[en] We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three-dimensional Anderson model at the metal-insulator transition. Based on our results, we conjecture that the sensitivity of quantum multifractality to perturbation is universal in the sense that it follows one of these two scenarios depending on the perturbation. We also discuss the experimental implications.
Disciplines :
Physics
Author, co-author :
Dubertrand, Rémy ; Université de Liège - ULiège > Département de physique > Optique quantique
Garcia-Mata, Ignacio; Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), CONICET–UNMdP, Funes 3350, B7602AYL Mar del Plata, Argentina
Georgeot, Bertrand; Université de Toulouse, UPS, Laboratoire de Physique Théorique (IRSAMC), F-31062 Toulouse, France
Giraud, Olivier; LPTMS, CNRS and Université Paris-Sud, UMR 8626, Bât. 100, 91405 Orsay, France
Lemarié, Gabriel; Université de Toulouse, UPS, Laboratoire de Physique Théorique (IRSAMC), F-31062 Toulouse, France
Martin, John ; Université de Liège - ULiège > Département de physique > Optique quantique
Language :
English
Title :
Two Scenarios for Quantum Multifractality Breakdown
Publication date :
June 2014
Journal title :
Physical Review Letters
ISSN :
0031-9007
eISSN :
1079-7114
Publisher :
American Physical Society, Ridge, United States - New York
Volume :
112
Pages :
234101
Peer reviewed :
Peer Reviewed verified by ORBi
Tags :
CÉCI : Consortium des Équipements de Calcul Intensif
A.D. Mirlin, Y.V. Fyodorov, F.-M. Dittes, J. Quezada, and T.H. Seligman, Phys. Rev. E 54, 3221 (1996); PLEEE8 1063-651X 10.1103/PhysRevE.54.3221
J.A. Mendez-Bermudez, A. Alcazar-Lopez, and I. Varga, Europhys. Lett. 98 37006 (2012). EULEEJ 0295-5075 10.1209/0295-5075/98/37006
Y.V. Fyodorov, A. Ossipov and A. Rodriguez, J. Stat. Mech. L12001 (2009). JSMTC6 1742-5468 10.1088/1742-5468/2009/12/L12001
N. Meenakshisundaram and A. Lakshminarayan, Phys. Rev. E 71, 065303(R) (2005). PLEEE8 1539-3755 10.1103/PhysRevE.71.065303
J.N. Bandyopadhyay, J. Wang, and J. Gong, Phys. Rev. E 81, 066212 (2010). PLEEE8 1539-3755 10.1103/PhysRevE.81.066212
A.M. García-García and J. Wang, Phys. Rev. Lett. 94, 244102 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.94.244102
E.B. Bogomolny, U. Gerland, and C. Schmit, Phys. Rev. E 59, R1315 (1999); PLEEE8 1063-651X 10.1103/PhysRevE.59.R1315
E.B. Bogomolny, O. Giraud, and C. Schmit, Phys. Rev. E 65, 056214 (2002). PLEEE8 1063-651X 10.1103/PhysRevE.65.056214
J. Wiersig, Phys. Rev. E 62, R21 (2000). PLEEE8 1063-651X 10.1103/PhysRevE.62.R21
O. Giraud, J. Marklof and S. O'Keefe, J. Phys. A 37, L303 (2004). JPHAC5 0305-4470 10.1088/0305-4470/37/28/L01
E.B. Bogomolny and C. Schmit, Phys. Rev. Lett. 93, 254102 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.93.254102
J. Martin, O. Giraud, and B. Georgeot, Phys. Rev. E 77, 035201(R) (2008). PLEEE8 1539-3755 10.1103/PhysRevE.77.035201
E.B. Bogomolny, R. Dubertrand, and C. Schmit, Nonlinearity 22, 2101 (2009). NONLE5 0951-7715 10.1088/0951-7715/22/9/003
J. Martin, I. García-Mata, O. Giraud and B. Georgeot, Phys. Rev. E 82, 046206 (2010). PLEEE8 1539-3755 10.1103/PhysRevE.82.046206
E.B. Bogomolny and O. Giraud, Phys. Rev. Lett. 106, 044101 (2011); PRLTAO 0031-9007 10.1103/PhysRevLett.106.044101
E.B. Bogomolny and O. Giraud Phys. Rev. E 84, 036212 (2011); PLEEE8 1539-3755 10.1103/PhysRevE.84.036212
E.B. Bogomolny and O. Giraud Phys. Rev. E 85, 046208 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.85.046208
I. García-Mata, J. Martin, O. Giraud, and B. Georgeot, Phys. Rev. E 86, 056215 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.86.056215
I. Guarneri and G. Mantica, Phys. Rev. Lett. 73, 3379 (1994). PRLTAO 0031-9007 10.1103/PhysRevLett.73.3379
R. Ketzmerick, K. Kruse, S. Kraut, and T. Geisel, Phys. Rev. Lett. 79, 1959 (1997). PRLTAO 0031-9007 10.1103/PhysRevLett.79.1959
G. Mantica, Electron Trans. Numer. Anal. 25, 409 (2006). 1068-9613
A. Richardella, P. Roushan, S. Mack, B. Zhou, D.A. Huse, D.D. Awschalom, and A. Yazdani, Science 327, 665 (2010). SCIEAS 0036-8075 10.1126/science. 1183640
G. Lemarié, H. Lignier, D. Delande, P. Szriftgiser, and J.-C. Garreau, Phys. Rev. Lett. 105, 090601 (2010); PRLTAO 0031-9007 10.1103/PhysRevLett.105.090601
M. Lopez, J.-F. Clément, G. Lemarié, D. Delande, P. Szriftgiser, and J.-C. Garreau, New J. Phys. 15, 065013 (2013). NJOPFM 1367-2630 10.1088/1367-2630/15/6/065013
Y. Sagi, M. Brook, I. Almog, and N. Davidson, Phys. Rev. Lett. 108, 093002 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.093002
S. Faez, A. Strybulevych, J.H. Page, A. Lagendijk, and B.A. van Tiggelen, Phys. Rev. Lett. 103, 155703 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103. 155703
