Variational approach to tunneling dynamics. Application to hot superfluid Fermi systems. Spontaneous and induced fission

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