2017
Том 69
№ 9

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Equilibrium in quantum systems of particles with magnetic interaction. Fermi and bose statistics

Skrypnik W. I.

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Abstract

Quantum systems of particles interacting via an effective electromagnetic potential with zero electrostatic component are considered (magnetic interaction). It is assumed that the j th component of the effective potential for n particles equals the partial derivative with respect to the coordinate of the jth particle of “magnetic potential energy” of n particles almost everywhere. The reduced density matrices for small values of the activity are computed in the thermodynamic limit for d-dimensional systems with short-range pair magnetic potentials and for one-dimensional systems with long-range pair magnetic interaction, which is an analog of the interaction of three-dimensional Chern-Simons electrodynamics (“magnetic potential energy” coincides with the one-dimensional Coulomb (electrostatic) potential energy).

English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 5, pp 770-778.

Citation Example: Skrypnik W. I. Equilibrium in quantum systems of particles with magnetic interaction. Fermi and bose statistics // Ukr. Mat. Zh. - 1997. - 49, № 5. - pp. 691–698.

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