Renyi entropy for the doped graphene at low temperatures
https://doi.org/10.17586/2220-8054-2015-6-2-274-279
Abstract
The distribution function for the perimeter of a simply connected cluster containing undoped lattice sites is based on percolation theory and the hypothesis of scale invariance. The Renyi entropy for doped graphene at low temperatures was calculated on the basis of this distribution function.
Supporting agencies: This work was supported by the Russian Foundation for Basic Research under project No. 12-02-31654.
About the Authors
N. N. Konobeeva
Volgograd State University
Russian Federation
Russian Federation
Volgograd
A. A. Polunina
Volgograd State University
Russian Federation
Russian Federation
Volgograd
M. B. Belonenko
Volgograd State University; Volgograd Institute of Business
Russian Federation
Russian Federation
Volgograd
References
1. Kirchanov V.S. Using the Renyi entropy to describe quantum dissipative systems in statistical mechanics. Theoretical and Mathematical Physics, 156(3), P. 444–453 (2008).
2. Chumak O.V. Entropy and fractals in data analysis. Moscow, Izhevsk: SRC “Regular and Chaotic Dynamics”, Institute of Computer Science, 164 p. (2011).
3. Hawking S.W. Black hole and thermodynamics collection of articles “Black hole”. News of fundamental physics. Issue 9. P. 204–221 (1978).
4. Schroeder M. Fractals, Chaos, Power Laws. Moscow, Izhevsk: R&C Dynamics, 527 p. (2001).
5. Assaad F.F., Lang T.C., Parisen Toldin F. Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations (2013). (http://arxiv.org/pdf/1311.5851.pdf).
6. Xiong H., Wu B. Atomic Quantum Corrals for Bose-Einstein Condensates. Phys. Rev. A., 82, P. 053634 (2010).
7. Rossi E., Morr D.K. Spatially dependent Kondo effect in Quantum Corrals. Phys. Rev. Lett., 97, P. 236602 (2006).
8. Novoselov K.S., Geim A.K., Morozov S.V., Jiang D., Katsnelson M.I., Grigorieva I.V., Firsov A.A. Two-dimensional gas of massless Dirac fermions in graphene. Nature, 438, P. 197 (2005).
9. Datta S., David J.R. Renyi entropies of free bosons on the torus and holography (2013). (http://arxiv.org/pdf/1311.1218.pdf).
10. Patashinskii A.Z., Pokrovskii V.L. Fluctuation theory of phase transitions. Moscow: Nauka, 381 p. (1982).
11. M¨uller H. Scaling as a fundamental property of natural vibrations of matter and the fractal structure of space-time. Foundations of physics and geometry. P. 189–209 (2008).
12. Gusynin V. P., Shaparov S.G., Carbotte J.P. AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics. Int. J. Mod. Phys. B., 21, P. 4611–4658 (2007).
13. Castro Neto A.H., Guinea F., Peres N.M.R., Novoselov K.S., Geim A.K. The electronic properties of graphene. Rev. Mod. Phys., 81, P. 109 (2009).
14. Logemann R., Reijnders K.J.A., Tudorovskiy T., Katsnelson M.I., Yuan S. Modeling Klein Tunneling and Caustics of Electron Waves in Graphene (2014). (http://arxiv.org/pdf/1409.1277v1.pdf).
15. Gantmaher V.F. Electrons in disordered media. Moscow: Fizmatlit, 288 p. (2013).
Review
For citations:
Konobeeva N.N., Polunina A.A., Belonenko M.B. Renyi entropy for the doped graphene at low temperatures. Nanosystems: Physics, Chemistry, Mathematics. 2015;6(2):274-279. https://doi.org/10.17586/2220-8054-2015-6-2-274-279
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