Exactly solvable tight-binding model on two scale-free networks with identical degree distribution

Pinchen Xie; Bo Wu; Zhongzhi Zhang

doi:10.1209/0295-5075/116/38002

All issues

Volume 116 / No 3 (November 2016)

EPL, 116 3 (2016) 38002

Abstract

Issue		EPL Volume 116, Number 3, November 2016


Article Number		38002
Number of page(s)		6
Section		Interdisciplinary Physics and Related Areas of Science and Technology
DOI		https://doi.org/10.1209/0295-5075/116/38002
Published online		09 December 2016

EPL, 116 (2016) 38002

Exactly solvable tight-binding model on two scale-free networks with identical degree distribution

Pinchen Xie¹^,2, Bo Wu³ and Zhongzhi Zhang²^,4^(a)

¹ Department of Physics, Fudan University - Shanghai 200433, China
² Shanghai Key Laboratory of Intelligent Information Processing, Fudan University - Shanghai 200433, China
³ Department of Applied Mathematics and Statistics, Stony Brook University - Stony Brook, NY 11794, USA
⁴ School of Computer Science, Fudan University - Shanghai 200433, China

^(a) zhangzz@fudan.edu.cn

Received: 11 October 2016
Accepted: 22 November 2016

Abstract

We study ideal Bose gas upon two scale-free structures $\mathcal{G}^1$ and $\mathcal{G}^2$ with identical degree distribution. Energy spectra belonging to tight-binding Hamiltonian are exactly solved and the related spectral dimensions of $\mathcal{G}^1$ and $\mathcal{G}^2$ are obtained as $d_{s_1}=2$ and $d_{s_2}=2\ln4/\ln3$ . We show that Bose-Einstein condensation only takes place upon $\mathcal{G}^2$ instead of $\mathcal{G}^1$ . The topology and thermodynamical property of the two structures are proven to be totally different.

PACS: 89.75.Hc – Networks and genealogical trees / 05.30.Jp – Boson systems / 02.10.Yn – Matrix theory

© EPLA, 2016

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