Integrals Involving Jacobi Theta Functions and Applications in Quantum Systems

Authors

  • Emerson B. S. Corrêa Institute of Exact Sciences, Federal University of the South and Southeast of Pará, ICE/UNIFESSPA, 68505-080, Marabá, PA, Brazil Author
  • Carlos A Bahia Faculty of Electrical Engineering, Federal University of the South and Southeast of Pará, FACEEL/UNIFESSPA, 68501-970, Marabá, PA, Brazil Author
  • Michelli S. R. Sarges Postgraduate Program in Chemistry, Federal University of Para, PPGQ/UFPA, 66075-900, Bel ém, PA, Brazil Author

DOI:

https://doi.org/10.47363/JPSOS/2023(5)206

Keywords:

Jacobi’s Theta Functions, Modified Bessel Functions, Applications in Quantum Gases

Abstract

We study four expressions involving the integrals of Jacobi’s theta functions. From Poisson’s summation formula, we write the integrals of the functions
θi, (i = 1,2,3,4) in terms of modified Bessel functions of the second kind. For the integrals of θ1, θ2 and θ3, we get expressions with real arguments, but for the integral of θ4, we find an expression with imaginary argument. In addition, we apply our results to the description of two kinds of interacting quantum systems: boson gas and fermion gas both under a thermal bath and an external magnetic field.
PACS numbers:

Author Biographies

  • Emerson B. S. Corrêa, Institute of Exact Sciences, Federal University of the South and Southeast of Pará, ICE/UNIFESSPA, 68505-080, Marabá, PA, Brazil

    Emerson BS Corrêa, Institute of Exact Sciences, Federal University of the South and Southeast of Pará, ICE/UNIFESSPA, 68505-080, Marabá, PA, Brazil.

  • Carlos A Bahia, Faculty of Electrical Engineering, Federal University of the South and Southeast of Pará, FACEEL/UNIFESSPA, 68501-970, Marabá, PA, Brazil

    Emerson BS Corrêa, Institute of Exact Sciences, Federal University of the South and Southeast of Pará, ICE/UNIFESSPA, 68505-080, Marabá, PA, Brazil.

  • Michelli S. R. Sarges, Postgraduate Program in Chemistry, Federal University of Para, PPGQ/UFPA, 66075-900, Bel ém, PA, Brazil

    Emerson BS Corrêa, Institute of Exact Sciences, Federal University of the South and Southeast of Pará, ICE/UNIFESSPA, 68505-080, Marabá, PA, Brazil.

Downloads

Published

2025-11-25

Issue

Vol. 5 No. 5 (2023): Volume 5 Issue 5

Section

Articles