Phase space distributions from variation of information measures

F. OLIVARES; F. PENNINI; A. PLASTINO

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

ELSEVIER SCIENCE BV

Lugar: NORTH-HOLLAND; Año: 2010 vol. 389 p. 2218 - 2226

0378-4371

Variational approaches constitute paradigmatic tools of theoretical physics, actions or energies being the preferred quantities for such procedures, underlying the most important physical theories (PTs) [1]. In the information theory approach to the subject, these quantities are replaced by information measures, and great progress has been made in trying to give an information basis to the above mentioned PTs [29]. Indeed, one of the major challenges of information physics, in the wake of Wheeler´s celebrated dictum ``it from bit´´, is to show that the whole of physics can be derived from information theoretic concepts [10,11], a program usually referred to as Wheeler´s one. In this communication we intend to fill a gap in such program with reference to special kinds of distributions. It will be shown that the most important phase space distributions, namely, Wigner´s [12] and Husimi´s [13], also emerge from the variation of information measures, at least in the case of the harmonic oscillator (HO). This is such an important system that corresponding insights usually have a wide impact, as the HO constitutes much more than a mere example. Nowadays it is of particular interest for the dynamics of bosonic or fermionic atoms contained in magnetic traps as well as for any system that exhibits an equidistant level spacing in the vicinity of the ground state, like nuclei or Luttinger liquids [1416].