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Progress of Theoretical Physics

Commutativity of Velocity Operators in a System of Bose Particles

Shuichiro Yamasaki, T. Kebukawa, Sigenobu Sunakawa

Published Nov 1, 1973• 1 citation
Publisher

Abstract

The commutator of the velocity operators which are appropriate for the collective description of an interacting Bose system is found to be zero. On the basis of this result, it will be shown that the collective description of many-Boson system is always possible without a subsidiary condition k×Vk|>=0.
DOI
10.1143/ptp.50.1490

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The hydrodynamical description of an interacting many boson system given in the foregoing papers is studied more carefully by making use of the so-called hydrodynamical approximation in the lattice space that the expectation value of the particle number in a cell is very large. We get the commutation relation of the velocity operator due to Landau and Thellung and the roton spectrum is computed. The phonon spectrum is obtained in the relation to the ground state of the system and the sound speed is evaluated for the rigid sphere problem. Further the relationship to the collective description of Bohm and Pines is discussed.
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A new well-defined velocity operator is proposed for the collective description of a many-boson system. It is shown that the new velocity operator is irrotational. The Hamiltonian of the system is successfully described in terms of the density-fluctuation operator and the velocity operator. The interaction term in the order of N-1 has a different form from that in previous papers. The range of validity of the present formalism is discussed in the final section in answer to the questions raised so far on the collective formalism of the many-boson system.