Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Low Temperature Physics

Self-consistent calculation of the spectrum of quasiparticles in a superfluid Bose liquid with a quenched Bose–Einstein condensate

Ernst A. Pashitskii, S. I. Vilchinskiĭ, Stefan V. Mashkevich

Published Feb 1, 2002• 8 citations
Publisher

Abstract

An iterative method is used in a self-consistent calculation, at T=0, of the normal Σ11 and anomalous Σ12 self-energy parts, the boson polarization operator Π on the “mass shell,” and the quasiparticle spectrum E(p) in a superfluid Bose liquid with an interaction-quenched single-particle Bose–Einstein condensate (BEC). The calculation is based on a system of “truncated” integral equations for Σ11 and Σ12 with allowance for terms of first order in the density n0/n≪1 of the BEC and with the “bare” interaction between bosons taken in the form of the repulsive pseudopotential in the “semitransparent spheres” model, for which the Fourier component of the pseudopotential is an oscillatory sign-varying function of the momentum transfer. By fitting with a single adjustable parameter—the amplitude of the initial repulsive pseudopotential—one can achieve completely satisfactory agreement of the theoretical quasiparticle spectrum E(p) with the measured spectrum of elementary excitations in superfluid helium from neutron-scattering experiments over a wide momentum range (0⩽p⩽pmax≃4 Å−1).

DOI
10.1063/1.1461918

Related papers

The Superfluid State of a Bose Liquid as a Superposition of a Suppressed Bose-Eistein Condensate and an Intensive Pair Coherent Condensate

Ernst A. Pashitskii, Stefan V. Mashkevich, S. I. Vilchynskyy

A self-consistent model of the superfluid (SF) state of a Bose liquid with strong interaction between bosons is considered, in which at T=0, along with a weak single-particle Bose-Einstein condensate (BEC), there exists an intensive pair coherent condensate (PCC) of bosons, analogous to the Cooper pair condensate of fermions. Such a PCC emerges due to an effective attraction between bosons in some regions of momentum space, which results from an oscillating sign-changing momentum dependence of the Fourier component V(p) of the interaction potential. The collective many-body effects of renormalization ("screening") of the initial interaction, which are described by the bosonic polarization operator Π(p,ω), lead to a suppression of the repulsion [V(p)>0] and an enhancement of the effective attraction [V(p)<0] in the respective domains of nonzero momentum transfer. The ratio of the BEC density n_0 to the total particle density n of the Bose liquid is used as a small parameter of the model. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is obtained with account for the terms of first order in the BEC density. In the framework of the ``soft spheres'' model with the single fitting parameter--the value of the repulsion potential at r=0, a theoretical quasiparticle spectrum E(p) is obtained, which is in good accordance with the experimental spectrum E_{exp}(p) of elementary excitations in superfluid $^4$He.

arXiv:cond-mat/0208350•Aug 19, 2002•0 citations

The Superfluid State of a Bose Liquid as a Superposition of a Single-Particle and Pair Coherent Condensates

Ernst A. Pashitskii, Stefan V. Mashkevich, S. I. Vilchynskyy

One considers the superfluid (SF) state of a Bose liquid with a strong repulsion between bosons, in which at T=0, along with a weak single-particle Bose-Einstein condensate (BEC), there exists an intensive pair coherent condensate (PCC), analogous to the Cooper condensate in a Fermi liquid with an attraction between the fermions. Such a PCC emerges in a system of bosons due to an oscillating sign-changing momentum dependence of the Fourier component of the pair interaction potential, which is characteristic of a certain family of repulsion potentials. In such cases, the Fourier component is negative in some domain of nonzero momentum transfer, which corresponds to an effective attraction. The collective effects of renormalization (``screening'') of the initial interaction lead to a suppression of the repulsion and an enhancement of the effective attraction. It is the ratio of the BEC density to the full density of the liquid $n_0/n\ll 1$ that is used as a small parameter---unlike in the Bogolyubov theory for a quasi-ideal Bose gas, in which the small parameter is the ratio of the number of supracondensate excitations to the number of particles in an intensive BEC, $(n-n_0)/n_0\ll 1$. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is obtained, in the framework of a renormalized perturbation theory built on combined hydrodynamic and field variables. In the framework of the hard-spheres model, a spectrum of quasiparticles is obtained, which is in good accordance with the experimental spectrum of elementary excitations in superfluid $^4$He. The question of applicability of the Landau criterion in the absence of quantum vortices is discussed.

