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arXiv:1210.6053

Quantum chaos in the perfect fluid: spectrum of initial fluctuations in the little bang

Kevin Dusling, Thomas Epelbaum, François Gelis, Raju Venugopalan B

Published Oct 22, 2012• 1 citation
arXivHTMLPDF

Abstract

We outline how unstable quantum fluctuations decohere classical fields in heavy ion collisions, leading to an equation of state and hydrodynamics. Explicit numerical realization of this framework in a scalar $ϕ^4$ theory demonstrates that anomalously low values of $η/s$ can be generated.

DOI
10.48550/arxiv.1210.6053

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We outline how unstable quantum fluctuations decohere classical fields in heavy ion collisions, leading to an equation of state and hydrodynamics. Explicit numerical realization of this framework in a scalar ϕ4ϕ^4ϕ4 theory demonstrates that anomalously low values of η/sη/sη/s can be generated.
In this paper, we study how quantum fluctuations modify the quantum evolution of an initially classical field theory. We consider a scalar ϕ 4 theory coupled to an external source as a toy model for the color glass condensate description of the early time dynamics of heavy-ion collisions. We demonstrate that quantum fluctuations considerably modify the time evolution driving the system to evolve in accordance with ideal hydrodynamics. We attempt to understand the mechanism behind this relaxation to ideal hydrodynamics by using modified initial spectra and studying the particle content of the theory.
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We discuss phenomenology associated with turbulent hydrodynamics in quantum fluids from a condensed-matter perspective. We begin with weakly-interacting superfluids, often modeled by a mean-field theory governed by the Gross-Pitaevskii equation. Considering the effect of quantum fluctuations beyond the mean-field approximation, we propose a study of many-body quantum effects in turbulent hydrodynamics, especially near zero temperature. We motivate examples of quantum many-body systems where such effects may be uncovered. These include bosons confined in a periodic potential in low spatial dimensions (one and two), and the associated quantum critical point of the superfluid-insulator transition, realized in present-day ultracold-atom and quantum computing platforms. We conclude by listing a set of (open) questions that may be answered using modern quantum many-body techniques. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.
We discuss phenomenology associated with turbulent hydrodynamics in quantum fluids from a condensed-matter perspective. We begin with weakly interacting superfluids, often modelled by a mean-field theory governed by the Gross-Pitaevskii (GP) equation. Considering the effect of quantum fluctuations beyond the mean-field approximation, we propose a study of many-body quantum effects in turbulent hydrodynamics, especially near zero temperature. We indicate examples of quantum many-body systems where such effects may be uncovered. These include bosons confined in a periodic potential in low spatial dimensions (one and two), and the associated quantum critical point of the superfluid-insulator transition, realized in present-day ultracold-atom and quantum computing platforms. We conclude by listing a set of (open) questions that may be answered using modern quantum many-body techniques. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.
Since the systems described by quantum fields are by definition extended, it is natural to think that in some limit they may reasonably well be approximated as fluids. This means that the state of the system is parameterized by a few locally well-defined fields such as temperature or energy density, obeying a set of hyperbolic equations of motion. A concrete example is the extensive use of fluid models to describe high-energy collisions [BelLan56, CarDuo73, CoFrSc74, Bjo83, CarZac83]. Our earlier derivation of quantum kinetic theory suggests a way to put this insight on a formal basis. Within its range of validity, the Boltzmann equation will drive the one-particle distribution function towards local thermal equilibrium. On scales much larger than the local thermalization scale, we expect to see hydrodynamical behavior [BeCoPa02]. This is, after all, the usual way of deriving hydrodynamics from kinetic theory [Hua87]. Beware, notwithstanding, that even at the level of classical kinetic theory there are still open questions regarding the cross-over from the kinetic to the hydro regime [KarGor02, KarGor03]. If we understand hydrodynamics as stated in the first paragraph of this chapter, then a system defined in terms of a quantum field may not have a hydrodynamic limit. This has been shown in [Elz02] for the case of a free Fermi field.
We propose new ideal hydrodynamics in the function space which describes a fluid composed of the 1+1 dimensional real scalar field in the framework of the stochastic variational method (SVM). In the derivation, the thermal equilibrium is assumed to the internal state of fluid elements in the function space of the scalar-field configuration. The deterministic trajectory of the functional fluid element is related to the functional generalization of the Bohmian trajectory in relativistic quantum field theory. To find the correspondence relation to standard hydrodynamics, a further coarse-graining should be introduced. Thus functional hydrodynamics is regarded as a mesoscopic theory such as the Boltzmann equation in the dynamical hierarchy of many-body systems. Functional hydrodynamics reproduces the exact behaviors of relativistic quantum field theory in a certain limit. We thus expect that our theory is applicable to study the influence of quantum-field theoretical fluctuation in collective flows of produced particles in relativistic heavy-ion collisions.