continuum mechanics and related problems of analysis - Razmadze ...
continuum mechanics and related problems of analysis - Razmadze ... continuum mechanics and related problems of analysis - Razmadze ...
150 Mathematical Physics September, 9–14, Tbilisi, Georgia Some New Aspects and New Quantum Kinetic Equations of Degenerate Fermi Gas NODAR TSINTSADZE E. Andronikashvili Institute of Physics, Department of Plasma Physics Tbilisi, Georgia email: nltsin@yahoo.com Answers to some salient questions, which arise in quantum plasmas, are given. Starting from the Schrodinger equation for a single particle it is demonstrated how the Wigner–Moyal equation can be derived. It is shown that the Wigner–Moyal type of equation also exists in the classical field theory. As an example, from the Maxwell equations the Wigner–Moyal type of equation is obtained for a dense photon gas, which is classical, concluding that the Wigner– Moyal type of equation can be derived for any system, classical of quantum. A new types of quantum kinetic equations are presented. these novel kinetic equations allows to obtain a set of quantum hydrodynamic equations, which is impossible to derive by the Wigner–Moyal equation. The propagation of small perturbation and instabilities of these perturbations are then discussed, presenting new modes of quantum plasma waves. In the case of low frequency oscillations with ions, a new Bogolyubov type of spectrum is found. furthermore, the Korteweg–de Vries (KdV) equations is derived and the contribution of the Madelung term in the formation of the KdV solitions is discussed. Low Energy Behavior of 1D Superconductor at Magnetic Field Induced Quantum Phase Transition TEMO VEKUA Institute of Theoretical Physics, Leibniz University of Hanover, Faculty of Mathematics and Physics Hanover, Germany email: vekua@itp.uni-hannover.de Exact solution of one-dimensional (1D) Hubbard model is combined with effective field theory description beyond the linearized hydrodynamic approximation to determine correlation functions and low temperature thermodynamic properties of one-dimensional superconductor in external magnetic field equal to the spin gap. In 1D system of the lattice electrons away of half filling, when discrete particle-hole symmetry is broken, spin and charge degrees of freedom are
September, 9–14, Tbilisi, Georgia Mathematical Physics 151 coupled by the curvature of the bare particle dispersion at the Fermi points. In many cases this coupling is irrelevant, and thus negligible in infrared limit, however in certain cases to describe even static low energy properties of the 1D electron system away of half filling one can not use linearized hydrodynamic approximation (which is known as bosonization procedure and results in spin-charge separation), but has to account for the non-linear dispersion of the bare electron spectrum. In particular, due to the finite curvature, at the magnetic field induced commensurateincommensurate quantum phase transition point the magnetic susceptibility stays finite and specific heat instead of the square root shows a linear behavior with temperature albeit with logarithmic corrections.
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- Page 173 and 174: Index Abbasov E. M., 139 Abramidze
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September, 9–14, Tbilisi, Georgia Mathematical Physics 151<br />
coupled by the curvature <strong>of</strong> the bare particle dispersion at the Fermi points. In many cases this<br />
coupling is irrelevant, <strong>and</strong> thus negligible in infrared limit, however in certain cases to describe<br />
even static low energy properties <strong>of</strong> the 1D electron system away <strong>of</strong> half filling one can not use<br />
linearized hydrodynamic approximation (which is known as bosonization procedure <strong>and</strong> results<br />
in spin-charge separation), but has to account for the non-linear dispersion <strong>of</strong> the bare electron<br />
spectrum. In particular, due to the finite curvature, at the magnetic field induced commensurateincommensurate<br />
quantum phase transition point the magnetic susceptibility stays finite <strong>and</strong><br />
specific heat instead <strong>of</strong> the square root shows a linear behavior with temperature albeit with<br />
logarithmic corrections.
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