arXiv:cond-mat/0104415•Apr 22, 2001•0 citations

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

The role of pair correlations in the formation of the ground state and the elementary excitation spectrum in a superfluid Bose liquid (A Review)

Ernst A. Pashitskii

The paradoxes and disparities in the contemporary microscopic theory of superfluid helium (He–II) are discussed along with possible ways of resolving them by taking pair correlations of He4 atoms into consideration. It is shown that most paradoxes are associated with the commonly accepted initial assumption concerning the dominating role of single-particle Bose condensate (SPBC) in the quantum microstructure of the superfluid component ρs. The existence of intensive SPBC leads to a strong hybridization of the elementary excitation branches and to a common dispersion law for all boson branches, which is identified with the quasiparticle spectrum E(p) observed experimentally from slow neutron scattering in liquid helium. However, the stability of this spectrum during a transition through the λ-point and the large value of the gap in the vicinity of the “rotonic” minimum contradict both the Landau theoretical criterion of superfluidity and the small value of experimentally measured critical velocity. At the same time, a strong interaction between particles in the Bose liquid He4 strongly suppresses the SPBC which amounts to less than 1% of all He4 atoms and hence cannot be the main constituent of the superfluid component, unlike the case of a weakly nonideal Bose gas. Moreover, for a quite strong attraction between particles in a certain region of the momentum space, bound pairs of bosons can be formed in the superfluid Bose liquid, and a coherent pair condensate (CPC) analogous to the Cooper pair condensate in superconductors may appear. Such a strong CPC may completely suppress the weak SPBC. In this case, the one-particle spectrum ε(p) of elementary excitations does not hybridize with the collective (two-particle) spectrum and does not appear in the structure of the dynamic form factor S(p,ε), i.e., does not coincide with the spectrum measured from neutron scattering. The dispersion of one-particle spectrum is defined by the momentum dependence of the pair order parameter Ψ̃(p) and may have a minimum or a point of inflection at p≠0. This peculiarity in the one-particle spectrum of a Bose liquid with CPC but without SPBC vanishes together with Ψ̃(p) at the temperature Tc=Tλ of the phase transition from the superfluid to the normal state (unlike the rotonic minimum in the collective spectrum), while the corresponding critical velocity vc=min[ε(p)/p] vanishes at the λ-point in accordance with the Landau criterion and the experimental data. The assumption that the strong “Cooper-like” CPC is responsible for the quantum structure of the superfluid component ρs is confirmed indirectly by the successful application of the Justrow approximation (based on strong pair correlations) for describing the properties of liquid He4 and quantum liquid mixtures He3–4He on one hand, and by an anomalously large effective mass of He3 impurity atoms in He4, which is approximately equal to total mass of He3 and He4 atoms, thus pointing to the existence of helium atoms in superfluid liquid He–II. The value of the superfluid velocity circulation quantum in the Onsager–Feynman vortices in a Bose liquid with CPC but without SPBC is discussed as well as the critical velocities of superfluid He4 in ultrathin films and channels in which the creation and motion of quantum vortices are ruled out, and the quasiparticle spectrum undergoes dimensional quantization.

Low Temperature Physics•Feb 1, 1999•14 citations

Quasiparticle spectrum and dynamical stability of an atomic Bose-Einstein condensate coupled to a degenerate Fermi gas

Christopher P. Search, Han Pu, W. Zhang +1 more

The quasiparticle excitations and dynamical stability of an atomic Bose-Einstein condensate coupled to a quantum degenerate Fermi gas of atoms at zero temperature is studied. The Fermi gas is assumed to be either in the normal state or to have undergone a phase transition to a superfluid state by forming Cooper pairs. The quasiparticle excitations of the Bose-Einstein condensate exhibit a dynamical instability due to a resonant exchange of energy and momentum with quasiparticle excitations of the Fermi gas. The stability regime for the bosons depends on whether the Fermi gas is in the normal state or in the superfluid state. We show that the energy gap in the quasiparticle spectrum for the superfluid state stabilizes the low-energy excitations of the condensate. In the stable regime, we calculate the boson quasiparticle spectrum, which is modified by the fluctuations in the density of the Fermi gas.

