arXiv subjects

G. V. Kalinin

Publications and source records attributed to G. V. Kalinin.

5 recordsLinked to original sources

arXiv1997

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 Green's 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.

hep-th↗

arXiv1997

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

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 Hori's formulation of Wick's 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.

hep-th↗

arXiv1995

Exact results on linear response of cyclic molecular aggregates

Basing on the picture of Frenkel excitons in molecular crystals described by the XY-model we consider the linear response of linear cyclic aggregates at finite temperature. The exact results for characteristics of the response are obtained. In particular, we calculate time-dependent two-point correlation functions at finite temperature for the cyclic 1-D XY-model.

cond-mat↗

arXiv1995

Exchange statistics in 1D: from the viewpoint of exact solution

We show that the exchange statistics have consequences in 1D systems with compact topology, contrary to the common opinion that exchange statistics is arbitrary in 1D. As examples of non-trivial statistical behavior we exactly calculate the partition function and correlators for systems of free q-particles on compactified chains using functional integral techniques and the supersymmetric trick. In particular we consider a spin 1/2 XY-chain with periodic boundary conditions that corresponds to the case of q=-1.

hep-th↗

arXiv1994

Supersymmetric Berry Index

We revise the sequences of SUSY for a cyclic adiabatic evolution governed by the supersymmetric quantum mechanical Hamiltonian. The condition (supersymmetric adiabatic evolution) under which the supersymmetric reductions of Berry (nondegenerated case) or Wilczek-Zee (degenerated case) phases of superpartners are taking place is pointed out. The analogue of Witten index (supersymmetric Berry index) is determined. As the examples of suggested concept of supersymmetric adiabatic evolution the Holomorphic quantum mechanics on complex plane and Meromorphic quantum mechanics on Riemann surface are considered. The supersymmetric Berry indexes for the models are calculated.

hep-th↗