Parametric instability of classical Yang-Mills fields in a color magnetic background

Abstract

We investigate instabilities of classical Yang-Mills fields in a time-dependent spatially homogeneous color magnetic background field in a nonexpanding geometry for elucidating the earliest stage dynamics of ultrarelativistic heavy-ion collisions. The background field configuration considered in this article is spatially homogeneous and temporally periodic and is introduced by Berges-Scheffler-Schlichting-Sexty (BSSS). We discuss the whole structure of instability bands of fluctuations around the BSSS background gauge field on the basis of Floquet theory, which enables us to discuss the stability in a systematic way. We find various instability bands on the ðp z ; p T Þ plane. These instability bands are caused by parametric resonance despite the fact that the momentum dependence of the growth rate for jpj ≤ ffiffiffi ffi B p is similar to a Nielsen-Olesen instability. Moreover, some of the instability bands are found to emerge not only in the low-momentum but also in the high-momentum region, typically of the order of the saturation momentum as jpj ∼ ffiffiffi ffi B p ∼ Q s .

Entropy production and isotropization in Yang–Mills theory using a quantum distribution function

“…Thirdly, the HW entropy in the product ansatz S (PA) HW is not gauge invariant. Nevertheless we might expect that the gauge dependence does not cause serious problems in entropy production because gauge degrees of freedom dose not significantly contribute to chaoticity and instability [19,31], and that the production rate of the HW entropy from random initial condition in the product ansatz agrees with the gauge invariant KS rate [33].…”

Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function

“…Instead, we concentrate on entropy production in quantum systems whose classical counter parts are chaotic, and the semiclassical approximation is valid. There are many physical systems satisfying these characteristics [39]: Among them, we have in mind the problem of the early thermaliztion in high-energy heavy-ion collisions (see review [7] and recent studies [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]) at the relativistic heavy-ion collider in the Brookhaven National Laboratory [26][27][28][29] and the large hadron collider at CERN [30]. * tsukiji@yukawa.kyoto-u.ac.jp † The present address: Keio University Chaotic classical systems are characterized by the sensitive dependence of the trajectory on the initial condition, and trajectories starting from adjacent initial conditions with the difference δX(0) in the phase space deviate exponentially |δX(t)| = exp(λt)|δX(0)| from each other: The exponent λ is called a Lyapunov exponent.…”

Parametric instability of classical Yang-Mills fields in an expanding geometry

“…(20) remains. This is the generalization of the nonexpanding case [29,30]. We also mention that there exists not only color magnetic fields but also transversely polarized color electric fields.…”

“…This is nothing but the homogeneous background field discussed in Refs. [29,30] in the nonexpanding geometry with a phase shift Δ quantifying the earlier time effects.…”

“…Recently, it has been suggested that the CYM field under a time-dependent homogeneous color magnetic background field shows instability in a nonexpanding geometry [29]. It has been clarified that the origin of the instability is parametric instability and the CYM field in a homogeneous background has multiple instability bands extending to the transverse as well as the longitudinal momentum directions [30]. The parametric instability is ubiquitous in physics from classical mechanical problems on a pendulum to quantum field theories [31], as well as in the cosmic inflation [32].…”