The short periodic orbit method for excited chaotic eigenfunctions

Abstract

In this paper [published in Phys. Rev. E 102, 042210 (2020)], a new method for the calculation of excited chaotic eigenfunctions in arbitrary energy windows is presented. We demonstrate the feasibility of using wavefunctions localized on unstable periodic orbits as efficient basis sets for this task in classically chaotic systems. The number of required localized wavefunctions is only of the order of the ratio t H /t E , with t H the Heisenberg time and t E the Ehrenfest time. As an illustration, we present convincing results for a coupled two-dimensional quartic oscillator with chaotic dynamics.

7 pages, 4 figures

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• Phase Space Approach to Solving the Time-independent Schrödinger Equation
• Semiclassical Theory of Short Periodic Orbits in Quantum Chaos
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Cited by in corpus (6)

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• Variational Scarring in Open Two-Dimensional Quantum Dots
• Adapting reservoir computing to solve the Schrödinger equation
• Estimating the spectral density of unstable scars