Solitons, chaos, and quantum phenomena: a deterministic approach to the Schrödinger equation
Gomila, Damià
Physical Review Research 7, 033276 (2025)
Physical Review Research 7, 033276 (2025)
We show that the Schrödinger equation describes the ensemble mean dynamics of solitons in a Galilean invariant field theory where we interpret solitons as particles. On a zero background, solitons move classically, following Newton`s second law, however, on a non-zero amplitude chaotic background, their momentum and position fluctuate fulfilling an exact uncertainty relation, which give rise to the emergence of quantum phenomena. The Schrödinger equation for the ensemble of solitons is obtained from this exact uncertainty relation, and the amplitude of the background fluctuations is what corresponds to the value of the Planck constant. We confirm our analytical results running simulations of solitons moving against a potential barrier and comparing the ensemble probabilities with the predictions of the time dependent Schrödinger equation, providing a deterministic version of the quantum tunneling effect. We conclude with a discussion of how our theory does not present statistical independence between measurement and experiment outcome.
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MdM-IFISC-2
Maria de Maeztu 2023-2026
I.P.: Ernesto Estrada, Ingo Fischer, Emilio Hernández-García, Rosa Lopez, Claudio Mirasso, Jose Javier Ramasco, Raúl Toral, Roberta Zambrini
After 15 years of its existence, IFISC can point to a proven track record of impactful research. The previous 2018-2022 MdM award has significantly enhanced the institute's capabilities, as demonstrated by an …
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