Quantum thermal avalanche: Spectral characteristics of size-invariant variations of energy landscapes

Size-invariant shape transformation is a technique of altering the shape of a domain by preserving its sizes. It leads to quantum shape effects in the thermodynamic and transport properties of quantum-confined systems. In this work, we investigate interesting spectral properties of systems involving size-invariant variations in their Hamiltonians. In particular, we show that the geometric couplings between levels generated by the size-invariant shape transformations cause nonuniform scaling in the spectra. The defining characteristics of such transformations are ground state reduction and differential modifications in the spectral gaps. Moreover, we find that the ground state reduction leads to so-called quantum thermal avalanche causing an unexpected swapping in the thermal occupation probabilities. Thermal occupation of the ground state abruptly increases while the that of excited states decreases. This transition has intriguing non-classical implications, including spontaneous shifts to lower-entropy states in systems that exhibit the quantum shape effect. We also identify avoided crossing effects in the spectra which are important in determining the peculiar behaviors in the thermodynamic properties. The implications of this study could be generalized to any potential energy profile with an appropriate variable causing size-invariant modifications of the energy landscape.