Takeji Kebukawa

On the Velocity Operator in Many-Boson System

Garrison, Morrison and W ong,l> however, have recently shown that the commutation relation (1) is inconsistent with the nonnegative character of the density operator, and asserted that existence of the velocity operator which satisfies the relation (1) is not admissible. The point of their arguments is essentially equivalent to the wellknown theorem that canonical variables satisfying a canonical commutation relation have as eigenvalues all real numbers from + oo to oo (e.g. see reference 2)). Their assertion is quite correct if one introduces the velocity operator as a canonical conjugate of the density operator itself defined by p(x)=cf;*(x)c{;(x) or by p(x)=(1/N) X2]aJ(x-ra).3l It is however a hasty conclusion to assert non-existence of the velocity operator which satisfies the commutation relation (1). The interacting Bose system enclosed in a cubic box of volume Q is represented by the Hamiltonian h2 H= 2m itk2ak*ak

Theory of ac Josephson Effect in Superfluid Helium

A microscopic theory of the ac Josephson effect in superfluid helium is proposed on the basis of the Heisenberg equation of the dressed-boson operators. The equation is solved exactly. The interference of the two eigen-oscillations in the exact solution produces the Josephson oscillation. It is verified that the oscillation occurs even when the quantum fluctuation of the relative phase is infinitely large. On the basis of these results, we propose an experiment to detect the tunnelling effect of the dressed-bosons. The formulation of this paper can be applied to the Josephson effect in superconductor.

Josephson Oscillation in Superfluid Helium

Abstract A microscopic theory is presented which interprets the Josephson oscillation in superfluid helium in the light of the Heisenberg equations for dressed-bosons.The equations are exactly solved to yield the solutions in the form of a linear combination of two eigen-oscillations. Consequently it is shown that the interference of these eigen-oscillations produces the Josephson oscillation in superfluid helium, and that the Josephson oscillation occurs even when the quantum fluctuation of the relative phase is infinitely large. These results lead us to propose an experiment to detect the tunneling effect of the dressed-bosons. The formulation in this paper can be applied to the Josephson oscillation in superconductors.