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Your search keyword '"Luiz Roberto Evangelista"' showing total 12 results
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12 results on '"Luiz Roberto Evangelista"'

1. Aspects of Quantum Statistical Mechanics: Fractional and Tsallis Approaches

Author

Ervin Kaminski Lenzi, Luiz Roberto Evangelista, and Luciano Rodrigues da Silva

Subjects
fractional dynamics, Tsallis entropy, power-law distributions, energy fluctuations, Mathematics, QA1-939
Abstract

We investigated two different approaches, which can be used to extend the standard quantum statistical mechanics. One is based on fractional calculus, and the other considers the extension of the concept of entropy, i.e., the Tsallis statistics. We reviewed and discussed some of the main properties of these approaches and used the thermal Green function formalism to perform the developments, simultaneously allowing us to analyze each case’s dynamics and thermodynamics aspects. In particular, the results allow us to understand how the extensions change the behavior of some quantities, particularly fluctuations related to the system.

Published
2023
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12. Schrödinger Equation with Geometric Constraints and Position-Dependent Mass: Linked Fractional Calculus Models

Author

Luiz Roberto Evangelista, Ervin Kaminski Lenzi, Richard Magin, and Haroldo Valentin Ribeiro

Subjects
Physics and Astronomy (miscellaneous), Astronomy and Astrophysics, Statistical and Nonlinear Physics, Atomic and Molecular Physics, and Optics, fractional dynamics, anomalous diffusion, comb-model
Abstract

We investigate the solutions of a two-dimensional Schrödinger equation in the presence of geometric constraints, represented by a backbone structure with branches, by taking a position-dependent effective mass for each direction into account. We use Green’s function approach to obtain the solutions, which are given in terms of stretched exponential functions. The results can be linked to the properties of the system and show anomalous spreading for the wave packet. We also analyze the interplay between the backbone structure with branches constraining the different directions and the effective mass. In particular, we show how a fractional Schrödinger equation emerges from this scenario.

Published
2022
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