A. Elsayed, TarekV. Fine, Boris2020-02-262020-02-262015[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).https://t.ly/ndWKYMSA Google ScholarWe 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.enUniversity of Large quantum spinsSensitivity to small perturbations in systems of large quantum spinsArticle