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

Physical Review A

Theory of Superfluidity

A. Mann

Published Aug 1, 1971• 4 citations
Publisher

Abstract

The generator-coordinate method, well known in nuclear physics, is employed to derive the Bogoliubov theory of superfluidity of a boson system. The treatment is fully number conserving. Analogies to a normal Fermi system (especially to the random-phase approximation for that system) are pointed out, and some further insight into the nature of superfluidity is gained. Possible generalizations are mentioned.

DOI
10.1103/physreva.4.750

Related papers

Number-conserving mean-field theory for Bose-Einstein condensates

E. J. V. de Passos

I formulate a mean-field theory of Bose-Einstein condensation based on number-conserving many-body theory. I use techniques commonly adopted in nuclear structure theories to derive the mean-field equations. I compare my formulation with the Bogoliubov approach and I emphasize the key role played by the zero-energy eigenmode when we contrast these two approaches. The differences with analogous previous formulation are also pointed out.

Journal of Physics B Atomic Molecular and Optical Physics•Nov 18, 1999•0 citations

Theory of superfluidity

Rafael F. Angulo G.

A theory of superfluidity (S.F.) is developed from first principles using two novel concepts, (1) that of a 'superfluid Ensemble' (S.E.) i.e. a 'Restricted Ensemble' constructed from a 'Separable Phase Space' (S.P.S.) admitting independent configurations, at least one set of which are statistically equivalent. (2) The notion of 'Dynamical Equivalence' (D.E.), satisfied if and only if (i) all dynamical symmetries are rearranged (not broken) for two Lagrangian formulations of the same problem and if (ii) the expectation values of all the constants of motion are the same, even if their functional expressions are not. The dynamical variables (d.v.) of the S.P.S. are defined from the ('q' and 'c' number) fields of the most general 'Linear Coherent State Representation', more general than those of Glauber and Bogoljubov-Valatin combined. Three independent pairs of d.v. are obtained. D.E. is proven for the Ideal Bose Gas and for a non-linear, interacting zero order Bose problem (I.Z.O.P.). An exact relation is obtained from the action principle, ensuring the cancellation of 'low and high order dangerous diagrams'. From this it follows that D.E. for the exact interacting problem must be demonstrable at infinite order of perturbation, in the finite volume limit. The I.Z.O.P. is posed in the Random Phase Approximation (R.P.A.), free from 'anomalous averages' and solved for the three branches of the excitation spectrum in a pure state description; the lowest branch is gapless, whilst the upper two coincide and show a gap. The standard strategy of linearization is found to be faulty. The partition functions for both superfluid and non-superfluid ensembles are obtained for the I.Z.O.P. in the R.P.A. The coincident upper two branches (in a pure state description) split into a band in thermal equilibrium for the superfluid ensemble, in agreement with an upper band recently observed experimentally. O.D.L.R.O. is found in the second reduced density matrix, but ruled out in the first. Integral equations are obtained in thermal equilibrium - for the I.Z.O.P. in the R.P.A.; which differ, however, from those of existing approaches for the same problem. Most existing theories of S.F. are in fact shown not to predict superfluid behaviour. The present theory is applicable to arbitrary Bose or Fermi systems, whether superfluid or not. O.D.L.R.O. is found to be sufficient for SF. No a priori assumption is made as to the occurrence of Bose-Einstein condensation, its existence being here contingent on the solution of the integral equation; in any case, it is not to be associated with O.D.L.R.O. or S.F.

•Sep 15, 2026•0 citations

Theory of a Charged Boson Gas Using the Random-Phase Approximation

J.C. Lee

The Brandow boson many-body theory is used to calculate the generalized dielectric constant within the random-phase approximation. The generalized dielectric constant obtained this way agrees with the Bogoliubov theory in the high-density limit and thus yields all of the well-known Bogoliubov results. The momentum distribution function for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ensuremath{\ne}0$ is also calculated. The treatment is fully number conserving.

Physical Review A•Apr 1, 1972•2 citations

Comparison of Heisenberg’s New Tamm-Dancoff Method with Approximation Schemes used in Many-Body Theory

K. Bleuler, A. Friederich, Herbert Rainer Petry +1 more

In the theoretical investigation of nonrelativistic feimion systems, several characteristic approximation schemes play a decisive role. Examples are the BCS theory of superconductivity, the Hartree-Fock method in atomic and molecular physics and its generalization by means of the Bogoliubov theory (containing also BCS as a special case) used in nuclear physics. Furthermore, the Random-Phase-Approximation (RPA) is of fundamental importance in plasma physics as well as in the explanation of the well known vibrational states of nuclei. In this connection, it should be pointed out that the socälled nuclear models, which to a certain extent brought nuclear physics into miscredit, represent in fact nothing else but a more or less intuitive substitute for special well defined approximation schemes: the introduction of an average potential in heavy nuclei stands for Hartree-Fock, whereas the so-called surface vibrations visualize RPA. In addition, the possibility to describe elementary excitations by the naive concept of independent particle motion is justified theoretically by the Bogoliubov transformation which leads to the so-called quasi-particles.

