1) in the long-wavelength limit, a single quasi-particle excitation exhausts the $f$-sum rule; the resulting excitation spectrum is identical to the phonon spectrum proposed by Feynman and found experimentally by Henshaw and Woods; (2) this asymptotic behavior of the density fluctuation spectrum may be used to normalize the experimental results of Henshaw and Woods; one thereby obtains a somewhat altered liquid structure-factor curve, detailed information on the efficiency of quasi-particle excitation from the condensed state of an incident slow neutron, and an estimate of the depletion of the zero-momentum state as a consequence of particle interaction; (3) the backflow introduced by Feynman and Cohen corresponds to taking into account the coupling between a Feynman excitation and higher configurations involving several elementary excitations.The physical picture of backflow is clarified by means of a study of impurity atom motion in an interacting-boson system. It is shown that in the Bogoliubov approximation the backflow around the impurity atom corresponds to a cloud of moving virtualphonon excitations which act to increase the impurity effective mass as well as to conserve current in the system. The generalization of these results to higher-order approximations, and to the coupling between quasi-particles in liquid helium, is discussed.The importance of accounting properly for depletion effects in a microscopic theory is emphasized; it is shown that such effects are neglected in the microscopic calculations of the interacting-boson excitation spectrum which have thus far been carried out, although they are of decisive importance in the determination of the density-fluctuation excitation spectrum.

The λ-Transition in Helium

RECENT experiments on the inelastic scattering of neutrons by superfluid helium1,2 have given a direct confirmation of the correctness of the elementary excitation spectrum (rotons and phonons) of Landau's theory3. As it is usually formulated, the theory postulates that the excitation spectrum is independent of temperature. However, the velocity of sound is known to vary somewhat with temperature4, and the neutron scattering experiments1 show an appreciable fall in the minimum roton energy Δ, as the temperature approaches the λ-point.

On the spectrum of elementary excitations in superfluid helium

Feynman has recently advanced physical arguments to deduce an approximate form for the wave function of an elementary excitation in helium. Qualitatively, his theory leads to an excitation spectrum similar to that postulated by Landau; however, serious quantitative discrepancies remain in the ‘roton ’ region of the spectrum. It is shown here that improved wave functions may be constructed by using combinations of wave functions for single and double Feynman excitations—this amounts to a self-energy correction to the roton spectrum, arising mainly from roton-phonon interactions. The numerical value of the roton energy agrees remarkably well with Landau’s value. The treatment depends, however, on the use of perturbation theory, where the perturbation is not small. Little confidence should therefore be placed in the actual value found.