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

NEW TRANSFORMATION FOR A NON-IDEAL BOSE SYSTEM

V. N. Minasyan, V. N. Samoylov

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

We present a new simple transformation for a dilute Bose gas with weak interactions between the atoms, used to describe superfluid liquid helium. This transformation, together with the Frohlich unitary transformation, leads to the formation of Bogoliubov quasiparticles. In this respect, we find the equation for density atoms in the condensate which coincides with Bogoliubov's famous equation.

Related papers

ELEMENTARY EXCITATION INTERACTIONS IN BOSE FLUIDS IN THE BOGOLIUBOV APPROXIMATION

Srećko Kilić

The effective interaction energy of quasiparticles in the Bose fluid, which is described by ”ladder state diagrams” in the Bogoliubov approximation, was studied for a model potential. It is shown that in the Bogoliubov approximation, the interaction of excitations in liquid He can not be described even qualitatively. It means that a model of the weakly interacting dilute Bose gas fails in describing the interaction between excitation in Bose-condensed liquid, although this model qualitatively incorporates superfluidity in itself.

•Jan 1, 2012•0 citations

Weakly Interacting Bose Gas

Lukong Cornelius Fai

This chapter examines a simple example of a quantum liquid that is a weakly nonideal gas. In this case, the interaction among gas particles is relatively small. The chapter examines a weakly interacting Bose gas at almost zero temperature. Interactions in atomic gases are usually very weak, but they can have important effects. It shows that the interactions among gas particles are repulsive. This implies that the scattering amplitude is positive. It is important to note that for the case of a Bose gas, the assumption is connected with the fact that even for infinitesimal attractive forces, a Bose gas cannot remain dilute at low temperatures. All particles in the condensate are in the ground state of an ideal Bose gas. This is for the zero-state energy. The gas is often said to be in the condensate or the condensed state. The diagonalization is done by introducing the canonical transformation known as a Bogoliubov transformation.

CRC Press eBooks•Jun 20, 2019•0 citations

Creation of neutron spinless pairs in a superfluid liquid $^4$He and a neutron gas mixture

V. N. Minasyan

First, the creation of a free neutron spinless pairs is predicted in a superfluid liquid $^4$He and a neutron gas mixture. For solving the given problem, it is presented an exact solution to the model of dilute Bose gas as an extension of the Bogoliubov model, at quantity of the condensate fraction varying in the state $0\leq\frac{N_0}{N}\leq 1$, which in turn might be useful for a description of the superfluid liquid $^4$He. Due to an application of presented new model of dilute Bose gas, we prove that an appearance of atoms in the condensate is a suppressor for the collective modes as well as a creator for single-particle excitations On other hand, it is shown that the terms of the interaction between the Bogoliubov excitations (Bogoliubov phonon-roton modes) and the density modes of the neutron meditate an attractive interaction via the neutron modes, which in turn leads to a bound state on a spinless neutron pair.

arXiv:0803.4433•Mar 31, 2008•1 citation

Quantization of Circulation in a Non-Ideal Bose Gas

Franklin Pollock

The dilute Bose gas is considered in the Bogoliubov approximation for the purpose of accounting for the quantization of circulation for the entire superfluid. It is found that the states of lowest energy have the motion of the entire system governed by the condensate.

The Physics of Fluids•Mar 1, 1967•11 citations

A condition for the Bose-Einstein transition in the superfluid liquid helium

V. N. Minasyan

First, a condition for the Bose-Einstein transition in the superfluid liquid helium is presented due to the creation of a free neutron spinless pairs in a liquid helium and a dilute neutron gas mixture. We proposed a new model of dilute Bose gas, where presence atoms in the condensate is a suppressor for the collective modes as well as a creator for single-particle excitations On other hand, it is shown that the terms, of the interaction between the excitations of the Bose gas and the density modes of the neutron, meditate an attractive interaction via the neutron modes, which in turn leads to a bound state on a spinless neutron pair. The lambda transition is defined by a condition for the Bose-Einstein transition, which transforms reflected neutron pair modes to single neutron modes.

