6,531 research outputs found

    The categories of free metabelian groups and Lie algebras

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    Algebraic Geometry over Free Metabelian Lie Algebra I: U-Algebras and Universal Classes

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    This paper is the first in a series of three, the aim of which is to lay the foundations of algebraic geometry over the free metabelian Lie algebra FF. In the current paper we introduce the notion of a metabelian Lie UU-algebra and establish connections between metabelian Lie UU-algebras and special matrix Lie algebras. We define the Δ\Delta -localisation of a metabelian Lie UU-algebra AA and the direct module extension of the Fitting's radical of AA and show that these algebras lie in the universal closure of AA.Comment: 34 page

    Thermodynamic uncertainty relation as a fundamental aspect of quantum thermodynamics

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    The paper addresses physics of thermodynamic fluctuations in temperature and energy. These fluctuations are interrelated and, hence, can affect various micro- and macro systems. It is shown that the thermodynamic uncertainty relation must be taken into account in the physics of superconductivity, in quantum computations and other branches of science, where temperature and energy fluctuations play a critical role. One of the most important applications of quantum thermodynamics is quantum computers. It is assumed that in the near future the state structures will create a specific quantum cryptocurrency obtained using quantumcomputing. The quantum cryptocurrency exhibits two main features: the maximum reliability (quantum protection against hacking threats) and the possibility of state control (at the moment, only large scientific state centers have quantum computers). The paper reviews the studies aimed to theoretically prove the validity of the thermodynamic uncertainty relation. This relation connects fluctuations in temperature and energy of a system. Other similar relations are considered, including the relationshipbetween fluctuations in pressure and volume, in entropy and temperature, and others. The main purpose of the paper is to validate the thermodynamic analogue of the uncertainty relation that interconnects temperature and energy fluctuations

    Theory of high-T_c superconductivity based on the fermion-condensation quantum phase transition

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    A theory of high temperature superconductivity based on the combination of the fermion-condensation quantum phase transition and the conventional theory of superconductivity is presented. This theory describes maximum values of the superconducting gap which can be as big as Δ10.1ϵF\Delta_1\sim 0.1\epsilon_F, with ϵF\epsilon_F being the Fermi level. We show that the critical temperature 2TcΔ12T_c\simeq\Delta_1. If there exists the pseudogap above TcT_c then 2TΔ12T^*\simeq\Delta_1, and TT^* is the temperature at which the pseudogap vanishes. A discontinuity in the specific heat at TcT_c is calculated. The transition from conventional superconductors to high-TcT_c ones as a function of the doping level is investigated. The single-particle excitations and their lineshape are also considered.Comment: 6 pages, Revte
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