arXiv:cond-mat/0112393•Physical Review A•Jun 14, 2002•10 citations

Scattering of neutrons on a Bose condensate

Dmitriy Baranov, Zh. A. Kozlov, L. Siurakshina +1 more

The spectrum of noncondensate excitations in neutron scattering on bosons is obtained in the framework of the Bogoliubov models both for liquid 4He and a dilute gas. The problem is solved using a path-integral representation of the partition function of the system. We describe the influence of scattering of neutrons on a Bose condensate in a stationary (time-independent) picture in the Gibbs equilibrium ensemble. This influence is a stationary boson response, and it depends on the initial neutron momentum k, transfer momentum p, and the neutron-boson interaction λ, which is related to the scattering length. The contribution of the neutrons to the initial Bogoliubov spectrum is found to be important for “quasi-elastic” scattering on the noncondensate, while the contribution of deep inelastic scattering is small; no contribution from elastic scattering on the Bose condensate is found. In the case of liquid Helium, the response is unlikely to be observable for all values p. On the other hand, for a gas one may expect a visible effect, in particular for a small momentum transfer p and a small density of the Bose condensate ϱ.

Annalen der Physik•Feb 1, 1999•3 citations
An iterative method is used in a self-consistent calculation, at T=0, of the normal Σ11 and anomalous Σ12 self-energy parts, the boson polarization operator Π on the “mass shell,” and the quasiparticle spectrum E(p) in a superfluid Bose liquid with an interaction-quenched single-particle Bose–Einstein condensate (BEC). The calculation is based on a system of “truncated” integral equations for Σ11 and Σ12 with allowance for terms of first order in the density n0/n≪1 of the BEC and with the “bare” interaction between bosons taken in the form of the repulsive pseudopotential in the “semitransparent spheres” model, for which the Fourier component of the pseudopotential is an oscillatory sign-varying function of the momentum transfer. By fitting with a single adjustable parameter—the amplitude of the initial repulsive pseudopotential—one can achieve completely satisfactory agreement of the theoretical quasiparticle spectrum E(p) with the measured spectrum of elementary excitations in superfluid helium from neutron-scattering experiments over a wide momentum range (0⩽p⩽pmax≃4 Å−1).
A self-consistent model of the superfluid (SF) state of a Bose liquid with strong interaction between bosons is considered, in which at T=0, along with a weak single-particle Bose-Einstein condensate (BEC), there exists an intensive pair coherent condensate (PCC) of bosons, analogous to the Cooper pair condensate of fermions. Such a PCC emerges due to an effective attraction between bosons in some regions of momentum space, which results from an oscillating sign-changing momentum dependence of the Fourier component V(p) of the interaction potential. The collective many-body effects of renormalization ("screening") of the initial interaction, which are described by the bosonic polarization operator Π(p,ω), lead to a suppression of the repulsion [V(p)>0] and an enhancement of the effective attraction [V(p)<0] in the respective domains of nonzero momentum transfer. The ratio of the BEC density n_0 to the total particle density n of the Bose liquid is used as a small parameter of the model. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is obtained with account for the terms of first order in the BEC density. In the framework of the ``soft spheres'' model with the single fitting parameter--the value of the repulsion potential at r=0, a theoretical quasiparticle spectrum E(p) is obtained, which is in good accordance with the experimental spectrum E_{exp}(p) of elementary excitations in superfluid 4^44He.
One considers the superfluid (SF) state of a Bose liquid with a strong repulsion between bosons, in which at T=0, along with a weak single-particle Bose-Einstein condensate (BEC), there exists an intensive pair coherent condensate (PCC), analogous to the Cooper condensate in a Fermi liquid with an attraction between the fermions. Such a PCC emerges in a system of bosons due to an oscillating sign-changing momentum dependence of the Fourier component of the pair interaction potential, which is characteristic of a certain family of repulsion potentials. In such cases, the Fourier component is negative in some domain of nonzero momentum transfer, which corresponds to an effective attraction. The collective effects of renormalization (``screening'') of the initial interaction lead to a suppression of the repulsion and an enhancement of the effective attraction. It is the ratio of the BEC density to the full density of the liquid n0/n≪1n_0/n\ll 1n0​/n≪1 that is used as a small parameter---unlike in the Bogolyubov theory for a quasi-ideal Bose gas, in which the small parameter is the ratio of the number of supracondensate excitations to the number of particles in an intensive BEC, (n−n0)/n0≪1(n-n_0)/n_0\ll 1(n−n0​)/n0​≪1. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is obtained, in the framework of a renormalized perturbation theory built on combined hydrodynamic and field variables. In the framework of the hard-spheres model, a spectrum of quasiparticles is obtained, which is in good accordance with the experimental spectrum of elementary excitations in superfluid 4^44He. The question of applicability of the Landau criterion in the absence of quantum vortices is discussed.
