Superfluidity of classical liquid in a nanotube for even and odd numbers of neutrons in a molecule
type: Item
instance of: scholarly article
title: Superfluidity of classical liquid in a nanotube for even and odd numbers of neutrons in a molecule
zbMATH Open document ID: 1176.82048
author: V. P. Maslov
published in: Theoretical and Mathematical Physics
publication date: 2008-09-23T00:00:00Z
review text: This paper deals with mean-fields equations of the type \[ ih(\varphi '(x))_t=\left(-\frac{h^2}{2m}\Delta +W_t(x)\right)\varphi^t(x),\quad W_t(x)=U(x)+\int dyV(x,y)| \varphi ^t(y)| ^2, \] subject to the initial conditions \(\varphi (x,0)=\varphi_0(x)\), where \(\varphi_0\in W_2^\infty ({\mathbb R}^\nu )\). These equations arise in the study of various superfluidity phenomena occurring for classical liquids in nanotubes. The theory developed in the present paper establishes that the viscosity is connected with collisions of particles. In the case of a nanotube, the presence of the Bose condensate leads to the weakening of viscosity and consequently to superfluidity. The author also establishes that the major role in fermionic superfluidity is played by the attraction at long distances, while the repulsion at short distances is important for the appearance of bosonic superfluidity. In both cases, the transition to the condensate state (for pairs in the Fermi liquid) is a phase transition that has no relation to superfluidity. The proofs strongly rely on variational arguments combined with analytic tools.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 82D50
Mathematics Subject Classification ID: 82D75
zbMATH DE Number: 5346138
zbMATH Keywords: superfluidity
zbMATH Keywords: boson
zbMATH Keywords: fermion
Wikidata QID: Q114223339
MaRDI profile type: Publication
full work available at URL: s11232-007-0140-y
OpenAlex ID: W2165532546
cites work: The complex germ method for statistical mechanics of model systems
cites work: Quantization of thermodynamics, ultrasecondary quantization, and a new variational principle.
cites work: A generalization of the second quantization method to the case of special tensor products of Fock spaces and quantization of free energy
cites work: Super-second quantisation and entropy quantisation with charge conservation
cites work: Ultratertiary quantization of thermodynamics
cites work: Dependence of the superfluidity criterion on the capillary radius
cites work: Quantization of Boltzmann entropy: Pairs and correlation function
cites work: Averaging method for a large number of clusters: Phase transitions
cites work: Ultra-second quantization and ``ghosts'' in quantized entropy
cites work: Q5530857
DOI: 10.1007/S11232-007-0140-Y
description: scientific article; zbMATH DE number 5346138