Investigating Quantum Chaos in Impact Osillators

Naik, Anusha (2025) Investigating Quantum Chaos in Impact Osillators. UNSPECIFIED thesis, UNSPECIFIED.

Text (MS Dissertation of Anusha Naik (20MS208)) 20MS208_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

This thesis explores the manifestation of quantum chaos in impact oscillator systems mechanical models characterized by non-linear, often discontinuous potentials. Drawing inspiration from their classically chaotic counterparts, we investigate both soft and hard impact oscillators in quantum settings, with and without periodic driving, to understand how chaos reveals itself in bounded quantum systems. The analysis employs two complementary diagnostics: the Nearest Neighbor Spacing Distribution (NNSD), a spectral method grounded in Random Matrix Theory, and the Out-of-Time-Ordered Correlator (OTOC), a dynamical measure sensitive to information scrambling and operator growth. We develop robust numerical algorithms to calculate eigenvalue statistics and compute OTOCs in both microcanonical and thermal ensembles. Validation is achieved through benchmarks against known results for the quantum harmonic oscillator and the quantum kicked rotor. Our NNSD results demonstrate that impact oscillators often exhibit spectral statistics deviating from both integrable (Poisson) and chaotic (Wigner-Dyson) ensembles, challenging the Bohigas-Giannoni-Schmit conjecture. Dynamical analyses using OTOCs reveal a rich variety of behaviors—including bounded oscillations, power-law growth, and exponential divergence—depending on system parameters and external forcing. These findings illuminate the subtleties in characterizing chaos in quantum systems lacking classical analogues and underscore the importance of combining spectral and dynamical tools. The work contributes a generalizable numerical framework that can be extended to more complex, open, or many-body quantum systems, thereby deepening our understanding of quantum chaos and quantum-classical correspondence.

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