Vieweg+Teubner eBooks•Jan 1, 1971•3 citations

Theory of superfluidity

Gretel Quintero Angulo, F Rafael

A theory of superfluidity (S.F.) is developed from first principles using two novel concepts, (1) that of a 'superfluid Ensemble' (S.E.) i.e. a 'Restricted Ensemble' constructed from a 'Separable Phase Space' (S.P.S.) admitting independent configurations, at least one set of which are statistically equivalent. (2) The notion of 'Dynamical Equivalence' (D.E.), satisfied if and only if (i) all dynamical symmetries are rearranged (not broken) for two Lagrangian formulations of the same problem and if (ii) the expectation values of all the constants of motion are the same, even if their functional expressions are not. The dynamical variables (d.v.) of the S.P.S. are defined from the ('q' and 'c' number) fields of the most general 'Linear Coherent State Representation', more general than those of Glauber and Bogoljubov-Valatin combined. Three independent pairs of d.v. are obtained. D.E. is proven for the Ideal Bose Gas and for a non-linear, interacting zero order Bose problem (I.Z.O.P.). An exact relation is obtained from the action principle, ensuring the cancellation of 'low and high order dangerous diagrams'. From this it follows that D.E. for the exact interacting problem must be demonstrable at infinite order of perturbation, in the finite volume limit. The I.Z.O.P. is posed in the Random Phase Approximation (R.P.A.), free from 'anomalous averages' and solved for the three branches of the excitation spectrum in a pure state description; the lowest branch is gapless, whilst the upper two coincide and show a gap. The standard strategy of linearization is found to be faulty. The partition functions for both superfluid and non-superfluid ensembles are obtained for the I.Z.O.P. in the R.P.A. The coincident upper two branches (in a pure state description) split into a band in thermal equilibrium for the superfluid ensemble, in agreement with an upper band recently observed experimentally. O.D.L.R.O. is found in the second reduced density matrix, but ruled out in the first. Integral equations are obtained in thermal equilibrium - for the I.Z.O.P. in the R.P.A.; which differ, however, from those of existing approaches for the same problem. Most existing theories of S.F. are in fact shown not to predict superfluid behaviour. The present theory is applicable to arbitrary Bose or Fermi systems, whether superfluid or not. O.D.L.R.O. is found to be sufficient for SF. No a priori assumption is made as to the occurrence of Bose-Einstein condensation, its existence being here contingent on the solution of the integral equation; in any case, it is not to be associated with O.D.L.R.O. or S.F.

•Jan 1, 1983•0 citations

Boson Systems: Bose–Einstein Condensation and Superfluidity

Michael El-Batanouny

Treats the Bose-Einstein condensation, and explains superfluidity from the Bogoliubov and Ginzburg-Landau perspectives. It also describes the concept of spontaneous symmetry breaking and Goldstone modes.

