{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:31:49Z","timestamp":1772253109847,"version":"3.50.1"},"reference-count":118,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,30]],"date-time":"2020-12-30T00:00:00Z","timestamp":1609286400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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 phenomena in a better way. Further, we demonstrate an equivalent formalism of computation using a general time-independent Hamiltonian having well-defined eigenstate representation 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. To visualize the impact of the given formalism, we consider the two well-known models, viz. Harmonic Oscillator and one-dimensional potential well within the framework of Supersymmetry. For the Harmonic Oscillator case, we obtain similar periodic time dependence but dissimilar parameter dependences compared to the results obtained from both microcanonical and canonical ensembles in quantum mechanics without Supersymmetry. On the other hand, for the One-Dimensional PotentialWell problem, we found significantly different time scales and the other parameter dependence compared to the results obtained from non-Supersymmetric quantum mechanics. Finally, to establish the consistency of the prescribed formalism in the classical limit, we demonstrate the phase space averaged version of the classical version of OTOCs from a model-independent Hamiltonian, along with the previously mentioned well-cited models.<\/jats:p>","DOI":"10.3390\/sym13010044","type":"journal-article","created":{"date-parts":[[2020,12,30]],"date-time":"2020-12-30T20:13:41Z","timestamp":1609359221000},"page":"44","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["The Generalized OTOC from Supersymmetric Quantum Mechanics\u2014Study of Random Fluctuations from Eigenstate Representation of Correlation Functions"],"prefix":"10.3390","volume":"13","author":[{"given":"Kaushik Y.","family":"Bhagat","sequence":"first","affiliation":[{"name":"Centre for High Energy Physics, Indian Institute of Science, Bengaluru, Karnataka 560012, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baibhab","family":"Bose","sequence":"additional","affiliation":[{"name":"Department of Physics &amp; Astrophysics, University of Delhi, Delhi 110007, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0459-3873","authenticated-orcid":false,"given":"Sayantan","family":"Choudhury","sequence":"additional","affiliation":[{"name":"Quantum Gravity and Unified Theory and Theoretical Cosmology Group, Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am M\u00fchlenberg 1, 14476 Potsdam-Golm, Germany"},{"name":"National Institute of Science Education and Research, Bhubaneswar, Odisha 752050, India"},{"name":"Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400085, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Satyaki","family":"Chowdhury","sequence":"additional","affiliation":[{"name":"National Institute of Science Education and Research, Bhubaneswar, Odisha 752050, India"},{"name":"Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400085, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rathindra N.","family":"Das","sequence":"additional","affiliation":[{"name":"Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saptarshhi G.","family":"Dastider","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Sree Chaitanya College, Prafullanagar, Habra 743268, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5855-2201","authenticated-orcid":false,"given":"Nitin","family":"Gupta","sequence":"additional","affiliation":[{"name":"Department of Physical Sciences, Indian Institute of Science Education &amp; Research Mohali, Punjab 140306, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Archana","family":"Maji","sequence":"additional","affiliation":[{"name":"Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gabriel D.","family":"Pasquino","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, University of Waterloo, 200 University Ave W, Waterloo, ON N2L 3G1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Swaraj","family":"Paul","sequence":"additional","affiliation":[{"name":"Discipline of Mathematics, Indian Institute of Technology Indore, Indore 453552, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,30]]},"reference":[{"key":"ref_1","first-page":"1200","article-title":"Quasiclassical method in the theory of superconductivity","volume":"28","author":"Larkin","year":"1969","journal-title":"Sov. 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