Thermodynamical properties by neglecting thermal noise in quantum systems: Effects of ground-state perturbations

Abstract

A quantum system defined by a Hamiltonian Hˆ0, represented by a diagonal matrix, presents zero Boltzmann–Gibbs entropy (SBG=0) at zero temperature (T=0). Herein it is shown that by introducing a perturbation λVˆ (λ>0), characterized by off-diagonal contributions, the Hamiltonian Hˆ=Hˆ0+λVˆ may present a nontrivial ground state, described by a new entropic form S (S≠SBG). The perturbation λVˆ is analyzed, and particularly its relation to an effective temperature θ, identified as the parameter thermodynamically conjugated to the entropy S. Two paradigmatic quantum-mechanical systems are considered, namely, the harmonic oscillator and the free particle in an infinite potential well, which are shown to display nontrivial thermodynamic properties by varying θ. Recent experiments on superconductor samples at very low temperatures, where the specific heat does not present a clear tendency to zero as T→0, is explained by means of a crossover between these two entropic forms.