We introduce a general variational framework to address the tunneling of hot Fermi systems. We use the representation of the trace of the imaginary time $\tau=it$ propagator as a functional integral type of a sum over complete sets of states at intermediate propagation slices. We assume that these states are $\tau$-dependent and generated by an arbitrary trial Hamiltonian $H_0(\tau)$. We then use the convexity inequality to derive $H_0(\tau)$ controlled variational bound for a trial action functional. This functional has a general structure consisting of two parts - statistically weighted quantum penetrability and dynamical tunneling entropy. We examine how this structure incorporates the basic physics of tunneling of hot Fermi systems. Using the variational inequality one can optimise the dynamical parameters controlling the action functional for any choice of the trial problem. As an application we take $H_0(\tau)$ to describe imaginary time dynamics of non interacting Bogoliubov-de Gennes (BdG) quasiparticles. Optimising its dynamical parameters we extend the tunneling theory of hot Fermi systems to the Hartree-Fock-Bogoliubov(HFB) frame and derive the corresponding generalisation of imaginary time temperature dependent BdG mean field equations. As in the trial action the prominent feature of these equations is an inseparable interplay between quantum dynamical and entropic statistical effects. In the zero temperature limit these equations describe the "false ground state" tunneling decay of superfluid Fermi systems (spontaneous fission in nuclear physics). With increasing excitation energy (effective temperature) the decay process is gradually evolving from pure quantum tunneling to statistical "bottle neck" escape mechanism.

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隧道动力学的变分方法。应用于热超流体费米系统。自发和诱导裂变

我们引入了一个通用的变分框架来解决热费米系统的隧道问题。我们使用虚时间 $\tau=it$ 传播器的轨迹表示作为在中间传播切片的完整状态集上求和的函数积分类型。我们假设这些状态是依赖于 $\tau$ 的，并且由任意试验哈密顿量 $H_0(\tau)$ 生成。然后我们使用凸性不等式来推导出 $H_0(\tau)$ 受控变分界限的试行功能。该泛函具有由两部分组成的一般结构 - 统计加权的量子穿透性和动态隧道熵。我们研究了这种结构如何结合热费米系统隧道效应的基本物理学。使用变分不等式可以优化控制任何试验问题选择的动作泛函的动态参数。作为一个应用，我们使用 $H_0(\tau)$ 来描述非相互作用 Bogoliubov-de Gennes (BdG) 准粒子的虚时间动力学。优化其动力学参数，我们将热费米系统的隧穿理论扩展到 Hartree-Fock-Bogoliubov(HFB) 框架，并推导出虚时间温度相关 BdG 平均场方程的相应推广。如同在审判中一样，这些方程的突出特点是量子动力学和熵统计效应之间不可分割的相互作用。在零温度极限下，这些方程描述了超流体费米系统（核物理中的自发裂变）的“假基态”隧道衰变。