Effects of quantum confinement on thermodynamic properties

Abstract

Confined quantum systems can present anomalous behaviour. In particular, thermodynamic properties such as specific heat can show special features when the system is subject to spatial confinement described, for instance, by a harmonic potential. The energy eigenvalues of this confined system can be obtained from a variational approach by using, as trial functions, the solution of a particle in a box multiplied by a gaussian. For a strong confinement regime, the energy eigenvalues converge to the same values of the particle in the box and, for a weak confinement regime, the energy eigenvalues converge to the free harmonic oscillator. This behaviour reflects in the thermodynamics properties. In the curves of specific heat as a function of temperature, for instance, it is possible to identify two regions, one when the contribution of the harmonic oscillator is dominant and the other one where the contribution of the particle in a box becomes more relevant. These results indicate a phase transition of second-order close to the Einstein temperature.

Coulomb correlation and information entropies in confined helium-like atoms

“…Quantum mechanical properties of confined systems are influenced by properties of confinement cage, for instance, the energy spectra and the polarizability experience significant changes [37,38]. With the increment of computational processing capacity and development of modern techniques for the effective confinement, this topic remains to be of interest [39][40][41][42][43][44][45][46][47][48][49][50]. In previous researches, we use the entropy sum to investigate the regions of the confined harmonic oscillator [51] and confined hydrogenic-like atoms [21] where the confinement effects has major impact.…”

Variational eigenfunctions for excited states inspired by supersymmetric quantum mechanics and the Gram–Schmidt process

“…The methodology starts from an exact or approximate superpotential that is used as a guess to build the trial wave functions (ansatz) via the Gram-Schmidt process for the excited states. In this way, the energy eigenvalues are computed via the variational method following the approach used in [19,20], where the values obtained for the variational parameters for each state are considered fixed for the calculation of the next state. The proposed method for finding eigenfunctions for excited states is an approximate approach that uses the variational principle to determine the energy eigenvalue.…”

Quantum states of hydrogen cations confined into spherical and nanotube-like potential wells: H2+ , H3+ (C 2h and C 2v ) and H3+ (D 3h )

“…In recent years, numerous studies were performed on confined simple molecular systems, that is, molecular systems within potential wells that limit the electron movement [1][2][3][4]. The effect of spatial constraints on the physical and chemical properties of atoms and molecules has been the subject of increasing interest: indeed, these properties of systems enclosed in a spatially limited region undergo significant changes, compared to their free equivalents [5,6].…”