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Register a new userMaxwell Times in Higher-Order Generalized Hydrodynamics: Classical Fluids, and Carriers and Phonons in Semiconductors
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A family of the so-called Maxwell times which arises in the contexto of Higher-Order Generalized Hydrodynamics (also called Mesoscopic Hydro-Thermodynamics) is evidenced. This is done in the framework of a HOGH build within a statistical foundation in terms of a Non-Equilibrium Statistical Ensemble Formalism. It consists in a description in terms of the densities of particles and energy and their fluxes of all orders, with the motion described by a set of coupled nonlinear integro-differential equations involving them. These Maxwell Times have a fundamental role in determining the type of hydrodynamic motion that the system would display in the given condition and constraints. The different types of motion are well described by contractions of the full description done in terms of a reduced number of fluxes up to a certain order.
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It is analyzed the hydrodynamics of carriers (charge and heat motion) and phonons (heat motion) in semiconductors in the presence of constant electric fields. This is done in terms of a so-called Higher-Order Generalized Hydrodynamics (HOGH), also referred to as Mesoscopic Hydro-Thermodynamics (MHT), that is, covering phenomena involving motions displaying variations short in space and fast in time and being arbitrarily removed from equilibrium, as it is the case in modern electronic devices. The particular case of a MHT of order 1 is described, covering wire samples from macro to nano sizes. Electric and thermal conductivities are obtained. As the size decreases towards the nanometric scale, the MHT of order 1 produces results that in some cases greatly differ from those of the usual hydro-thermodynamics. The so-called Maxwell times associated to the different fluxes present in MHT are evidenced and analyzed; they have a quite relevant role in determining the characteristics of the motion.
Thermal transport in classical fluids is analyzed in terms of a Higher-Order Generalized Hydrodynamics (or Mesoscopic Hydro-Thermodynamics), that is, depending on the evolution of the energy density and its fluxes of all orders. It is derived in terms of a Kinetic Theory based on the Non-Equilibrium Statistical Ensemble Formalism. The general system of coupled evolution equations is derived. Maxwell times - which are of large relevance to determine the character of the motion - are derived. They also have a quite important role for the choice of the contraction of description (limitation in the number of fluxes to be retained) in the study of the hydrodynamic motion. In a description of order 1 it is presented an analysis of the technological process of thermal prototyping.
Quantum effects in material systems are often pronounced at low energies and become insignificant at high temperatures. We find that, perhaps counterintuitively, certain quantum effects may follow the opposite route and become sharp when extrapolated to high temperature within a classical liquid phase. In the current work, we suggest basic quantum bounds on relaxation (and thermalization) times, examine kinetic theory by taking into account such possible fundamental quantum time scales, find new general equalities connecting semi-classical dynamics and thermodynamics to Plancks constant, and compute current correlation functions. Our analysis suggests that, on average, the extrapolated high temperature dynamical viscosity of general liquids may tend to a value set by the product of the particle number density ${sf n}$ and Plancks constant $h$. We compare this theoretical result with experimental measurements of an ensemble of 23 metallic fluids where this seems to indeed be the case. The extrapolated high temperature viscosity of each of these liquids $eta$ divided (for each respective fluid by its value of ${sf n} h$) veers towards a Gaussian with an ensemble average value that is close to unity up to an error of size $0.6 %$. Inspired by the Eigenstate Thermalization Hypothesis, we suggest a relation between the lowest equilibration temperature to the melting or liquidus temperature and discuss a possible corollary concerning the absence of finite temperature ideal glass transitions. We suggest a general quantum mechanical derivation for the viscosity of glasses at general temperatures. We invoke similar ideas to discuss other transport properties and demonstrate how simple behaviors including resistivity saturation and linear $T$ resistivity may appear very naturally. Our approach suggests that minimal time lags may be present in fluid dynamics.
We, for the first time, report a first-principle proof of the equations of state used in the hydrodynamic theory for integrable systems, termed generalized hydrodynamics (GHD). The proof makes full use of the graph theoretic approach to Thermodynamic Bethe ansatz (TBA) that was proposed recently. This approach is purely combinatorial and relies only on common structures shared among Bethe solvable models, suggesting universal applicability of the method. To illustrate the idea of the proof, we focus on relativistic integrable quantum field theories with diagonal scatterings and without bound states such as strings.
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.
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