Kirill Ilinski

q-functional Wick's theorems for particles with exotic statistics

In this paper we begin by giving a description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and are the q-generalization of the coloured particles which appear in many problems of condensed matter physics, magnetism and quantum optics. Motivated by the general ideas of standard field theory we prove the q-functional analogues of Horis formulation of Wicks theorems for the different ordered q-particle creation and annihilation operators. The formulae have the same formal expressions as fermionic and bosonic ones but differ by the nature of fields. This allows us to derive the perturbation series for the theory and develop analogues of standard quantum field theory constructions in q-functional form.In the paper we begin a description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and are the q-generalization of the colored particles which appear in many problems of condensed matter physics, magnetism and quantum optics. Motivated by the general ideas of standard field theory we prove the q-functional analogues of Horis formulation of Wicks theorems for the different ordered q-particle creation and annihilation operators. The formulae have the same formal expressions as fermionic and bosonic ones but differ by a nature of fields. This allows us to derive the perturbation series for the theory and develop analogues of standard quantum field theory constructions in q-functional form.

q-Functional field theory for particles with exotic statistics

In the paper we give consecutive description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and appear in many problems of condensed matter physics, magnetism and quantum optics. Motivated by the general ideas of standard field theory we derive formulae in q-functional derivatives for the partition function and Greens functions generating functional for systems of exotic particles. This leads to a corresponding perturbation series and a diagram technique. Results are illustrated by a consideration of an one-dimensional q-particle system and compared with some exact expressions obtained earlier.Abstract In the paper we give a consecutive description of functional methods of quantum field theory for systems of interacting q -particles. These particles obey exotic statistics and appear in many problems of condensed matter physics, magnetism and quantum optics. Motivated by the general ideas of standard field theory we derive formulae in q -functional derivatives for the partition function and Greens functions generating functional for systems of exotic particles. This leads to a corresponding perturbation series and a diagram technique. Results are illustrated by a consideration of a one-dimensional q -particle system and compared with some exact expressions obtained earlier.

Aspect ratio analysis for ground states of bosons in anisotropic traps

Characteristics of the initial condensate in the recent experiment on Bose-Einstein condensation (BEC) of87Rb atoms in an anisotropic magnetic trap is discussed. Given the aspect ratioR, the quality of BEC is estimated. A simple analytical Ansatz for the initial condensate wave function is proposed as a function of the aspect ratio which, in contrast to the Baym-Pethick trial wave function, can be used for any interaction strength, reproduces both the weak and the strong interaction limits, and which is in better agreement with numerical results than the latter.

Aspect Ratio Analysis for Ground States of Bosons in Anisotropic Traps

Characteristics of the initial condensate in the recent experiment on Bose-Einstein condensation (BEC) of 87Rb atoms in an anisotropic magnetic trap are discussed. Given the aspect ratio R, the quality of BEC is estimated. A simple analytical ansatz for the initial condensate wave function is proposed as a function of the aspect ratio which, in contrast to the Baym-Pethick trial wave function, can be used for any interaction strength, reproduces both the weak and the strong interaction limits, and which is in better agreement with numerical results than the latter.