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arXiv:2102.09016 · Physical review. D/Physical review. D.

Relativistic quantum fluid with boost invariance

Davide Rindori, Leonardo Tinti, F. Becattini, Dirk H. Rischke

Published Mar 7, 2022• 10 citations
arXivHTMLPDF

Abstract

We study a relativistic fluid with longitudinal boost invariance in a quantum-statistical framework as an example of a solvable nonequilibrium problem. For the free quantum field, we calculate the exact form of the expectation values of the stress-energy tensor and the entropy current. For the stress-energy tensor, we find that a finite value can be obtained only by subtracting the vacuum of the density operator at some fixed proper time ${\ensuremath{\tau}}_{0}$. As a consequence, the stress-energy tensor acquires nontrivial quantum corrections to the classical free-streaming form.

DOI
10.1103/physrevd.105.056003

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Abstract It has recently been shown that relativistic quantum theory leads to a local interpretation of quantum mechanics wherein the universal wavefunction in configuration space is entirely replaced with an ensemble of local fluid equations in spacetime. For want of a fully relativistic quantum fluid treatment, we develop a model using the nonrelativistic Madelung equations, and obtain conditions for them to be local in spacetime. Every particle in the Madelung fluid is equally real, and has a definite position, momentum, kinetic energy, and potential energy. These are obtained by defining quantum momentum and kinetic energy densities for the fluid and separating the momentum into average and symmetric parts, and kinetic energy into classical kinetic and quantum potential parts. The two types of momentum naturally give rise to a single classical kinetic energy density, which contains the expected kinetic energy, even for stationary states, and we define the reduced quantum potential as the remaining part of the quantum kinetic energy density. We treat the quantum potential as a novel mode of internal energy storage within the fluid particles, which explains most of the nonclassical behavior of the Madelung fluid. For example, we show that in tunneling phenomena, the quantum potential negates the barrier so that nothing prevents the fluid from flowing through. We show how energy flows and transforms in this model, and that enabling local conservation of energy requires defining a quantum potential energy current that flows through the fluid rather than only flowing with it. The nonrelativistic treatment generally contains singularities in the velocity field, which undermines the goal of local dynamics, but we expect a proper relativistic treatment will bound the fluid particle velocities at c.