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Register a new userA Model for Hydrodynamics in Kinetic Field Theory
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In this work, we introduce an effective model for both ideal and viscous fluid dynamics within the framework of kinetic field theory (KFT). The main application we have in mind is cosmic structure formation where gaseous components need to be gravitationally coupled to dark matter. However, we expect that the fluid model is much more widely applicable. The idea behind the effective model is similar to that of smoothed particle hydrodynamics. By introducing mesoscopic particles equipped with a position, a momentum, and an enthalpy, we construct a free theory for such particles and derive suitable interaction operators. We then show that the model indeed leads to the correct macroscopic evolution equations, namely the continuity, Euler, Navier-Stokes, and energy conservation equations of both ideal and viscous hydrodynamics.
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Using generalized hydrodynamics (GHD), we develop the Euler hydrodynamics of classical integrable field theory. Classical field GHD is based on a known formalism for Gibbs ensembles of classical fields, that resembles the thermodynamic Bethe ansatz of quantum models, which we extend to generalized Gibbs ensembles (GGEs). In general, GHD must take into account both solitonic and radiative modes of classical fields. We observe that the quasi-particle formulation of GHD remains valid for radiative modes, even though these do not display particle-like properties in their precise dynamics. We point out that because of a UV catastrophe similar to that of black body radiation, radiative modes suffer from divergences that restrict the set of finite-average observables; this set is larger for GGEs with higher conserved charges. We concentrate on the sinh-Gordon model, which only has radiative modes, and study transport in the domain-wall initial problem as well as Euler-scale correlations in GGEs. We confirm a variety of exact GHD predictions, including those coming from hydrodynamic projection theory, by comparing with Metropolis numerical evaluations.
Recently Mazenko and Das and Mazenko introduced a non-equilibrium field theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the ensemble. For the free theory, we recover the continuity and Jeans equations of a collisionless gas. For a theory containing two-particle interactions in a canonical perturbation series, we find the macroscopic evolution equations to be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy (BBGKY hierarchy) with a truncation criterion depending on the order in perturbation theory. This establishes a direct link between the classical and the field-theoretical approaches to kinetic theory that might serve as a starting point to investigate kinetic theory beyond the classical limits.
We have examined the stationary state solutions of a bond diluted kinetic Ising model under a time dependent oscillating magnetic field within the effective-field theory (EFT) for a honeycomb lattice $(q=3)$. Time evolution of the system has been modeled with a formalism of master equation. The effects of the bond dilution, as well as the frequency $(omega)$ and amplitude $(h/J)$ of the external field on the dynamic phase diagrams have been discussed in detail. We have found that the system exhibits the first order phase transition with a dynamic tricritical point (DTCP) at low temperature and high amplitude regions, in contrast to the previously published results for the pure case cite{Ling}. Bond dilution process on the kinetic Ising model gives rise to a number of interesting and unusual phenomena such as reentrant phenomena and has a tendency to destruct the first-order transitions and the DTCP. Moreover, we have investigated the variation of the bond percolation threshold as functions of the amplitude and frequency of the oscillating field.
This work presents a novel derivation of the expressions that describe the distortions of the cosmic microwave background curve due to the interactions between photons and the electrons present in dilute ionized systems. In this approach, a simplified one-dimensional evolution equation for the photon number occupation is applied to describe the mentioned interaction. This methodology emphasizes the physical features of the Sunyaev-Zeldovich effect and suggests the existence of links between basic statistical physics and complex applications involving radiative processes.
The Navier--Stokes transport coefficients of multicomponent granular suspensions at moderate densities are obtained in the context of the (inelastic) Enskog kinetic theory. The suspension is modeled as an ensemble of solid particles where the influence of the interstitial gas on grains is via a viscous drag force plus a stochastic Langevin-like term defined in terms of a background temperature. In the absence of spatial gradients, it is shown first that the system reaches a homogeneous steady state where the energy lost by inelastic collisions and viscous friction is compensated for by the energy injected by the stochastic force. Once the homogeneous steady state is characterized, a emph{normal} solution to the set of Enskog equations is obtained by means of the Chapman--Enskog expansion around the emph{local} version of the homogeneous state. To first-order in spatial gradients, the Chapman--Enskog solution allows us to identify the Navier--Stokes transport coefficients associated with the mass, momentum, and heat fluxes. In addition, the first-order contributions to the partial temperatures and the cooling rate are also calculated. Explicit forms for the diffusion coefficients, the shear and bulk viscosities, and the first-order contributions to the partial temperatures and the cooling rate are obtained in steady-state conditions by retaining the leading terms in a Sonine polynomial expansion. The results show that the dependence of the transport coefficients on inelasticity is clearly different from that found in its granular counterpart (no gas phase). The present work extends previous theoretical results for emph{dilute} multicomponent granular suspensions [Khalil and Garzo, Phys. Rev. E textbf{88}, 052201 (2013)] to higher densities.
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