arXiv:0804.1220•Apr 8, 2008•0 citations

Thermodynamics of a Bose-Einstein condensate with weak disorder

G. M. Falco, Axel Pelster, R. Graham

We consider the thermodynamics of a homogeneous superfluid dilute Bose gas in the presence of weak quenched disorder. Following the zero-temperature approach of Huang and Meng, we diagonalize the Hamiltonian of a dilute Bose gas in an external random $\ensuremath{\delta}$-correlated potential by means of a Bogoliubov transformation. We extend this approach to finite temperature by combining the Popov and the many-body $T$-matrix approximations. This approach permits us to include the quasiparticle interactions within this temperature range. We derive the disorder-induced shifts of the Bose-Einstein critical temperature and of the temperature for the onset of superfluidity by approaching the transition points from below, i.e., from the superfluid phase. Our results lead to a phase diagram consistent with that of the finite-temperature theory of Lopatin and Vinokur which was based on the replica method, and in which the transition points were approached from above.

arXiv:cond-mat/0702123•Physical Review A•Jun 19, 2007•67 citations
We present a new simple transformation for a dilute Bose gas with weak interactions between the atoms, used to describe superfluid liquid helium. This transformation, together with the Frohlich unitary transformation, leads to the formation of Bogoliubov quasiparticles. In this respect, we find the equation for density atoms in the condensate which coincides with Bogoliubov's famous equation.
The effective interaction energy of quasiparticles in the Bose fluid, which is described by ”ladder state diagrams” in the Bogoliubov approximation, was studied for a model potential. It is shown that in the Bogoliubov approximation, the interaction of excitations in liquid He can not be described even qualitatively. It means that a model of the weakly interacting dilute Bose gas fails in describing the interaction between excitation in Bose-condensed liquid, although this model qualitatively incorporates superfluidity in itself.
This chapter examines a simple example of a quantum liquid that is a weakly nonideal gas. In this case, the interaction among gas particles is relatively small. The chapter examines a weakly interacting Bose gas at almost zero temperature. Interactions in atomic gases are usually very weak, but they can have important effects. It shows that the interactions among gas particles are repulsive. This implies that the scattering amplitude is positive. It is important to note that for the case of a Bose gas, the assumption is connected with the fact that even for infinitesimal attractive forces, a Bose gas cannot remain dilute at low temperatures. All particles in the condensate are in the ground state of an ideal Bose gas. This is for the zero-state energy. The gas is often said to be in the condensate or the condensed state. The diagonalization is done by introducing the canonical transformation known as a Bogoliubov transformation.
Creation of neutron spinless pairs in a superfluid liquid 4^44He and a neutron gas mixture
First, the creation of a free neutron spinless pairs is predicted in a superfluid liquid 4^44He and a neutron gas mixture. For solving the given problem, it is presented an exact solution to the model of dilute Bose gas as an extension of the Bogoliubov model, at quantity of the condensate fraction varying in the state 0≤N0N≤10\leq\frac{N_0}{N}\leq 10≤NN0​​≤1, which in turn might be useful for a description of the superfluid liquid 4^44He. Due to an application of presented new model of dilute Bose gas, we prove that an appearance of atoms in the condensate is a suppressor for the collective modes as well as a creator for single-particle excitations On other hand, it is shown that the terms of the interaction between the Bogoliubov excitations (Bogoliubov phonon-roton modes) and the density modes of the neutron meditate an attractive interaction via the neutron modes, which in turn leads to a bound state on a spinless neutron pair.
First, a condition for the Bose-Einstein transition in the superfluid liquid helium is presented due to the creation of a free neutron spinless pairs in a liquid helium and a dilute neutron gas mixture. We proposed a new model of dilute Bose gas, where presence atoms in the condensate is a suppressor for the collective modes as well as a creator for single-particle excitations On other hand, it is shown that the terms, of the interaction between the excitations of the Bose gas and the density modes of the neutron, meditate an attractive interaction via the neutron modes, which in turn leads to a bound state on a spinless neutron pair. The lambda transition is defined by a condition for the Bose-Einstein transition, which transforms reflected neutron pair modes to single neutron modes.
We consider the thermodynamics of a homogeneous superfluid dilute Bose gas in the presence of weak quenched disorder. Following the zero-temperature approach of Huang and Meng, we diagonalize the Hamiltonian of a dilute Bose gas in an external random $\ensuremath{\delta}$-correlated potential by means of a Bogoliubov transformation. We extend this approach to finite temperature by combining the Popov and the many-body TTT-matrix approximations. This approach permits us to include the quasiparticle interactions within this temperature range. We derive the disorder-induced shifts of the Bose-Einstein critical temperature and of the temperature for the onset of superfluidity by approaching the transition points from below, i.e., from the superfluid phase. Our results lead to a phase diagram consistent with that of the finite-temperature theory of Lopatin and Vinokur which was based on the replica method, and in which the transition points were approached from above.