Abstract
Chaotic scattering is a manifestation of transient chaos realized by the scattering with non-integrable potential. When the initial position is taken in the potential, a particle initially exhibits chaotic motion, but escapes outside after a certain period of time. The time to stay inside the potential can be seen as lifetime and this escape process may be regarded as a kind of instability. The process of this type exists in the Banks-Fischler-Shenker-Susskind (BFSS) matrix model in which the potential has flat directions. We discuss this chaotic instability by reducing the system with an ansatz to a simple dynamical system and present the associated fractal structure. We also show the singular behavior of the time delay function and compute the fractal dimension. This chaotic instability is the basic mechanism by which membranes are unstable, which is also common to supermembranes at quantum level.
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References
V. Rosenhaus, Chaos in the quantum field theory S-matrix, Phys. Rev. Lett. 127 (2021) 021601 [arXiv:2003.07381] [INSPIRE].
D. J. Gross and V. Rosenhaus, Chaotic scattering of highly excited strings, JHEP 05 (2021) 048 [arXiv:2103.15301] [INSPIRE].
V. Rosenhaus, Chaos in a many-string scattering amplitude, Phys. Rev. Lett. 129 (2022) 031601 [arXiv:2112.10269] [INSPIRE].
S. G. Matinyan, G. K. Savvidy and N. G. Ter-Arutunian Savvidy, Classical yang-mills mechanics. Nonlinear color oscillations, Sov. Phys. JETP 53 (1981) 421 [INSPIRE].
T. Banks, W. Fischler, S. H. Shenker and L. Susskind, M theory as a matrix model: a conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].
I. Y. Aref’eva, P. B. Medvedev, O. A. Rytchkov and I. V. Volovich, Chaos in M(atrix) theory, Chaos Solitons Fractals 10 (1999) 213 [hep-th/9710032] [INSPIRE].
D. E. Berenstein, J. M. Maldacena and H. S. Nastase, Strings in flat space and pp waves from N = 4 superYang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].
Y. Asano, D. Kawai and K. Yoshida, Chaos in the BMN matrix model, JHEP 06 (2015) 191 [arXiv:1503.04594] [INSPIRE].
B. de Wit, J. Hoppe and H. Nicolai, On the quantum mechanics of supermembranes, Nucl. Phys. B 305 (1988) 545 [INSPIRE].
B. de Wit, M. Lüscher and H. Nicolai, The supermembrane is unstable, Nucl. Phys. B 320 (1989) 135 [INSPIRE].
J. M. Seoane, and M. A. F. Sanjuán, New developments in classical chaotic scattering, Rept. Prog. Phys. 76 (2012) 016001.
H. C. Lai, T. Tél, Transient chaos: complex dynamics on finite time scales, volume 173, Springer Science & Business Media (2011).
H. E. Nusse and J. A. Yorke, The equality of fractal dimension and uncertainty dimension for certain dynamical systems, Commun. Math. Phys. 150 (1992) 1.
G. H. Hsu, E. Ott and C. Grebogi, Strange saddles and the dimensions of their invariant-manifolds, Phys. Lett. A 127 (1988) 199.
D. N. Kabat and W. Taylor, Spherical membranes in matrix theory, Adv. Theor. Math. Phys. 2 (1998) 181 [hep-th/9711078] [INSPIRE].
D. Berenstein and Y. Guan, Improved semiclassical model for real-time evaporation of matrix black holes, Int. J. Mod. Phys. A 36 (2021) 2150219 [arXiv:2105.04577] [INSPIRE].
K. Hashimoto, K. Murata, N. Tanahashi and R. Watanabe, A bound on energy dependence of chaos, arXiv:2112.11163 [INSPIRE].
P. Yi, Witten index and threshold bound states of D-branes, Nucl. Phys. B 505 (1997) 307 [hep-th/9704098] [INSPIRE].
S. Sethi and M. Stern, D-brane bound states redux, Commun. Math. Phys. 194 (1998) 675 [hep-th/9705046] [INSPIRE].
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Fukushima, O., Yoshida, K. Chaotic instability in the BFSS matrix model. J. High Energ. Phys. 2022, 39 (2022). https://doi.org/10.1007/JHEP09(2022)039
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DOI: https://doi.org/10.1007/JHEP09(2022)039