Nonlinearity in Quantum Mechanics may have extrinsic or intrinsic origins and is a liable route to a chaotic behaviour that can be of difficult observations. In this paper, we propose two forms of nonlinear Hamiltonian, which explicitly depend upon the phase of the wave function and produce chaotic behaviour. To speed up the slow manifestation of chaotic effects, a resonant laser field assisting the time evolution of the systems causes cumulative effects that might be revealed, at least in principle. The nonlinear Schrödinger equation is solved within the two-state approximation; the solution displays features with characteristics similar to those found in chaotic Classical Mechanics: sensitivity on the initial state, dense power spectrum, irregular filling of the Poincaré map and exponential separation of the trajectories of the Bloch vector σ in the Bloch sphere.

Fiordilino E (2020). The Emergence of Chaos in Quantum Mechanics. SYMMETRY, 12(5), 785-797 [10.3390/sym12050785].

The Emergence of Chaos in Quantum Mechanics

Fiordilino E
Writing – Review & Editing
2020

Abstract

Nonlinearity in Quantum Mechanics may have extrinsic or intrinsic origins and is a liable route to a chaotic behaviour that can be of difficult observations. In this paper, we propose two forms of nonlinear Hamiltonian, which explicitly depend upon the phase of the wave function and produce chaotic behaviour. To speed up the slow manifestation of chaotic effects, a resonant laser field assisting the time evolution of the systems causes cumulative effects that might be revealed, at least in principle. The nonlinear Schrödinger equation is solved within the two-state approximation; the solution displays features with characteristics similar to those found in chaotic Classical Mechanics: sensitivity on the initial state, dense power spectrum, irregular filling of the Poincaré map and exponential separation of the trajectories of the Bloch vector σ in the Bloch sphere.
Settore FIS/02 - Fisica Teorica, Modelli E Metodi Matematici
https://doi.org/10.3390/sym12050785
Fiordilino E (2020). The Emergence of Chaos in Quantum Mechanics. SYMMETRY, 12(5), 785-797 [10.3390/sym12050785].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/428836
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