Quantum Control of Nonlinear Dynamics in Confined Systems

Abstract

Investigating nonlinear fluid dynamics remains a challenge across physics from nanofluidics and biophysics to astrophysics. Here we introduce a quantum/classical theoretical approach that takes into account both quantum correlations and classical behaviour within a 2D fluid that is confined in a 3 μm side square. We employ a modified Gross-Pitaevskii equation, encompassing many-body interactions and confinement. This system reveals complex fluid dynamics characterised by dissipative solitons; a significant outcome is an asymptotic function that describes the soliton behaviour. The solitons exhibit intriguing geometrical and temporal transformations, guided by subtle phase gradients. We trace the soliton evolution from 1 to 83 ns, revealing the emergence of geometric oscillations in amplitude and phase angles. Under these phase gradients, solitons transition to states with reduced amplitude and expanded spatial profiles. These results show that geometric solitons can emerge from a quantum noisy environment, and lead us to propose an interesting possibility: it is feasible to control and manipulate nonlinear dynamics in systems with finite-range interactions and confinement using quantum control. By bridging quantum and classical dynamics, this study links various scientific disciplines, including non-equilibrium phases of condensed matter, unconventional/quantum computing and advanced control of nanofluidics. From a more fundamental perspective, this possibility of quantum control of classical behaviour advances our understanding of physics within multidimensional Hilbert spaces.