Out-of-time-ordered density correlators in Luttinger liquids

Information scrambling and the butterfly effect in chaotic quantum systems can be diagnosed by out-of-time-ordered (OTO) commutators through an exponential growth and large late time value. We show that the latter feature shows up in a strongly correlated many-body system, a Luttinger liquid, whose density fluctuations we study at long and short wavelengths, both in equilibrium and after a quantum quench. We find rich behaviour combining robustly universal and non-universal features. The OTO commutators display temperature and initial state independent behaviour, and grow as $t^2$ for short times. For the short wavelength density operator, they reach a sizeable value after the light cone only in an interacting Luttinger liquid, where the bare excitations break up into collective modes. We benchmark our findings numerically on an interacting spinless fermion model in 1D, and find persistence of central features even in the non-integrable case. As a non-universal feature, the short time growth exhibits a distance dependent power.Comment: 6 pages, 2 figure

Stochastic Thermodynamics of oscillators networks

We apply the stochastic thermodynamics formalism to describe the dynamics of systems of complex Langevin and Fokker-Planck equations. We provide in particular a simple and general recipe to calculate thermodynamical currents, dissipated and propagating heat for networks of nonlinear oscillators. By using the Hodge decomposition of thermodynamical forces and fluxes, we derive a formula for entropy production that generalises the notion of non-potential forces and makes trans- parent the breaking of detailed balance and of time reversal symmetry for states arbitrarily far from equilibrium. Our formalism is then applied to describe the off-equilibrium thermodynamics of a few examples, notably a continuum ferromagnet, a network of classical spin-oscillators and the Frenkel-Kontorova model of nano friction.Comment: 8 pages, 1 figur

Pairing of Parafermions of Order 2: Seniority Model

As generalizations of the fermion seniority model, four multi-mode Hamiltonians are considered to investigate some of the consequences of the pairing of parafermions of order two. 2-particle and 4-particle states are explicitly constructed for H_A = - G A^+ A with A^+}= 1/2 Sum c_{m}^+ c_{-m}^+ and the distinct H_C = - G C^+ C with C^+}= 1/2 Sum c_{-m}^+ c_{m}^+, and for the time-reversal invariant H_(-)= -G (A^+ - C^+)(A-C) and H_(+) = -G (A^+dagger + C^+)(A+C), which has no analogue in the fermion case. The spectra and degeneracies are compared with those of the usual fermion seniority model.Comment: 18 pages, no figures, no macro

Spin-1 Antiferromagnetic Heisenberg Chains in an External Staggered Field

We present in this paper a nonlinear sigma-model analysis of a spin-1 antiferromagnetic Heisenberg chain in an external commensurate staggered magnetic field. After rediscussing briefly and extending previous results for the staggered magnetization curve, the core of the paper is a novel calculation, at the tree level, of the Green functions of the model. We obtain precise results for the elementary excitation spectrum and in particular for the spin gaps in the transverse and longitudinal channels. It is shown that, while the spectral weight in the transverse channel is exhausted by a single magnon pole, in the longitudinal one, besides a magnon pole a two-magnon continuum appears as well whose weight is a stedily increasing function of the applied field, while the weight of the magnon decreases correspondingly. The balance between the two is governed by a sum rule that is derived and discussed. A detailed comparison with the present experimental and numerical (DMRG) status of the art as well as with previous analytical approaches is also made.Comment: 23 pages, 3 figures, LaTe

The Abelianization of QCD Plasma Instabilities

QCD plasma instabilities appear to play an important role in the equilibration of quark-gluon plasmas in heavy-ion collisions in the theoretical limit of weak coupling (i.e. asymptotically high energy). It is important to understand what non-linear physics eventually stops the exponential growth of unstable modes. It is already known that the initial growth of plasma instabilities in QCD closely parallels that in QED. However, once the unstable modes of the gauge-fields grow large enough for non-Abelian interactions between them to become important, one might guess that the dynamics of QCD plasma instabilities and QED plasma instabilities become very different. In this paper, we give suggestive arguments that non-Abelian self-interactions between the unstable modes are ineffective at stopping instability growth, and that the growing non-Abelian gauge fields become approximately Abelian after a certain stage in their growth. This in turn suggests that understanding the development of QCD plasma instabilities in the non-linear regime may have close parallels to similar processes in traditional plasma physics. We conjecture that the physics of collisionless plasma instabilities in SU(2) and SU(3) gauge theory becomes equivalent, respectively, to (i) traditional plasma physics, which is U(1) gauge theory, and (ii) plasma physics of U(1)x U(1) gauge theory.Comment: 36 pages; 15 figures [minor changes made to text, and new figure added, to reflect published version

Over-populated gauge fields on the lattice

We study nonequilibrium dynamics of SU(2) pure gauge theory starting from initial over-population, where intense classical gauge fields are characterized by a single momentum scale Q_s. Classical-statistical lattice simulations indicate a quick evolution towards an approximate scaling behavior with exponent 3/2 at intermediate times. Remarkably, the value for the scaling exponent may be understood as arising from the leading O(g^2) contribution in the presence of a time-dependent background field. The phenomenon is associated to weak wave turbulence describing an energy cascade towards higher momenta. This particular aspect is very similar to what is observed for scalar theories, where an effective cubic interaction arises because of the presence of a time-dependent Bose condensate.Comment: 15 pages, 4 figure

From dynamical scaling to local scale-invariance: a tutorial

Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced. Schr\"odinger-invariance, the most simple example of local scale-invariance, will be introduced as a dynamical symmetry in the Edwards-Wilkinson universality class of interface growth. The Lie algebra construction, its representations and the Bargman superselection rules will be combined with non-equilibrium Janssen-de Dominicis field-theory to produce explicit predictions for responses and correlators, which can be compared to the results of explicit model studies. At the next level, the study of non-stationary states requires to go over, from Schr\"odinger-invariance, to ageing-invariance. The ageing algebra admits new representations, which acts as dynamical symmetries on more general equations, and imply that each non-equilibrium scaling operator is characterised by two distinct, independent scaling dimensions. Tests of ageing-invariance are described, in the Glauber-Ising and spherical models of a phase-ordering ferromagnet and the Arcetri model of interface growth.Comment: 1+ 23 pages, 2 figures, final for