Classical Mechanical Systems with one-and-a-half Degrees of Freedom and Vlasov Kinetic Equation

Canonical Gibbs distribution and thermodynamics of mechanical systems with a finite number of degrees of freedom

Traditional derivation of Gibbs canonical distribution and the justification of thermodynamics are based on the assumption concerning an isoenergetic ergodicity of a system of $n$ weakly interacting identical subsystems and passage to the limit $n\to\infty$. In the presented work we develop another approach to these problems assuming that $n$ is fixed and $n\ge2$. The ergodic hypothesis (which frequently is not valid due to known results of the KAM-theory) is substituted by a weaker assumption that the perturbed system does not have additional first integrals independent of the energy integral…

Euler top and freedom in supersymmetrization of one-dimensional mechanics

Recently A.Galajinsky has suggested the N=1 supersymmetric extension of Euler top and made a few interesting observations on its properties [arXiv:2111.06083 [hep-th]]. In this paper we use the formulation of the Euler top as a system on complex projective plane, playing the role of phase space, i.e. as a one-dimensional mechanical system. Then we suggest the supersymmetrization scheme of the generic one-dimensional systems with positive Hamiltonian which yields a priori integrable family of N=2k supersymmetric Hamiltonians parameterized by N/2 arbitrary real functions.

与正能量自由度耦合的幽灵场的全局与局部稳定性

Global and Local Stability for Ghosts Coupled to Positive Energy Degrees of Freedom

本文构造并分析了一类正能量自由度与幽灵场耦合的可积稳定力学系统，证明其运动有界并给出李雅普诺夫稳定条件，同时用数值计算验证了稳定性。