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arXiv 2007.02575nucl-th
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隧道动力学的变分方法。应用于热超流费米系统。自发性和诱导性Fission

Variational Approach to Tunneling Dynamics. Application to Hot Superfluid Fermi Systems. Spontaneous and Induced Fission

Shimon Levit

发表信息：
Physics Letters B 813 (2021) 136042
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摘要：

我们引入了一个通用的变分框架来处理热费米系统的隧穿。我们使用虚时间$τ=it$传播子的迹的表示作为在中间传播切片的完整状态集合上的和的函数积分类型。我们假设这些态是$τ$依赖的，并且由任意的试探哈密顿量$H_0(τ)$产生.然后利用凸性不等式得到了试探作用泛函的$H_0(τ)$控制变分界。该泛函具有一般结构，由两部分组成-统计加权量子穿透性和动力学隧道熵。我们研究如何将这种结构的热费米系统的隧穿的基本物理。使用变分不等式可以优化的动力学参数控制的作用功能的任何选择的试验问题。作为应用，我们用$H_0(τ)$描述了非相互作用Bogoliubov-de Gennes（BdG）准粒子的虚时动力学.优化其动力学参数，我们扩展的Hartree-Fock-Bogoliubov（HFB）框架的热费米系统的隧道理论，并推导出相应的推广虚时间温度相关的BdG平均场方程。在审判行动中，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。在零温极限下，这些方程描述了超流费米系统（核物理中的自发裂变）的“假基态“隧穿衰变。随着激发能（有效温度）的增加，衰变过程逐渐从纯粹的量子隧穿演化为统计“瓶颈”逃逸机制。

英文摘要：

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 $τ=it$ propagator as a functional integral type of a sum over complete sets of states at intermediate propagation slices. We assume that these states are $τ$-dependent and generated by an arbitrary trial Hamiltonian $H_0(τ)$. We then use the convexity inequality to derive $H_0(τ)$ 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 $H_0(τ)$ 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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