Connection of Microscopic with Macroscopic Dynamics: Towards a Hydrodynamical Description of Quantum Mechanics

José Luis López, Jesús Montejo–Gámez

This paper is intended to provide the reader with a review of the authors’ latest results dealing with the modeling of quantum dissipation/diffusion effects at the level of Schrodinger systems, in connection with the corresponding phase space and fluid formulations of such kind of phenomena, especially in what concerns the role of the Fokker–Planck mechanism in the description of open quantum systems and the macroscopic dynamics associated with some viscous hydrodynamic models of Euler and Navier–Stokes type.

Sebastiano Sonego

C. S. Unnikrishnan

Quantum mechanics (QM) is the description of dynamics in the microscopic world of atoms, photons, electrons, etc. Similar to Newton’s law of dynamics, dp/dt = F, which is the statement on the time evolution of the dynamical physical state associated with matter, the Schrödinger equation iħdψ/dt = Hψ is the statement of the time evolution on the quantum physical state of matter, denoted with the function ψ ( x, t ). Though the wavefunction ψ ( x, t ) is not a dynamical quantity like momentum, the role of time in the description of dynamics is similar and straightforward, if the final results are interpreted as the average over a statistical ensemble (collection). In the conventional interpretation of quantum mechanics, the wavefunction is supposed to be the complete description of the physical state of the particle, like an electron or an atom. It is complex-valued, mathematically, and needs two real quantities for its specification. It evolves in ‘magnitude’ and ‘phase’ as the reference clock advances in time. The evolution progresses causally, connecting the past to the present and into the future, as one expects in dynamics. Thus, the variable called ‘time’ in the microscopic world of quantum mechanics is the same as the time that is familiar in our macroscopic world.

Mario Schönberg

Jasper van Wezel

During the past decade, the experimental development of being able to create ever larger and heavier quantum superpositions has brought the discussion of the connection between microscopic quantum mechanics and macroscopic classical physics back to the forefront of physical research. Under equilibrium conditions this connection is in fact well understood in terms of the mechanism of spontaneous symmetry breaking, while the emergence of classical dynamics can be described within an ensemble averaged description in terms of decoherence. The remaining realm of individual-state quantum dynamics in the thermodynamic limit was addressed in a recent paper proposing that the unitarity of quantum mechanical time evolution in macroscopic objects may be susceptible to a spontaneous breakdown. Here we will discuss the implications of this theory of spontaneous unitarity breaking for the modern experiments involving truly macroscopic Schrodinger cat states.

Pavel Bóna