Exact Equipartition Research Articles

Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach

We study the symmetry resolved entanglement entropies in gapped integrable lattice models. We use the corner transfer matrix to investigate two prototypical gapped systems with a U(1) symmetry: the complex harmonic chain and the XXZ spin-chain. While the former is a free bosonic system, the latter is genuinely interacting. We focus on a subsystem being half of an infinitely long chain. In both models, we obtain exact expressions for the charged moments and for the symmetry resolved entropies. While for the spin chain we found exact equipartition of entanglement (i.e. all the symmetry resolved entropies are the same), this is not the case for the harmonic system where equipartition is effectively recovered only in some limits. Exploiting the gaussianity of the harmonic chain, we also develop an exact correlation matrix approach to the symmetry resolved entanglement that allows us to test numerically our analytic results.

Decay of the standard model Higgs field after inflation

We study the nonperturbative dynamics of the Standard Model (SM) after inflation, in the regime where the SM is decoupled from (or weakly coupled to) the inflationary sector. We use classical lattice simulations in an expanding box in (3+1) dimensions, modeling the SM gauge interactions with both global and Abelian-Higgs analogue scenarios. We consider different post-inflationary expansion rates. During inflation, the Higgs forms a condensate, which starts oscillating soon after inflation ends. Via nonperturbative effects, the oscillations lead to a fast decay of the Higgs into the SM species, transferring most of the energy into $Z$ and $W^{\pm}$ bosons. All species are initially excited far away from equilibrium, but their interactions lead them into a stationary stage, with exact equipartition among the different energy components. From there on the system eventually reaches equilibrium. We have characterized in detail, in the different expansion histories considered, the evolution of the Higgs and of its dominant decay products, until equipartition is established. We provide a useful mapping between simulations with different parameters, from where we derive a master formula for the Higgs decay time, as a function of the coupling constants, Higgs initial amplitude and postinflationary expansion rate.

GIANT LOBES OF CENTAURUS A RADIO GALAXY OBSERVED WITH THE SUZAKU X-RAY SATELLITE

[abridged] We report on Suzaku observations of selected regions within the Southern giant lobe of the radio galaxy Centaurus A. We focus on distinct X-ray features likely associated with fine radio structure of the lobe. We find that the spectral properties of the detected X-ray features are equally consistent with thermal emission from hot gas, or with a power-law radiation continuum. However, the plasma parameters implied by these different models favor a synchrotron origin for the analyzed X-ray spots, indicating that a very efficient acceleration of electrons is taking place within the giant structure of Centaurus A, albeit only in isolated and compact regions. We also present a detailed analysis of the diffuse X-ray emission, resulting in a tentative detection of a soft excess component best fitted by a thermal model with a temperature of 0.5 keV. The exact origin of the observed excess remains uncertain, although energetic considerations point to thermal gas filling the bulk of the volume of the lobe and mixed with the non-thermal plasma. The corresponding pressure of the thermal gas in such a case appears to be in almost exact equipartition with the pressure provided by the radio-emitting electrons and the magnetic field. Although tentative, our findings potentially imply that the structure of the extended lobes in active galaxies is likely to be highly inhomogeneous, with magnetic reconnection processes continuously converting magnetic energy to internal energy of the plasma particles, leading to spatial and temporal variations in the plasma parameters around the equilibrium condition.

Brownian motion of black holes in stellar systems with non-Maxwellian distribution of the field stars

AbstractA massive black hole at the center of a dense stellar system, such as a globular cluster or a galactic nucleus, is subject to a random walk due gravitational encounters with nearby stars. It behaves as a Brownian particle, since it is much more massive than the surrounding stars and moves much more slowly than they do. If the distribution function for the stellar velocities is Maxwellian, there is a exact equipartition of kinetic energy between the black hole and the stars in the stationary state. However, if the distribution function deviates from a Maxwellian form, the strict equipartition cannot be achieved.The deviation from equipartition is quantified in this work by applying the Tsallis q-distribution for the stellar velocities in a q-isothermal stellar system and in a generalized King model.

On the Saturation of Astrophysical Dynamos: Numerical Experiments with the No-Cosines Flow

In the context of astrophysical dynamos we illustrate that the no-cosines flow, with zero mean helicity, can drive fast dynamo action and we study the dynamo’s mode of operation during both the linear and non-linear saturation regimes. It turns out that in addition to a high growth rate in the linear regime, the dynamo saturates at a level significantly higher than normal turbulent dynamos, namely at exact equipartition when the magnetic Prandtl number Prm∼ 1. Visualization of the magnetic and velocity fields at saturation will help us to understand some of the aspects of the non-linear dynamo problem.

Unsteady equipartition MHD solutions

The unsteady equipartition solutions are introduced that describe a plasma relaxation in regime of a strong interaction between the plasma velocity V and the magnetic field B and depend on all four variables t,x,y,z. The solutions exist when the kinematic viscosity ν is equal to the magnetic diffusivity η and V=±B/ρμ. The exact equipartition solutions to the boundary value problem with the “no-slip” boundary condition are derived. The solutions depend on infinitely many parameters and describe the plasma relaxation in a ball with a constant pressure at the boundary. The translationally invariant exact solutions are obtained for ν≠η for which plasma is confined in cylindrical domains by the magnetic field B only while the plasma pressure P is zero at the boundary and is positive inside the domains.

Smoothing of the mode-power fluctuations in lossless optical fibers due to the source spectral bandwidth

The statistical variance associated with the mode-power equipartition process taking place over an ensemble of similar lossless fibers, is shown to vanish after a traveled distance proportional to the inverse of the source bandwidth. Accordingly, exact equipartition takes place in each sample of the statistical ensemble, thus justifying measurements performed on the single fiber.

Exact Equilibration of Harmonically Bound Oscillator Chains

The approach to equilibrium of a finite segment of an infinite chain of harmonically coupled, harmonically bound oscillators is treated exactly, both when the initial description of the rest of the chain is canonical and when it is Gaussian. The necessary mathematical properties of the bound oscillator functions are developed and used to demonstrate exact equipartition of energy. The entropy of the finite segment, or system, is shown to evolve to a time-independent equilibrium state that is, in the limit of weak coupling, the correct one for a system of noninteracting harmonic oscillators.