[en] We study a version of the mathematical Ruijsenaars-Schneider model and reinterpret it physically in order to describe the spreading with time of quantum wave packets in a system where multifractality can be tuned by varying a parameter. We compare different methods to measure the multifractality of wave packets and identify the best one. We find the multifractality to decrease with time until it reaches an asymptotic limit, which is different from the multifractality of eigenvectors but related to it, as is the rate of the decrease. Our results could guide the study of experimental situations where multifractality is present in quantum systems.
Disciplines :
Physics
Author, co-author :
Garcia-Mata, Ignacio
Martin, John ; Université de Liège - ULiège > Département de physique > Optique quantique
Giraud, Olivier
Georgeot, Bertrand
Language :
English
Title :
Multifractality of quantum wave packets
Publication date :
November 2012
Journal title :
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
ISSN :
1539-3755
eISSN :
1550-2376
Publisher :
American Physical Society, College Park, United States - Maryland
Volume :
86
Pages :
056215
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 PLEEE8 1539-3755 10.1103/PhysRevE.54.3221 54, 3221 (1996);
J. A. Mendez-Bermudez, A. Alcazar-Lopez, and I. Varga, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/98/37006 98, 37006 (2012).
Y. V. Fyodorov, A. Ossipov, and A. Rodriguez, J. Stat. Mech. 10.1088/1742-5468/2009/12/L12001 (2009) L12001.
N. Meenakshisundaram and A. Lakshminarayan, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.71.065303 71, 065303 (R) (2005). (Pubitemid 41663811)
J. N. Bandyopadhyay, J. Wang, and J. Gong, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.066212 81, 066212 (2010).
A. M. García-García and J. Wang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.244102 94, 244102 (2005). (Pubitemid 41636476)
E. B. Bogomolny, U. Gerland, and C. Schmit, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.59.R1315 59, R1315 (1999);
E. B. Bogomolny, O. Giraud, and C. Schmit, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.65.056214 65, 056214 (2002). (Pubitemid 40606880)
O. Giraud, J. Marklof, and S. O'Keefe, J. Phys. A 1361-6447 10.1088/0305-4470/37/28/L01 37, L303 (2004). (Pubitemid 38963440)
E. B. Bogomolny and C. Schmit, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.254102 93, 254102 (2004). (Pubitemid 40141845)
J. Martin, O. Giraud, and B. Georgeot, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.77.035201 77, 035201 (R) (2008). (Pubitemid 351431340)
J. Martin, I. García-Mata, O. Giraud, and B. Georgeot, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.046206 82, 046206 (2010).
E. Bogomolny and O. Giraud, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.044101 106, 044101 (2011).
E. Bogomolny and O. Giraud, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.84.036212 84, 036212 (2011).
E. Bogomolny and O. Giraud, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.046208 85, 046208 (2012).
S. Faez, A. Strybulevych, J. H. Page, A. Lagendijk, and B. A. van Tiggelen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.155703 103, 155703 (2009).
A. Richardella, P. Roushan, S. Mack, B. Zhou, D. A. Huse, D. D. Awschalom, and A. Yazdani, Science SCIEAS 0036-8075 10.1126/science.1183640 327, 665 (2010).
G. Lemarié, H. Lignier, D. Delande, P. Szriftgiser, and J.-C. Garreau, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.090601 105, 090601 (2010);
Y. Sagi, M. Brook, I. Almog, and N. Davidson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.108.093002 108, 093002 (2012).
J. T. Chalker and G. J. Daniell, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.61.593 61, 593 (1988).
B. Huckestein and L. Schweitzer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.713 72, 713 (1994).
I. Guarneri and G. Mantica, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.3379 73, 3379 (1994).
R. Ketzmerick, K. Kruse, S. Kraut, and T. Geisel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.1959 79, 1959 (1997).
J. Zhong, R. B. Diener, D. A. Steck, W. H. Oskay, M. G. Raizen, E. W. Plummer, Z. Zhang, and Q. Niu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.2485 86, 2485 (2001). (Pubitemid 32286686)
H. Grussbach and M. Schreiber, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.48.6650 48, 6650 (1993).
S. N. Evangelou and D. E. Katsanos, J. Phys. A 1361-6447 10.1088/0305-4470/26/23/010 26, L1243 (1993).
S. N. M. Ruijsenaars and H. Schneider, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/0003-4916(86)90097-7 170, 370 (1986).
A. Arneodo, in Wavelets: Theory and Applications, edited by, G. Erlebacher, M. Y. Hussaini, and, L. M. Jameson, (Oxford University Press, New York, 1996), pp. 349-502.
J. W. Kantelhardt, H. E. Roman, and M. Greiner, Phys. A PHYADX 0378-4371 10.1016/0378-4371(95)00267-B 220, 219 (1995).
I. García-Mata, O. Giraud, and B. Georgeot, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.052321 79, 052321 (2009).
