Related papers: Current operators in integrable models: A review
We theoretically describe the dynamics of swimmer populations confined in thin liquid films. We first demonstrate that hydrodynamic interactions between confined swimmers only depend on their shape and are independent of their specific…
Motivated by a long-standing debate concerning the nature and interrelations of surface-tension variables in fluid membranes, we reformulate the thermodynamics of a membrane vesicle as a generic two-dimensional finite system enclosing a…
We address spin transport in the easy-axis Heisenberg spin chain subject to integrability-breaking perturbations. We find that spin transport is subdiffusive with dynamical exponent $z=4$ up to a timescale that is parametrically long in the…
Scientific machine learning for inferring dynamical systems combines data-driven modeling, physics-based modeling, and empirical knowledge. It plays an essential role in engineering design and digital twinning. In this work, we primarily…
Active gel theory has recently been very successful in describing biologically active materials such as actin filaments or moving bacteria in temporally fixed and simple geometries such as cubes or spheres. Here we develop a computational…
We prove under certain assumptions that there exists a solution of the Schrodinger or the Heisenberg equation of motion generated by a linear operator H acting in some complex Hilbert space H, which may be unbounded, not symmetric, or not…
We propose an exact flow equation for composite operators and their correlation functions. This can be used for a scale-dependent partial bosonization or "flowing bosonization" of fermionic interactions, or for an effective change of…
The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.…
In recent years we have witnessed a concentrated effort to make sense of thermodynamics for small-scale systems. One of the main difficulties is to capture a suitable notion of work that models realistically the purpose of quantum machines,…
Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium…
Suspensions of swimming particles exhibit complex collective behaviors driven by hydrodynamic interactions, showing persistent large-scale flows and long-range correlations. While heavily studied, it remains unclear how such structures…
We consider current-current deformations that generalise $T\bar{T}$ ones, and show that they may be also introduced for integrable spin chains. In analogy with the integrable QFT setup, we define the deformation as a modification of the S…
We analyze the conservation properties of various discretizations of the system of compressible Euler equations for shock-free flows, with special focus on the treatment of the energy equation and on the induced discrete equations for other…
In an effort to address integrability breaking in cold gas experiments, we extend the integrable hydrodynamics of the 1d Lieb-Liniger model with two additional components representing the population of atoms in the first and second…
We introduce calculus-based formulas for the continuous Euler and homotopy operators. The 1D continuous homotopy operator automates integration by parts on the jet space. Its 3D generalization allows one to invert the total divergence…
For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians…
The article describes various aspects of mathematical modeling of fluid flows, both in general and with reference to hydraulic machinery. The article reviews historical development of corresponding methods of mathematical modeling.…
We derive an explicit mapping between the spectra of conserved local operators of integrable quantum lattice models and the density distributions of their thermodynamic particle content. This is presented explicitly for the Heisenberg XXZ…
We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A…
The Koopman and Perron Frobenius transport operators are fundamentally changing how we approach dynamical systems, providing linear representations for even strongly nonlinear dynamics. Although there is tremendous potential benefit of such…