Cambridge University Press eBooks•Mar 6, 2020•0 citations
The generator-coordinate method, well known in nuclear physics, is employed to derive the Bogoliubov theory of superfluidity of a boson system. The treatment is fully number conserving. Analogies to a normal Fermi system (especially to the random-phase approximation for that system) are pointed out, and some further insight into the nature of superfluidity is gained. Possible generalizations are mentioned.
A theory of superfluidity (S.F.) is developed from first principles using two novel concepts, (1) that of a 'superfluid Ensemble' (S.E.) i.e. a 'Restricted Ensemble' constructed from a 'Separable Phase Space' (S.P.S.) admitting independent configurations, at least one set of which are statistically equivalent. (2) The notion of 'Dynamical Equivalence' (D.E.), satisfied if and only if (i) all dynamical symmetries are rearranged (not broken) for two Lagrangian formulations of the same problem and if (ii) the expectation values of all the constants of motion are the same, even if their functional expressions are not. The dynamical variables (d.v.) of the S.P.S. are defined from the ('q' and 'c' number) fields of the most general 'Linear Coherent State Representation', more general than those of Glauber and Bogoljubov-Valatin combined. Three independent pairs of d.v. are obtained. D.E. is proven for the Ideal Bose Gas and for a non-linear, interacting zero order Bose problem (I.Z.O.P.). An exact relation is obtained from the action principle, ensuring the cancellation of 'low and high order dangerous diagrams'. From this it follows that D.E. for the exact interacting problem must be demonstrable at infinite order of perturbation, in the finite volume limit. The I.Z.O.P. is posed in the Random Phase Approximation (R.P.A.), free from 'anomalous averages' and solved for the three branches of the excitation spectrum in a pure state description; the lowest branch is gapless, whilst the upper two coincide and show a gap. The standard strategy of linearization is found to be faulty. The partition functions for both superfluid and non-superfluid ensembles are obtained for the I.Z.O.P. in the R.P.A. The coincident upper two branches (in a pure state description) split into a band in thermal equilibrium for the superfluid ensemble, in agreement with an upper band recently observed experimentally. O.D.L.R.O. is found in the second reduced density matrix, but ruled out in the first. Integral equations are obtained in thermal equilibrium - for the I.Z.O.P. in the R.P.A.; which differ, however, from those of existing approaches for the same problem. Most existing theories of S.F. are in fact shown not to predict superfluid behaviour. The present theory is applicable to arbitrary Bose or Fermi systems, whether superfluid or not. O.D.L.R.O. is found to be sufficient for SF. No a priori assumption is made as to the occurrence of Bose-Einstein condensation, its existence being here contingent on the solution of the integral equation; in any case, it is not to be associated with O.D.L.R.O. or S.F.
In the theoretical investigation of nonrelativistic feimion systems, several characteristic approximation schemes play a decisive role. Examples are the BCS theory of superconductivity, the Hartree-Fock method in atomic and molecular physics and its generalization by means of the Bogoliubov theory (containing also BCS as a special case) used in nuclear physics. Furthermore, the Random-Phase-Approximation (RPA) is of fundamental importance in plasma physics as well as in the explanation of the well known vibrational states of nuclei. In this connection, it should be pointed out that the socälled nuclear models, which to a certain extent brought nuclear physics into miscredit, represent in fact nothing else but a more or less intuitive substitute for special well defined approximation schemes: the introduction of an average potential in heavy nuclei stands for Hartree-Fock, whereas the so-called surface vibrations visualize RPA. In addition, the possibility to describe elementary excitations by the naive concept of independent particle motion is justified theoretically by the Bogoliubov transformation which leads to the so-called quasi-particles.
A theory of superfluidity (S.F.) is developed from first principles using two novel concepts, (1) that of a 'superfluid Ensemble' (S.E.) i.e. a 'Restricted Ensemble' constructed from a 'Separable Phase Space' (S.P.S.) admitting independent configurations, at least one set of which are statistically equivalent. (2) The notion of 'Dynamical Equivalence' (D.E.), satisfied if and only if (i) all dynamical symmetries are rearranged (not broken) for two Lagrangian formulations of the same problem and if (ii) the expectation values of all the constants of motion are the same, even if their functional expressions are not. The dynamical variables (d.v.) of the S.P.S. are defined from the ('q' and 'c' number) fields of the most general 'Linear Coherent State Representation', more general than those of Glauber and Bogoljubov-Valatin combined. Three independent pairs of d.v. are obtained. D.E. is proven for the Ideal Bose Gas and for a non-linear, interacting zero order Bose problem (I.Z.O.P.). An exact relation is obtained from the action principle, ensuring the cancellation of 'low and high order dangerous diagrams'. From this it follows that D.E. for the exact interacting problem must be demonstrable at infinite order of perturbation, in the finite volume limit. The I.Z.O.P. is posed in the Random Phase Approximation (R.P.A.), free from 'anomalous averages' and solved for the three branches of the excitation spectrum in a pure state description; the lowest branch is gapless, whilst the upper two coincide and show a gap. The standard strategy of linearization is found to be faulty. The partition functions for both superfluid and non-superfluid ensembles are obtained for the I.Z.O.P. in the R.P.A. The coincident upper two branches (in a pure state description) split into a band in thermal equilibrium for the superfluid ensemble, in agreement with an upper band recently observed experimentally. O.D.L.R.O. is found in the second reduced density matrix, but ruled out in the first. Integral equations are obtained in thermal equilibrium - for the I.Z.O.P. in the R.P.A.; which differ, however, from those of existing approaches for the same problem. Most existing theories of S.F. are in fact shown not to predict superfluid behaviour. The present theory is applicable to arbitrary Bose or Fermi systems, whether superfluid or not. O.D.L.R.O. is found to be sufficient for SF. No a priori assumption is made as to the occurrence of Bose-Einstein condensation, its existence being here contingent on the solution of the integral equation; in any case, it is not to be associated with O.D.L.R.O. or S.F.