Density and Phase Variables in the Theory of Interacting Bose Systems

Murray Holland

Summary form only given. The dilute gas experiments on the Bose-Einstein condensation of magnetically confined alkali vapors have already generated widespread interest across a broad spectrum of traditional fields of physics. They have provided an exciting stage on which to build bridges linking the theory of complex and collective phenomena in superconducting and superfluid systems with the single particle microscopic physics described in quantum optics and laser physics. The approach I discuss is based on a derivation of the quantum kinetic theory from first principles. Based on a microscopic picture of the weakly interacting bosonic gas, a generalized kinetic theory for a Markovian many-body density operator is derived. The density operator is functionally dependent on a few key variables, which must be carefully chosen. These quantities serve as master variables and determine the system's evolution on a coarse-grained time scale. The weak interactions allow a perturbative expansion of the evolution, from which kinetic equations that describe the dynamics of the expectation value of any single-time observable are obtained. The final structure of the theory has many analogies with the quantum theory of the laser, such as amplitude and phase noise for the macroscopic field, squeezing dynamics, and a nonlinear master equation describing the underlying evolution.

精久 松田

Sigenobu Sunakawa, Hiroshi Nakatani, Yoshimatsu Yokoo

The collective behavior of the three-dimensional Bose system is investigated. Along the line of reasoning of the preceding paper, the momentum density operator is modified and it is shown that the modified momentum density operator is equivalent to the velocity operator of the quantum hydrodynamics. The Hamiltonian is described in terms of the collective variables for the case of irrotational motion. The result is compared with other theories.

Vivek B. Shenoy

Gergely T. Zimányi

Yoshikazu Suzumura, Tetsuro Saso

The effect of impurities on a spin-density wave (SDW) state in one-dimensional interacting electron systems is investigated by applying a phase representation and the theory of the weak impurity pinning. With the help of numerical simulation, it is shown that the pinned SDW is characterized by both a rapidly varying phase variable of the spin-density fluctuation and a slowly varying phase variable of the charge-density fluctuation. Based on this, the critical condition on the magnitude of interactions for localization-delocalization transition is determined by use of the self-consistent harmonic approximation.