Sensitivity to small perturbations in systems of large quantum spins
Date
2015
Authors
Journal Title
Journal ISSN
Volume Title
Type
Article
Publisher
IOP Publishing
Series Info
Physica Scripta;Volume: 2015 Issue: T165 Pages: 1-4
Doi
Scientific Journal Rankings
Abstract
We investigate the sensitivity of nonintegrable large-spin quantum lattices to small perturbations
with a particular focus on the time reversal experiments known in statistical physics as “Loschmidt
echoes” and in nuclear magnetic resonance (NMR) as “magic echoes.” Our numerical simulations
of quantum spin-7 1
2
clusters indicate that there is a regime, where Loschmidt echoes exhibit nearly
exponential sensitivity to small perturbations with characteristic constant approximately equal to
twice the value of the largest Lyapunov exponent of the corresponding classical spin clusters. The
above theoretical results are verifiable by NMR experiments on solids containing large-spin nuclei.
Description
MSA Google Scholar
Keywords
University of Large quantum spins
Citation
[1] S. Chaudhury, A. Smith, B. Anderson, S. Ghose, and P. Jessen, Nature 461, 768 (2009). [2] L. Benet, T. H. Seligman, and H. A. Weidenm¨uller, Phys. Rev. Lett. 71, 529 (1993). [3] P. G. Silvestrov, J. Tworzyd lo, and C. W. J. Beenakker, Phys. Rev. E 67, 025204 (2003). [4] D. A. Wisniacki, E. G. Vergini, H. M. Pastawski, and F. M. Cucchietti, Phys. Rev. E 65, 055206 (2002). [5] R. Bl¨umel, Phys. Rev. Lett. 73, 428 (1994). [6] R. Vilela Mendes, Journal of Physics A: Mathematical and General 24, 4349 (1991). [7] R. Schack and C. M. Caves, Phys. Rev. Lett. 71, 525 (1993). [8] P. Gaspard, M. E. Briggs, M. K. Francis, J. V. Sengers, R. W. Gammon, J. R. Dorfman, and R. V. Calabrese, Nature 394, 865 (1998). [9] C. P. Dettmann, E. G. D. Cohen, and H. van Beijeren, Nature 401, 875 (1999). [10] P. Grassberger and T. Schreiber, Nature 401, 875 (1999). [11] F. Cecconi, M. Cencini, M. Falcioni, and A. Vulpiani, Chaos 15, 026102 (2005). [12] T. A. Elsayed, B. Hess, and B. V. Fine, Phys. Rev. E 90, 022910 (2014). [13] B. V. Fine, J. Stat. Phys. 112, 319 (2003). [14] B. V. Fine, Int. J. Mod. Phys. B 18, 1119 (2004). [15] B. V. Fine, Phys. Rev. Lett. 94, 247601 (2005). [16] S. W. Morgan, B. V. Fine, and B. Saam, Phys. Rev. Lett. 101, 067601 (2008). [17] E. G. Sorte, B. V. Fine, and B. Saam, Phys. Rev. B 83, 064302 (2011). [18] B. Meier, J. Kohlrautz, and J. Haase, Phys. Rev. Lett. 108, 177602 (2012). [19] A. S. de Wijn, B. Hess, and B. V. Fine, Phys. Rev. Lett. 109, 034101 (2012). [20] A. de Wijn, B. Hess, and B. Fine, Journal of Physics A: Mathematical and Theoretical 46, 254012 (2013). [21] B. V. Fine, T. A. Elsayed, C. M. Kropf, and A. S. de Wijn, Phys. Rev. E 89, 012923 (2014). [22] H. M. Pastawski, P. R. Levstein, G. Usaj, J. Raya, and J. Hirschinger, Physica A: Statistical Mechanics and its Applications 283, 166 (2000). [23] W.-K. Rhim, A. Pines, and J. S. Waugh, Phys. Rev. B 3, 684 (1971). [24] C. P. Slichter, Principles of magnetic resonance, Vol. 1 (Springer, 1990). [25] L. G. Yaffe, Rev. Mod. Phys. 54, 407 (1982). [26] E. Lieb, Communications in Mathematical Physics 31, 327 (1973). [27] J. Fr¨ohlich, A. Knowles, and E. Lenzmann, Letters in Mathematical Physics 82, 275 (2007). [28] T. A. Elsayed and B. V. Fine, Physical Review Letters 110, 070404 (2013). [29] C. Bartsch and J. Gemmer, Phys. Rev. Lett. 102, 110403 (2009).