The q-deformed heat equation and q-deformed diffusion equation with q-translation symmetry

Authors

  • W. Sang Chung Gyeongsang National University
  • Hassan Hassanabadi
  • J. Křiž University of Hradec Králové

DOI:

https://doi.org/10.31349/RevMexFis.68.060602

Keywords:

q-deformed, q-translation

Abstract

In this paper we consider the discrete heat equation with a certain non-uniform space interval which is related to q-addition appearing in the non-extensive entropy theory. By taking the continuous limit, we obtain the q-deformed heat equation. Similarly, we obtain the solution of the q-deformed diffusion equation

References

J. Fourier, Theorie Analytique de la Chaleur Firmin Didot (1822). (reissued by Cambridge University Press, 2009; ISBN 978-1-108-00180-9)

J. Cadzow, Int. J. Control 11 (1970) 393.

J. Logan, Aequat. Math. 9 (1973) 210.

T. Durt, B.Englert, I.Bengtsson, and K. Zyczkowski, International Journal of quantum information 8 (2010) 535.

W. Wootters and B. Fields, Annals of Physics 191 (1989) 363.

C. Miquel, J.Paz, and M.Saraceno, Phys. Rev. A 65 (2002) 062309.

J. Paz, Phys. Rev. A 65 (2002) 062311.

E. Davies and J. Lewis, Communications in Mathematical Physics 17 (1970) 239.

A. Barth and A. Lang, Stochastics. 84 (2012) 217.

I. Gyöngy, Potential Anal. 9 (1998) 1.

M. Sauer and W. Stannat, Math. Comp. 84 (2015) 743.

T. Shardlow, Numer. Funct. Anal. Optim. 20 (1999) 121.

Y. Yan, SIAM J. Numer. Anal. 43 (2005) 1363.

C. Mueller and K. Lee, Amer. Math. Soc. 137 (2009) 1467.

M. Friesl, A. Slavk, P. Stehlk, Appl. Math. Lett. 37 (2014) 86.

C. Tsallis, J. Stat. Phys. 52 (1988) 479.

E. Borges, Physica A 340 (2004) 95.

L.Nivanen, A.Le Mehaute, Q.Wang, Rep. Math. Phys. 52 (2003) 437

W. Chung and H.Hassanabadi, Mod. Phys. Lett. B 33 (2019) 1950368.

Won Sang Chung and H. Hassanabadi, Fortschr. Phys. 2019 1800111.

C. De Boor, Good approximation by splines with variable knots II in Lecture Notes in Mathematics 363, Springer-Verlag, New York, 1974, pp. 12-20.

E. Dorfi and L.Drury, J. Comput. Phys. 69 (1987) 175.

A. Dwyer, R.Kee and B. Sanders, AIAA J 18 (1980) 1205.

D. Hawken, J.Gottlieb and J. Hanssen, J. Comput. Phys. 95 (1991) 254.

W. Chung and H.Hassanabadi, q-deformed mechanics from the discrete mechanics in q-lattice and Nother theorem PREPRINT 2022.

W. Chung and H.Hassanabadi, Bloch theorem and tight binding model in q-Bravais lattice PREPRINT 2022.

P. Kalinay and J. Percus, J. Chem. Phys. 122 (2005) 204701.

R. Zwanzig, J. Stat. Phys. 9 (1973) 215.

D. Reguera and J. Rubi, Phys. Rev. E 64 (2001) 061106.

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Published

2022-11-01

How to Cite

[1]
W. Sang Chung, H. Hassanabadi, and J. Křiž, “The q-deformed heat equation and q-deformed diffusion equation with q-translation symmetry”, Rev. Mex. Fís., vol. 68, no. 6 Nov-Dec, pp. 060602 1–, Nov. 2022.