Properties of nonclassical maximum-entropy states
Istok P. Mendaš, Marko Djordjević, M Markovic · Journal of Physics A Mathematical and General · 2000
The density matrix in the position and momentum representation, the position-momentum uncertainty product, the Wigner and Q functions, and thermal properties of the family of the nonclassical maximum-entropy states of a single harmonic oscillator are determined. Any such state, having the mean number of quanta n , has the uncertainty product x p = (2 n +1)( /2), and this product attains its minimum value for the temperature parameter 0. Generically, the Wigner function has alternating sign so that the underlying maximum-entropy state is truly nonclassical. The von Neumann entropy and the heat capacity, expressed via the temperature parameter , coincide with the corresponding quantities for the thermal state. The properties discussed here are of interest for the description and analysis of the vibrational motion of a trapped ion in a harmonic-oscillator potential since the equilibrium states which result under certain conditions are the maximum-entropy states.