A consistent form of reduced density matrices of superfluids

P. Thiankusol, Kitt Visoottiviseth

В. А. Головко

The hierarchy of equations for reduced density matrices that describes a thermodynamically equilibrium quantum system obtained earlier by the author is investigated in the momentum representation. In the paper it is shown that the use of the momentum representation opens up new opportunities in studies of macroscopic quantum systems both nonsuperfluid and superfluid. It is found that the distribution over momenta in a quantum fluid is not a Bose or Fermi distribution even in the limit of practically noninteracting particles. The distribution looks like a Maxwellian one although, strictly speaking, it is not Maxwellian. The momentum distribution in a quantum crystal depends upon the interaction potential and the crystalline structure. The momentum distribution in a superfluid contains a delta function. The momentum distribution for the condensate in a superfluid crystal consists of delta peaks that are arranged periodically in momentum space. The periodical structure remains if the condensate crystal is not superfluid.

H. Haug, K. Weiss

В. А. Головко

The hierarchy of equations for reduced density matrices relevant to thermodynamic equilibrium with account taken of the spin obtained earlier is modified in order to describe the state of a Fermi system with a condensate. Although the procedure is to some extent analogous with the one carried out by the author earlier for a Bose liquid peculiarities relevant to Fermi statistics complicate considerably the treatment. As in the case of the Bose liquid the condensate phase can be superfluid as well as nonsuperfluid, the physical causes of superfluidity being identical. A new mechanism of fermion pairing that acts even in the case of a purely repulsive Hamiltonian is pointed out. Special attention is given to the thermodynamics of a superfluid Fermi system. The example of a hard-sphere system is used to find out the form of phase diagrams, the character of the phase transition to a condensate phase and the properties of the last. Noticeable dissimilarities from a Bose system with the same Hamiltonian are revealed. Application of the present approach to superconductivity is discussed as well.

MANFRED L. RISTIG, G. Senger, Mohammed Serhan +1 more

Luis M. Tel, Encarnación Pérez-Romero, F. J. Casquero +1 more

The objective of this paper is to identify the necessary and sufficient minimum information carried by Reduced Density Matrices (RDMs). This minimum of essential information determines a set of equivalent compact-form matrices that are devoid of the redundant information present in the original RDMs when the system possesses symmetry invariances. The basic properties and algebra operations of these compact-form matrices are obtained here. The use of these new mathematical objects renders far more economical the operations and storage of RDMs and will thus be of interest in the study of systems with symmetry invariances. In particular, it opens the possibility of using large basis for medium-sized systems when solving iteratively the contracted Schr\"odinger equation.