Deterministic model equations of motion for quantum mechanics and some new modes of quantum behaviour

Nicolas Gisin

Ram K. Varma

It is pointed out that the behaviour of certain appropriate ensembles of a class of Hamiltonian systems can be described in terms of a set of probability amplitudes obeying Schrodinger like equations. Such a description leads to a new concept of described by the different equations. Such have in fact been observed experimentally recently in a certain classical mechanical system and thus testify to the validity of the probability amplitude description for the classical deterministic system. The possibility of the existence of new modes of quantum behaviour corresponding to the new ensemble modes other than the Schrodinger mode is also pointed out.

Niall Shanks

M. Diver, Gordon R. M. Robb, Gian‐Luca Oppo

Summary form only given. We perform a theoretical and numerical analysis of a system comprising a Bose-Einstein condensate (BEC) interacting with a laser beam in an optical cavity. Recent studies have modelled this system with two motional modes coupled with a light mode and have shown nonlinear behaviour, e.g. bistability [1,2]. Our approach tackles the full Gross-Pitaevskii equation coupled to the cavity field as well as expansions in a number of motional modes.We consider a fixed value of the cavity-pump detuning and increase the pump intensity to cross the region of bistability (see Fig. 1 left panel). The system then displays a variety of behaviours, including regular oscillations, chaotic dynamics, and quasi-periodic behaviour, as displayed in the right panel of Fig. 1. In Fig. 1 we have used a coupled-equation system comprising the Schrödinger wave equation and a cavity-field evolution [3], where we have adiabatically eliminated the latter leading to a conservative dynamics. The chaotic dynamics here is not induced by the detector noise and is an intrinsic property of the light-BEC interaction.Our second model considers a multiple-modes expansion. By using just three modes, the chaotic dynamics observed in the full simulation is recovered. The bifurcation structure, typical of conservative dynamics in the vicinity of a separatrix, is identified through the use of projections and power spectra. Our results suggest that chaotic oscillations in this system are deterministic in nature and arise purely from nonlinear effects. In more general terms, the model is a novel example of quantum matter exhibiting chaotic behaviour and invites further research.

pEduardo NahmadAcharp

Chanda Prosper

Prosper's Unified Position Equation (PUPE) is a novel theoretical framework that unifies classical mechanics, special relativity, quantum mechanics, and electromagnetism into a single deterministic model of motion. By integrating a particle’s momentum, wave amplitude, and ambient electromagnetic fields, PUPE provides precise trajectories for particles, removing the need for probabilistic interpretations in quantum mechanics. The framework reproduces established results in various physical regimes and opens new avenues for deterministic modeling of multi-particle systems, quantum field theory, and cosmological phenomena.