ON THE SPATIAL DENSITY-MATRIX FOR THE CENTER-OF-MASS OF A ONE-DIMENSIONAL PERFECT GAS

We examine the reduced density matrix of the centre of mass on positio n basis considering a one-dimensional system of N noninteracting disti nguishable particles in a infinitely deep square potential well. We fi nd a class of pure states of the system for which the off-diagonal ele ments of the matrix above go to zero as N increases. This property hol ds also for the state vectors which are factorized in the single parti cle wave functions. In this last case, if the average energy of each p article is less than a common bound, the diagonal elements are distrib uted according to the normal law with a mean square deviation which be comes smaller and smaller as N increases towards infinity. Therefore w hen the state vectors are of the type considered we cannot experience spatial superpositions of the centre of mass and we may conclude that position is a preferred basis for the collective variable.