National Undergraduate Physics Conference (NUPC) 2026

Instability Without Chaos: Classical and Quantum Signatures in an Inverted Harmonic Oscillator like system via Out-of-Time-Order Correlators (OTOCs)

Not scheduled

20m

Indian Institute of Science Education and Research (IISER), Tirupati

Poster Presentation Complex systems and nonlinear dynamics

Speaker

Adrish Pati (National Institute of Science Education and Research (NISER) Bhubaneswar)

Description

Out of time order correlators (OTOCs) are widely used as a measure of
quantum chaos, but exponential OTOC growth might also arise from unstable
saddle points in a non-chaotic system. We investigate this disctinction for a
one-dimensional double well potential with an Inverted Harmonic Oscillator
barrier. The Schr¨odinger equation is diagonalized by finite differences, and
microcanonical OTOCs are computed from position matrix elements and en
ergy spectra. Classically, RK4 trajectories are bounded and Benettin Lyapunov exponents
tend to zero, confirming non-chaoticity. Quantum OTOCs grow exponentially
only for levels near the barrier top (n ≈ 9–13 for λ = 2, g = 1/50), reflecting
local instability rather than chaos. We aim to extend the analysis to canonical
OTOCs via Boltzmann-weighted averaging to examine the temperature depen
dence of the growth rate, which is expected to remain of the order of the saddle
exponent.

Other Fields of Research (Track) for Abstract

Basic Quantum Chaos