Related papers: Current operators in integrable models: A review
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
We address the detailed study of the energy current and its components, heat and work, in the boundary-driven 1D XXZ quantum model. We carry out the investigation by considering two different approaches present in the literature. First, we…
We define the current of a quantum observable and, under well defined conditions, we connect its ensemble average to the index of a Fredholm operator. The present work builds on a formalism developed by Kellendonk and Schulz-Baldes…
In this study we investigate shallow turbidity density currents and underflows from mechanical point of view. We propose a simple hyperbolic model for such flows. On one hand, our model is based on very basic conservation principles. On the…
Gravity currents are a ubiquitous density driven flow occurring in both the natural environment and in industry. They include: seafloor turbidity currents, primary vectors of sediment, nutrient and pollutant transport; cold fronts; and…
Generalized hydrodynamics is a framework to study the large scale dynamics of integrable models, special fine-tuned one-dimensional many-body systems that possess an infinite number of local conserved quantities. Unlike classical models,…
We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical…
We present a novel analysis of the boundary integral operators associated to the wave equation. The analysis is done entirely in the time-domain by employing tools from abstract evolution equations in Hilbert spaces and semi-group theory.…
According to the dynamic van der Waals theory, we propose a thermodynamically consistent model for non-isothermal compressible two-phase flows with contact line motion. In this model, fluid temperature is treated as a primary variable,…
Integrable discretizations are introduced for the rational and hyperbolic spin Ruijsenaars--Schneider models. These discrete dynamical systems are demonstrated to belong to the same integrable hierarchies as their continuous--time…
This paper is a contribution to the theory of dynamical sampling. Our purpose is twofold. We first consider representations of sequences in a Hilbert space in terms of iterated actions of a bounded linear operator. This generalizes recent…
Recent experiments on active materials, such as dense bacterial suspensions and microtubule-kinesin motor mixtures, show a promising potential for achieving self-sustained flows. However, to develop active microfluidics it is necessary to…
We consider the hydrodynamics of the ideal fluid on a 2-torus and its Moyal deformations. The both type of equations have the form of the Euler-Arnold tops. The Laplace operator plays the role of the inertia-tensor. It is known that 2-d…
In ergodic quantum spin chains, locally conserved quantities such as energy or particle number generically evolve according to hydrodynamic equations as they relax to equilibrium. We investigate the complexity of simulating hydrodynamics at…
Unlike standard quantum mechanics, dynamical reduction models assign no particular a priori status to `measurement processes', `apparata', and `observables', nor self-adjoint operators and positive operator valued measures enter the…
We develop operator renewal theory for flows and apply this to obtain results on mixing and rates of mixing for a large class of finite and infinite measure semiflows. Examples of systems covered by our results include suspensions over…
In this Chapter, we present recent theoretical developments on the finite temperature transport of one dimensional electronic and magnetic quantum systems as described by a variety of prototype models. In particular, we discuss the…
The asymptotic dynamical correlation functions in one-dimensional spin chains are described by power-laws. The corresponding exponents characterize different bulk and boundary critical behavior. We present novel results for the logarithmic…
A representation of current is presented which can account for ideal conduction and distinguish superconductors, superfluids, ideal, and non-ideal conductors. The idea of the scheme is that different current operators and transport weights…
We review various formulations of conductivity for one-particle Hamiltonians and relate them to the current-current correlation measure. We prove that the current-current correlation measure for random Schr\"odinger operators has a density…