Open AccessKinetic energy of Bose systems and variation of statistical averages
Author(s) -
Yukalov V. I.
Publication year - 2006
Publication title -
laser physics letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.59
H-Index - 72
eISSN - 1612-202X
pISSN - 1612-2011
DOI - 10.1002/lapl.200510065
Subject(s) - kinetic energy , adiabatic process , operator (biology) , internal energy , derivative (finance) , parametric statistics , energy (signal processing) , physics , second derivative , statistical physics , thermodynamics , mathematics , mathematical analysis , quantum mechanics , statistics , chemistry , biochemistry , repressor , gene , transcription factor , financial economics , economics
The problem of defining the average kinetic energy of statistical systems is addressed. The conditions of applicability for the formula, relating the average kinetic energy with the mass derivative of the internal energy, are analysed. It is shown that incorrectly using this formula, outside its region of validity, leads to paradoxes. An equation is found for a parametric derivative of the average for an arbitrary operator. A special attention is paid to the mass derivative of the internal energy, for which a general formula is derived, without invoking the adiabatic approximation and taking into account the mass dependence of the potentialenergy operator. The results are illustrated by the case of a lowtemperature dilute Bose gas. (© 2006 by Astro, Ltd. Published exclusively by WILEY‐VCH Verlag GmbH & Co. KGaA)