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)
The paradoxes and disparities in the contemporary microscopic theory of superfluid helium (He–II) are discussed along with possible ways of resolving them by taking pair correlations of He4 atoms into consideration. It is shown that most paradoxes are associated with the commonly accepted initial assumption concerning the dominating role of single-particle Bose condensate (SPBC) in the quantum microstructure of the superfluid component ρs. The existence of intensive SPBC leads to a strong hybridization of the elementary excitation branches and to a common dispersion law for all boson branches, which is identified with the quasiparticle spectrum E(p) observed experimentally from slow neutron scattering in liquid helium. However, the stability of this spectrum during a transition through the λ-point and the large value of the gap in the vicinity of the “rotonic” minimum contradict both the Landau theoretical criterion of superfluidity and the small value of experimentally measured critical velocity. At the same time, a strong interaction between particles in the Bose liquid He4 strongly suppresses the SPBC which amounts to less than 1% of all He4 atoms and hence cannot be the main constituent of the superfluid component, unlike the case of a weakly nonideal Bose gas. Moreover, for a quite strong attraction between particles in a certain region of the momentum space, bound pairs of bosons can be formed in the superfluid Bose liquid, and a coherent pair condensate (CPC) analogous to the Cooper pair condensate in superconductors may appear. Such a strong CPC may completely suppress the weak SPBC. In this case, the one-particle spectrum ε(p) of elementary excitations does not hybridize with the collective (two-particle) spectrum and does not appear in the structure of the dynamic form factor S(p,ε), i.e., does not coincide with the spectrum measured from neutron scattering. The dispersion of one-particle spectrum is defined by the momentum dependence of the pair order parameter Ψ̃(p) and may have a minimum or a point of inflection at p≠0. This peculiarity in the one-particle spectrum of a Bose liquid with CPC but without SPBC vanishes together with Ψ̃(p) at the temperature Tc=Tλ of the phase transition from the superfluid to the normal state (unlike the rotonic minimum in the collective spectrum), while the corresponding critical velocity vc=min[ε(p)/p] vanishes at the λ-point in accordance with the Landau criterion and the experimental data. The assumption that the strong “Cooper-like” CPC is responsible for the quantum structure of the superfluid component ρs is confirmed indirectly by the successful application of the Justrow approximation (based on strong pair correlations) for describing the properties of liquid He4 and quantum liquid mixtures He3–4He on one hand, and by an anomalously large effective mass of He3 impurity atoms in He4, which is approximately equal to total mass of He3 and He4 atoms, thus pointing to the existence of helium atoms in superfluid liquid He–II. The value of the superfluid velocity circulation quantum in the Onsager–Feynman vortices in a Bose liquid with CPC but without SPBC is discussed as well as the critical velocities of superfluid He4 in ultrathin films and channels in which the creation and motion of quantum vortices are ruled out, and the quasiparticle spectrum undergoes dimensional quantization.
The quasiparticle excitations and dynamical stability of an atomic Bose-Einstein condensate coupled to a quantum degenerate Fermi gas of atoms at zero temperature is studied. The Fermi gas is assumed to be either in the normal state or to have undergone a phase transition to a superfluid state by forming Cooper pairs. The quasiparticle excitations of the Bose-Einstein condensate exhibit a dynamical instability due to a resonant exchange of energy and momentum with quasiparticle excitations of the Fermi gas. The stability regime for the bosons depends on whether the Fermi gas is in the normal state or in the superfluid state. We show that the energy gap in the quasiparticle spectrum for the superfluid state stabilizes the low-energy excitations of the condensate. In the stable regime, we calculate the boson quasiparticle spectrum, which is modified by the fluctuations in the density of the Fermi gas.
The spectrum of noncondensate excitations in neutron scattering on bosons is obtained in the framework of the Bogoliubov models both for liquid 4He and a dilute gas. The problem is solved using a path-integral representation of the partition function of the system. We describe the influence of scattering of neutrons on a Bose condensate in a stationary (time-independent) picture in the Gibbs equilibrium ensemble. This influence is a stationary boson response, and it depends on the initial neutron momentum k, transfer momentum p, and the neutron-boson interaction λ, which is related to the scattering length. The contribution of the neutrons to the initial Bogoliubov spectrum is found to be important for “quasi-elastic” scattering on the noncondensate, while the contribution of deep inelastic scattering is small; no contribution from elastic scattering on the Bose condensate is found. In the case of liquid Helium, the response is unlikely to be observable for all values p. On the other hand, for a gas one may expect a visible effect, in particular for a small momentum transfer p and a small density of the Bose condensate ϱ.