Exact solution of the one-dimensional Hubbard model with U = ∞ in a magnetic field, theoretical arithmetic, foundations of geometry, discrete mathematics, mathematical foundations of classical mechanics, electrodynamics and statistical physics.
Subject:
1) Exact solutions of models of statistical physics;
2) Foundations of Mathematics and Classical Physics.
Main publications:
S. G. Ovchinnikov, K. A. Sidorov, E. I. Shneyder, “Anomaluos thermodynamics of Mott-Hubbard doped insulators”, In the framework of the t-J model, the concentration dependence of the entropy of doped Mott-Hubbard insulators is considered. It is shown that the change in the type and statistics of the current carriers in comparison with Fermi gas leads to a radical change in the entropy s, in particular, to a giant increase in entropy
with doping. The quantity ∂s/ ∂x ≈ kB, which is approximately consistent with the experimental data for HTSC cuprates in the pseudogap phase., Physics of the Solid State, 53:2 (2011), 280-283
K. A. Sidorov, S. G. Ovchinnikov, N. V. Tikhonov., “A simple way for exact calculation of the thermodynamic properties of the one-dimensional Hubbard model with infinite repulsion.”, It is shown that the canonical partition function of a one-dimensional Hubbard model with U = ∞ in the nearest-neighbor approximation is determined by the product of the canonical partition functions of spinons and holons. For the electron concentration 0 <ne <1, in this approximation, the concentration and temperature dependences of free and internal energies, chemical potentials,
entropy and heat capacity are obtained., JETP, 143:2 (2013), 379 - 387
K. A. Sidorov, N. V. Tikhonov, S. G. Ovchinnikov, “Exact calculation of the thermodynamics of the one-dimensional Hubbard model with infinite repulsion in a magnetic field”, It is shown that in the nearest-neighbor approximation the canonical partition function of the one-dimensional Hubbard model in the limit of infinite repulsion in a magnetic field splits into a product of partition functions of holons
and spinons, which are calculated exactly. Due to this, exact numerical dependences of free energy, entropy, internal energy, heat capacity, chemical potential and magnetic susceptibility on hole concentration, temperature and magnetic field induction., Theoretical and Mathematical Physics, 180:1 (2014), 94 - 111
Kirill A. Sidorov, “To the question of rigorous axiomatization of thermodynamics”, J. Sib. Fed. Univ. Math. Phys., 16:5 (2023), 553–561
2014
2.
V. N. Simonenko, P. I. Kalmykov, A. B. Kiskin, O. G. Glotov, V. E. Zarko, K. A. Sidorov, B. V. Pevchenko, R. G. Nikitin, “Combustion of model compositions based on furazanotetrazine dioxide and dinitrodiazapentane. I. Binary systems”, Fizika Goreniya i Vzryva, 50:3 (2014), 68–77; Combustion, Explosion and Shock Waves, 50:3 (2014), 306–314
K. A. Sidorov, N. V. Tikhonov, S. G. Ovchinnikov, “Exact solution for the thermodynamics of the one-dimensional Hubbard model with infinite repulsion in a magnetic field”, TMF, 180:1 (2014), 94–111; Theoret. and Math. Phys., 180:1 (2014), 825–849
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