The Liouville equation in infinitely dimensional separable Hilbert space
type: Item
instance of: scholarly article
title: The Liouville equation in infinitely dimensional separable Hilbert space
zbMATH Open document ID: 0588.70014
published in: Bulletin of the Polish Academy of Sciences. Technical Sciences
publication date: 1985-01-01T00:00:00Z
review text: The Liouville equation is derived in the case when the phase space of a system with an infinite countable number of degrees of freedom is an infinitely dimensional separable Hilbert space. For such systems it is possible to define the counterparts of the basic concepts of mechanics with a finite number of degrees of freedom. In this work, use is made of the counterpart of the notion of divergence. The almost-invariant measure was assumed as the initial state of the system with an infinite countable number of degrees of freedom. The obtained Liouville equation contains an additional term dependent also on the assumed initial state which vanished when we pass to a system with a finite number of degrees of freedom but which is not equal to zero when we consider a system with an infinite countable number of degrees of freedom.
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 46N99
Mathematics Subject Classification ID: 46C99
zbMATH DE Number: 3945399
zbMATH Keywords: infinite countable number of degrees of freedom
zbMATH Keywords: Liouville equation
zbMATH Keywords: infinitely dimensional separable Hilbert space
zbMATH Keywords: almost-invariant measure
author: Janusz Szczepański
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3945399