Condensed Matter Physics

GENERALIZED CONDENSATION AND THE BOGOLIUBOV THEORY OF SUPERFLUIDITY

Zagrebnov

Published Jan 1, 2000• 6 citations

Abstract

In this paper we scrutinize the Bogoliubov theory of superfluidity on the level of the first Bogoliubov ansatz.This ansatz preconizes the Bogoliubov truncated Hamiltonian as a starting point of this theory.Since this ansatz is based on the hypothesis concerning the Bose-Einstein condensation in zero-mode as well as on its stability with respect to interactions, we present some rigorous results, which cast doubt on this hypothesis.

DOI: 10.5488/cmp.3.2.265

Related papers

Bose–Einstein Condensation

Tim Byrnes, Ebubechukwu O. Ilo-Okeke

This chapter introduces the basic physics of Bose--Einstein condensation. We first start with why there is a difference between distinguishable and indistinguishable particles in terms of the number of states that are available in a composite system. Then Bose and Einstein's argument of why one expects a high probability of occupation of the ground state is discussed. This is derived then more rigorously for the grand canonical ensemble, showing that at some critical temperature there should be a macroscopic occupation of the ground state. Next, the low-lying energy spectrum of an interacting Bose--Einstein condensate is derived, leading to the Bogoliubov dispersion. The significance of the Bogoliubov dispersion as the origin of superfluidity is then discussed, in terms of superfluditysuperfluidity. Laudau'sLandau's criterion for superfluidity is derived, by general principles of Galilean transformations of Schrodinger's equation.

Cambridge University Press eBooksJul 23, 20211 citation

A century of the Bose–Einstein condensation concept and half a century of the JINR experiments for observation of condensate in superfluid 4He (He II)

Valentin Anatol'evich Zagrebnov

This short review is devoted to the celebration of two major events in quantum physics. The first one is the birth of the concept of Bose–Einstein condensation (1925) and the second is the experimental proof that it does exist and appears in liquid 4He simultaneously with superfluidity below the λ-point (1975).Both of these events are tightly related to the Bogoliubov theory of superfluidity (1947). The existence of condensate in the system of interacting bosons is the key ansatz of this theory. Therefore, the experiments started at JINR-Dubna in 1975 confirmed this prediction of the Bogoliubov theory that superfluidity of liquid 4He (He II) should emerge at the same time as the Bose–Einstein condensation. Corrected: 13 November 2025 (the captions to Figures 1 and 2 were changed)26 November 2025 (changes were made in formulas (53) and (55))

arXiv:2510.03378Natural Science ReviewNov 7, 20250 citations

Formulation for the zero mode of a Bose-Einstein condensate beyond the Bogoliubov approximation

Yusuke Nakamura, J. Takahashi, Y. Yamanaka

The unperturbed Hamiltonian for the Bose-Einstein condensate, which includes not only the first and second powers of the zero mode operators but also the higher ones, is proposed to determine a unique and stationary vacuum at zero temperature. From the standpoint of quantum field theory, it is done in a consistent manner that the canonical commutation relation of the field operator is kept. In this formulation, the condensate phase does not diffuse and is robust against the quantum fluctuation of the zero mode. The standard deviation for the phase operator depends on the condensed atom number with the exponent of $\ensuremath{-}1/3$, which is universal for both homogeneous and inhomogeneous systems.

arXiv:1311.5302Physical Review AJan 16, 201422 citations

Bose gases in the Gross–Pitaevskii limit: A survey of some rigorous results

Benjamin Schlein

We review some mathematical work on the Bose gas in the Gross–Pitaevskii regime. We start with the classical results by Lieb, Seiringer and Yngvason on the ground-state energy and by Lieb and Seiringer on the existence of Bose–Einstein condensation. Afterwards, we discuss some more recent progress, based on a rigorous version of Bogoliubov theory.

arXiv:2203.10855EMS Press eBooksJun 29, 20229 citations

Colloquium: Bulk Bogoliubov excitations in a Bose-Einstein condensate

Roee Ozeri, Nadav Y. Katz, Jeff Steinhauer +1 more

Bogoliubov theory for excitations in Bose-Einstein condensates was formulated over 50 years ago to qualitatively explain strongly interacting superfluids. Quantitative experimental verification of this theory came with the long-awaited realization of gaseous, weakly interacting condensates. This Colloquium reviews recent experimental advances in the study of Bogoliubov bulk excitations in Bose-Einstein condensates, obtained using two-photon Bragg scattering.

Reviews of Modern PhysicsApr 8, 2005187 citations

ON THEORY OF BOSE-EINSTEIN CONDENSATION OF PARTICLES WITH ARBITRARY INTEGER SPIN

Abdus Salam

The Bogoliubov theory of weakly interacting Bose gas is generalized to Bose-Einstein condensates (BEC) of particles with arbitrary integer spin in a magnetic eld. On the basis of the Bogoliubov method of quasiaverages, an equation for the condensate wave function is obtained. The ground state properties, thermodynamic stability, and excitation spectra of such BEC are studied. The obtained results are compared to spin-1 Bose condensate.

Jan 1, 20050 citations