THE GENERALIZED OTOC from SUPERSYMMETRIC QUANTUM MECHANICS Study of Random Fluctuations from Eigenstate Representation of Correlation Functions
THE GENERALIZED OTOC FROM SUPERSYMMETRIC QUANTUM MECHANICS Study of Random Fluctuations from Eigenstate Representation of Correlation Functions Kaushik Y. Bhagat1, Baibhab Bose2, Sayantan Choudhury3;4;5‡; §, Satyaki Chowdhury4;5, Rathindra N. Das6, Saptarshhi G. Dastider7, Nitin Gupta8, Archana Maji6, Gabriel D. Pasquino9, Swaraj Paul10 1Indian Institute of Science, Bengaluru, Karnataka-560012, India 2Department of Physics & Astrophysics, University of Delhi, Delhi-11007, India 3Quantum Gravity and Unified Theory and Theoretical Cosmology Group, Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mu¨hlenberg 1, 14476 Potsdam-Golm, Germany. 4National Institute of Science Education and Research, Bhubaneswar, Odisha - 752050, India 5Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai - 400085, India 6Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai - 400076, India 7Sree Chaitanya College, Prafullanagar, Habra, West Bengal - 743268 8Department of Physical Sciences, Indian Institute of Science Education & Research Mohali, Punjab - 140306, India 9University of Waterloo, 200 University Ave W, Waterloo, ON, Canada, N2L 3G1 10Discipline of Mathematics, Indian Institute of Technology Indore, Indore 453 552, India Abstract The concept of the out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical mechanics. In this paper, we define a general class of OTOC, which can perfectly capture quantum randomness phe- nomena in a better way. Further, we demonstrate an equivalent formalism of computation using a general time-independent Hamiltonian having well-defined eigenstate representa- tion for integrable supersymmetric quantum systems. We found that one needs to consider two new correlators apart from the usual one to have a complete quantum description.
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