A rigorous microscopic analysis of a weakly interacting Bose gas at zero temperature shows that the elementary excitation spectrum $\ensuremath{\omega}(k)$ is not an analytic function of the wave vector $k$ in the long-wavelength limit but has the form $k[{c}_{0}+{c}_{2}{k}^{2}+{c}_{L4}{k}^{4}\mathrm{ln}(\frac{1}{k})+\ensuremath{\cdots}]$. It is pointed out that the structure factor $S(k)$ is not an analytic function of $k$ and that the specific heat ${C}_{v}(T)$ at low temperatures $T$ has the form ${C}_{v}={T}^{3}[{C}_{0}+{C}_{2}{T}^{2}+{C}_{L4}{T}^{4}\mathrm{ln}(\frac{1}{T})+\ensuremath{\cdots}]$. The extension of these results to liquid ${\mathrm{He}}^{4}$ is discussed.A rigorous microscopic analysis of a weakly interacting Bose gas at zero temperature shows that the elementary excitation spectrum $\ensuremath{\omega}(k)$ is not an analytic function of the wave vector $k$ in the long-wavelength limit but has the form $k[{c}_{0}+{c}_{2}{k}^{2}+{c}_{L4}{k}^{4}\mathrm{ln}(\frac{1}{k})+\ensuremath{\cdots}]$. It is pointed out that the structure factor $S(k)$ is not an analytic function of $k$ and that the specific heat ${C}_{v}(T)$ at low temperatures $T$ has the form ${C}_{v}={T}^{3}[{C}_{0}+{C}_{2}{T}^{2}+{C}_{L4}{T}^{4}\mathrm{ln}(\frac{1}{T})+\ensuremath{\cdots}]$. The extension of these results to liquid ${\mathrm{He}}^{4}$ is discussed.

Physical Review LettersAug 9, 197116 citations

ASPECTS OF MANY-BODY PERTURBATION THEORY

WORLD SCIENTIFIC eBooksFeb 19, 20190 citations

Filling-factor-dependent electron correlations observed in cyclotron resonance

M. Manger, Edwin Batke, Robert Bruce Hey +3 more

Cyclotron resonances of electron space-charge layers in GaAs were studied at ${}^{3}\mathrm{He}$ temperatures covering a density regime from 2 to $13\ifmmode\times\else\texttimes\fi{}{10}^{11} {\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}.$ For densities higher than about $6\ifmmode\times\else\texttimes\fi{}{10}^{11} {\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ many-body influences are sufficiently reduced such that line splittings due to band-structure influences were involved. At integer filling factors the spin-up and spin-down electrons are not completely decoupled as predicted by theory. Inter Landau-level optical gaps are renormalized at odd fillings, and there is a correlation gap between spin- and charge-density excitations in the long-wavelength limit.Cyclotron resonances of electron space-charge layers in GaAs were studied at ${}^{3}\mathrm{He}$ temperatures covering a density regime from 2 to $13\ifmmode\times\else\texttimes\fi{}{10}^{11} {\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}.$ For densities higher than about $6\ifmmode\times\else\texttimes\fi{}{10}^{11} {\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ many-body influences are sufficiently reduced such that line splittings due to band-structure influences were involved. At integer filling factors the spin-up and spin-down electrons are not completely decoupled as predicted by theory. Inter Landau-level optical gaps are renormalized at odd fillings, and there is a correlation gap between spin- and charge-density excitations in the long-wavelength limit.

Physical review. B, Condensed matterMar 13, 200117 citations

Hyperspherical Cluster Model for Bosons: Application to Sub-threshold Halo States in Helium Drops

N. K. Timofeyuk

Abstract To describe long-range behaviour of one particle removed from a few- or a many-body system, a hyperspherical cluster model has been developed. It has been applied to the ground and first excited states of helium drops with five, six, eight and ten atoms interacting via a two-body soft gaussian potential. Convergence of the hyperspherical cluster harmonics expansion is studied for binding energies, root-mean-squared radii and overlaps of the wave functions of two helium drops differing by one atom. It was shown that with increasing model space the functional form of such overlaps at large distances converges to the correct asymptotic behaviour. The asymptotic normalization coefficients that quantify the overlaps’ amplitudes in this region are calculated. It was also shown that in the first excited state one helium atom stays far apart from the rest forming a two-body molecule, or a halo. The probability of finding the halo atom in the classically-forbidden region of space depends on the definition of the latter and on the valence atom binding energy. The total norm of the overlap integrals, the spectroscopic factor, represents the number of partitions of a many-body state into a chosen state of the system with one particle removed. The spectroscopic factors have been calculated and their sum rules are discussed giving a further insight into the structure of helium drops.Abstract To describe long-range behaviour of one particle removed from a few- or a many-body system, a hyperspherical cluster model has been developed. It has been applied to the ground and first excited states of helium drops with five, six, eight and ten atoms interacting via a two-body soft gaussian potential. Convergence of the hyperspherical cluster harmonics expansion is studied for binding energies, root-mean-squared radii and overlaps of the wave functions of two helium drops differing by one atom. It was shown that with increasing model space the functional form of such overlaps at large distances converges to the correct asymptotic behaviour. The asymptotic normalization coefficients that quantify the overlaps’ amplitudes in this region are calculated. It was also shown that in the first excited state one helium atom stays far apart from the rest forming a two-body molecule, or a halo. The probability of finding the halo atom in the classically-forbidden region of space depends on the definition of the latter and on the valence atom binding energy. The total norm of the overlap integrals, the spectroscopic factor, represents the number of partitions of a many-body state into a chosen state of the system with one particle removed. The spectroscopic factors have been calculated and their sum rules are discussed giving a further insight into the structure of helium drops.

arXiv:2304.06679Few-Body SystemsMay 17, 20231 citation

Some results on many-body scattering theory

Paul G. Federbush

Annals of PhysicsSep 1, 19682 citations

k

in the long-wavelength limit but has the form $k[{c}_{0}+{c}_{2}{k}^{2}+{c}_{L4}{k}^{4}\mathrm{ln}(\frac{1}{k})+\ensuremath{\cdots}]$. It is pointed out that the structure factor

S(k)

is not an analytic function of

k

and that the specific heat

{C}_{v}(T)

at low temperatures

T

has the form ${C}_{v}={T}^{3}[{C}_{0}+{C}_{2}{T}^{2}+{C}_{L4}{T}^{4}\mathrm{ln}(\frac{1}{T})+\ensuremath{\cdots}]$. The extension of these results to liquid

{\mathrm{He}}^{4}

is discussed.

Cyclotron resonances of electron space-charge layers in GaAs were studied at

{}^{3}\mathrm{He}

temperatures covering a density regime from 2 to $13\ifmmode\times\else\texttimes\fi{}{10}^{11} {\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}.$ For densities higher than about $6\ifmmode\times\else\texttimes\fi{}{10}^{11} {\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ many-body influences are sufficiently reduced such that line splittings due to band-structure influences were involved. At integer filling factors the spin-up and spin-down electrons are not completely decoupled as predicted by theory. Inter Landau-level optical gaps are renormalized at odd fillings, and there is a correlation gap between spin- and charge-density excitations in the long-wavelength limit.