Related papers: Causality and classical dispersion relations
We consider wave models with lower order terms and recollect some recent results on energy and dispersive estimates for their solution based on symbolic type estimates for coefficients and partly stabilisation conditions. The exposition is…
Causality imposes strong restrictions on the type of operators that may be observables in relativistic quantum theories. In fact, causal violations arise when computing conditional probabilities for certain partial causally connected…
We derive necessary and sufficient conditions under which a large class of relativistic generalizations of Braginskii's magnetohydrodynamics with shear, bulk, and heat diffusion effects is causal and strongly hyperbolic in the fully…
We investigate analytically the magnetic instability in a rotating and electrically conducting fluid induced by an imposed magnetic field with its associated electric current. The short-wavelength approximation is used in the linear…
The effect of hydrodynamic interactions on the non-equilibrium stochastic dynamics of particles -- arising from the conservation of momentum in the fluid medium -- is examined in the context of the relationship between fluctuations,…
Discovery of causal relations is fundamental for understanding the dynamics of complex systems. While causal interactions are well defined for acyclic systems that can be separated into causally effective subsystems, a mathematical…
We derive the constitutive equations of causal relativistic dissipative hydrodynamics ($d$-hydrodynamics) from perfect nonextensive hydrodynamics ($q$-hydrodynamics) using the nonextensive/dissipative correspondence (NexDC) proposed by us…
The classical relativistic wave equations are presented as partial difference equations in the arena of covariant discrete phase space. These equations are also expressed as difference-differential equations in discrete phase space and…
We develop the relativistic theory of hydrodynamic fluctuations for application to high energy heavy ion collisions. In particular, we investigate their effect on the expanding boost-invariant (Bjorken) solution of the hydrodynamic…
The goal of this work is to determine classes of travelling solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz. It is shown that spurious solitary waves can occur in…
We construct a causal and covariantly stable kinetic model whose spectrum at real wavenumbers $k$ reproduces any rest-frame stable dissipative dispersion relation $\omega(k)$ via suitable initialization of the microscopic degrees of…
Relativity, time reversal invariance in mechanics and principle of causality can be in the bases of a type of vibration of the extensive objects. It is because, the detailed analysis of the relativistic movement of an extensive body entail…
Hydrodynamics provides a concise but powerful description of long-time and long-distance physics of correlated systems out of thermodynamic equilibrium. Here we construct hydrodynamic equations for nonrelativistic particles with a…
In this paper we investigate some properties, including causality, of a particular class of relativistic dissipative fluid theories of divergence type. This set is defined as those theories coming from a statistical description of matter,…
Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian…
In this work, we provide a novel method to constrain the causal parameter space of a relativistic hydrodynamic system exclusively from its linear stability analysis at non-zero momenta. Our approach exploits the Lorentz-invariant stability…
We summarize our recent investigations on how causality violations in Israel-Stewart-type relativistic viscous hydrodynamic simulations can give rise to both analytical and numerical instabilities. The classification of spacetime regions…
In the context of the M\"{u}ller-Israel-Stewart second order phenomenological theory for dissipative fluids, we analyze the effects of thermal conduction and viscosity in a relativistic fluid, just after its departure from hydrostatic…
We examine the stability of a class of quasilinear parabolic partial differential equations under perturbations. We are interested in the behavior of viscosity solutions as the perturbation parameter vanishes and establish explicit…
We present the results of a detailed study of energy correlations at steady state for a 1-D model of coupled energy and matter transport. Our aim is to discover -- via theoretical arguments, conjectures, and numerical simulations -- how…