K. Ilinski: Key results in physics and mathematics

Exact Analytical solution of 1-dimensional XY model with arbitrary boundary conditions in final volume and at finite temperature. First explicitly solvable example of non-trivial quantum statistics in 1 dimension

Common belief is that quantum statistics is trivial (Fermi or Bose) in 1-dimension. Here is the counterexample. There are exotic statistics in 1D if the geometry of the space is non-trivial and XY model (and its q-deformations) in finite volume and finite temperature is the simplest example!

All major quantum statistical characteristics and correlation functions of this famous model are obtained for the first time by a new method borrowed from Supersymmetrical Quantum Field Theory at finite temperature and volume.

K.N. Ilinski, G.V. Kalinin “Cyclic XY model and exotic statistics in one dimension”, Phys.Rev. E 54 (1996), R1017-R1020

A.V. Ilinskaia, K.N. Ilinski, G.V. Kalinin, V.V. Melezhik and A.S. Stepanenko, “Exact results on linear response of cyclic molecular aggregates”, cond-mat/9509040 (September 1995)

K.N. Ilinski, G.V. Kalinin and V.S. Kapitonov, “Exchange statistics in 1D: from the viewpoint of exact solution”, hep-th/9504038 (April 1995)

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