Effet Mpemba par effet tunnel quantique : un refroidissement paradoxal dans des potentiels à double puits ouverts ✛ ✦

Résumé original

tel que rédigé par les auteurs, en anglais arXiv:2607.03845

The quantum tunneling Mpemba effect is investigated within a continuous one-dimensional symmetric double-well potential open to external environmental sinks at the boundaries ($$x=\pm L$$). Using a non-Hermitian spectral decomposition of the effective Hamiltonian, we characterize the open-system relaxation dynamics without relying on abstract state-space quenches. We mathematically prove that the non-monotonic behavior of the first non-trivial even-parity spectral coefficient, $$a_{2}(T_{i})$$, with respect to the initial preparation temperature $$T_{i}$$ is a universal topological property born from quantum statistical mechanics. Crucially, we demonstrate that this intermediate thermal peak is governed by the Sturm-Liouville oscillation theorem and remains completely invariant with respect to the global system size $$L$$, contrasting sharply with the boundary-driven classical Mpemba effect. This universal peak arises from the geometric and nodal alignment between highly localized unperturbed states and extended non-Hermitian decay channels. Furthermore, we clarify that while this mechanism is robust, the actual observation of anomalous crossings in the total survival probability trace $$S(t,T_{i})$$ and the trace distance $$\mathcal{D}(t,T_i)$$ demand a strict separation of timescales, requiring the over-barrier escape rate to vastly exceed the decay rate of the deep-well tunneling doublet ($$\Gamma_{2}\gg \Gamma_{0}$$ and $$\Gamma_2\gg \Gamma_1$$). Our continuous formulation successfully bridges real-space classical boundary-driven dissipation with open quantum dynamics, providing novel insights for engineering non-equilibrium states via tailored boundary loss.