Quantum graphs and random-matrix theory

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10315330" target="_blank" >RIV/00216208:11320/15:10315330 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1088/1751-8113/48/27/275102" target="_blank" >http://dx.doi.org/10.1088/1751-8113/48/27/275102</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1751-8113/48/27/275102" target="_blank" >10.1088/1751-8113/48/27/275102</a>

Result language

angličtina

Original language name

Quantum graphs and random-matrix theory

Original language description

For simple connected graphs with incommensurate bond lengths and with unitary symmetry we prove the Bohigas-Giannoni-Schmit (BGS) conjecture in its most general form. Using supersymmetry and taking the limit of infinite graph size, we show that the generating function for every (P, Q) correlation function for both closed and open graphs coincides with the corresponding expression of random-matrix theory. We show that the classical Perron-Frobenius operator is bistochastic and possesses a single eigenvalue +1. In the quantum case that implies the existence of a zero (or massless) mode of the effective action. That mode causes universal fluctuation properties. Avoiding the saddle-point approximation we show that for graphs that are classically mixing (i.e. for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap) and that do not carry a special class of bound states, the zero mode dominates in the limit of infinite graph size.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BG - Nuclear, atomic and molecular physics, accelerators

OECD FORD branch

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Project

<a href="/en/project/GA13-07117S" target="_blank" >GA13-07117S: Statistical approaches to quantum many-body systems</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2015

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Physics A: Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

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Volume of the periodical

48

Issue of the periodical within the volume

27

Country of publishing house

GB - UNITED KINGDOM

Number of pages

30

Pages from-to

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UT code for WoS article

000356343300003

EID of the result in the Scopus database

2-s2.0-84935885322