Journal of Holography Applications in Physics
Entropies for coupled harmonic oscillators and temperature
Document Type : Regular article
Authors
1 Laboratory of Theoretical Physics Faculty of Sciences Ibn Maachou Street
2 Physics Department, College of Science, King Faisal University, PO Box 380, Alahsa 31982, Saudi Arabia
Abstract
We study two entropies of a system composed of two coupled harmonic oscillators which is
brought to a canonical thermal equilibrium with a heat-bath at temperature T . Using the purity
function, we explicitly determine the Rényi and van Newmon entropies in terms of different physical
parameters. We will numerically analyze these two entropies under suitable conditions and show
their relevance.
Keywords
Article PDF
[2] A. Renyi, ”On measures of entropy and information”, Proc. Fourth Berkeley Symp. on Math. Statist. Prob. 1, 547 (Univ. of Calif. Press, 1961).
[3] H. Li and F. D. M. Haldane, ”Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States”, Phys. Rev. Lett. 101, 010504 (2008), [Arxiv:0805.0332].
[4] M. Headrick, ”Entanglement Renyi entropies in holographic theories”, Phys. Rev. D 82, 126010 (2010), [Arxiv 1006.0047].
[5] X. Dong, ”Holographic Renyi Entropy at High Energy Density”, Phys. Rev. Lett. 122, 041602 (2019).
[6] E. Konishi, ”Holographic Interpretation of Shannon Entropy of Coherence of Quantum Pure States”, EPL 129, 11006 (2020).
[7] A. Merdaci, A. Jellal, A. Al Sawalha and A. Bahaoui, ”Purity temperature dependency for coupled harmonic oscillator”, J. Stat. Mech. 2018, 093101 (2018).
[8] A. Jellal, F. Madouri and A. Merdaci, ”Entanglement in coupled harmonic oscillators studied using a unitary transformation”, J. Stat. Mech. 2011, P09015 (2011).
[9] A. Jellal, E.H. El Kinani and M. Schreiber, ”Two Coupled Harmonic Oscillators on Non-commutative Plane”, Int. J. Mod. Phys. A 20, 1515 (2005).
[10] I. Kosztin, B. Faber and K. Schulten, ”Introduction to the diffusion Monte Carlo method”, Am. J. Phys. 64, 633 (1996).
[11] M. Rossi, M. Nava, L. Reatto and D.E. Galli, ”Exact ground state Monte Carlo method for Bosons without importance sampling”, J. Chem. Phys 131, 154108 (2009).
[12] H. Kleinert, ”Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets” (World Scientific, Singapore 2009).
[13] A. R`enyi, ”Probability Theory” (North Holland, Amsterdam, 1970).
[14] M. J. Bastiaans, ”New class of uncertainty relations for partially coherent light”, J. Opt. Soc. Am. 1, 711 (1984).
[15] M. J. Bastiaans, ”Uncertainty principle and informational entropy for partially coherent light”, J. Opt. Soc. Am. 3, 1243 (1986).
[16] C. Tsallis, ”Possible generalization of Boltzmann-Gibbs statistics”, J. Stat. Phys. 52, 479 (1988).
[17] G. Adesso, A. Serafini and F. Illuminati, ”Extremal entanglement and mixedness in continuous variable systems”, Phys. Rev. A 70, 022318 (2004) [arXiv:quant-ph/0402124].
[18] J. Pipek and I. Nagy, ”Measures of spatial entanglement in a two-electron model atom”, Phys. Rev. A 79, 052501 (2009).
[19] G. Adesso, A. Serafini and F. Illuminati, ”Entanglement, Purity, and Information Entropies in Continuous Variable Systems”, Open Syst. Inf. Dyn. 12, 189 (2005).
[20] S. Mahesh Chandran and S. Shankaranarayanan, ”Divergence of entanglement entropy in quantum systems: Zero-modes”, Phys. Rev. D 99, 045010 (2019).
)
Volume 2, Issue 2
May 2022Pages 15-30
- Receive Date: 13 October 2021
- Revise Date: 26 January 2022
- Accept Date: 30 April 2022