Visualisation of wave functions of chaotic quantum systems

Martin C. Gutzwiller

Jincheng Zhang

Quantum-enhanced chaos theory aims to leverage quantum phenomena to improve our understanding and prediction of chaotic systems. This paper explores a novel algorithm, Quantum-Enhanced Chaos Theory via Wave Function Optimization, which utilizes quantum superposition to accelerate the analysis and prediction of chaotic dynamics. We propose a quantum algorithm, specifically a modified Grover's algorithm, to efficiently explore the wave function space, thereby enabling faster identification of critical states and improved forecasting accuracy. The core mechanism relies on the superposition of multiple wave functions, allowing for a parallel exploration of potential configurations within the chaotic system. This research will investigate the potential for enhanced sensitivity and predictability within chaotic systems through the application of this quantum optimization technique.

M. S. Santhanam

Joanna K. Kalaga, A. Kowalewska-Kudłaszyk, W. Leoński +1 more

We discuss a system of the Kerr-like quantum nonlinear oscillator excited by a series of ultrashort external pulses.These coherent excitations, along with the nonlinearity involved in the system, can lead to the quantum chaotic behaviour.For that model, we calculate the fidelities of the wave function which describe the system's dynamics.We show that such defined fidelity and its decay rate can be applied as an indicator of the quantum chaotic behaviour appearance.We also discuss the problem of how the initial distance between the two close wave functions can influence the fidelity changes.

Helmut Linde

Abstract Quantum field theory (QFT) is the basis of some of the most fundamental theories in modern physics, but it is not an easy subject to learn. In the present article we intend to pave the way from quantum mechanics to QFT for students at early graduate or advanced undergraduate level. More specifically, we propose a new way of visualising the wave function Ψ of a linear chain of interacting quantum harmonic oscillators, which can be seen as a model for a simple one-dimensional bosonic quantum field. The main idea is to draw randomly chosen classical states of the chain superimposed upon each other and use a grey scale to represent the value of Ψ at the corresponding coordinates of the quantised system. Our goal is to establish a better intuitive understanding of the mathematical objects underlying quantum field theories and solid state physics.

Frank-Michael Dittes, I. Rotter, T. H. Seligman