Related papers: Flows of Calogero-Moser Systems
The exhaustive classification of stationary incompressible flows with constant total pressure of ideal infinitely electrically conducting fluid is given. By introduction of curvilinear coordinates based on streamlines and magnetic lines of…
In this article we consider two particular examples of general construction proposed in arXiv:2012.15529. We consider the integrable extensions of the classical elliptic Calogero-Moser model of N particles with spin and the integrable…
In this paper we discuss a family of models of particle and energy diffusion on a one-dimensional lattice, related to those studied previously in [Sasamoto-Wadati], [Barraquand-Corwin] and [Povolotsky] in the context of KPZ universality…
The Calogero-Sutherland model represents a paradigmatic example of an integrable quantum system with applications ranging from cold atoms to random matrix theory. Combining sum rules with the Monte Carlo technique, we introduce a stochastic…
A method for constructing coherent states (CS) of finite-level systems with a given angular momentum is proposed. To this end we generalize the known spin equation (SE) to an infinite-dimensional Fock space. The equation describes a special…
In this work, we derive the equations of motion governing the hydrodynamics of spin-F spinor condensates. We pursue a description based on standard physical variables (total density and superfluid velocity), alongside 2F `spin-nodes': unit…
A new ansatz is presented for a Lax pair describing systems of particles on the line interacting via (possibly nonsymmetric) pairwise forces. Particular cases of this yield the known Lax pairs for the Calogero-Moser and Toda systems, as…
We introduce spin Calogero-Moser systems associated with root systems of simple Lie algebras and give the associated Lax representations (with spectral parameter) and fundamental Poisson bracket relations. The associated integrable models…
Over the past few years, we developed a mathematically rigorous method to study the dynamical processes associated to nonlinear Forchheimer flows for slightly compressible fluids. We have proved the existence of a geometric transformation…
The rational quantum algebraically integrable systems are non-trivial generalizations of Laplacian operators to the case of elliptic operators with variable coefficients. We study corresponding extensions of Laplacian growth connected with…
As an approximate theory that is highly regarded for its computational efficiency, geometrical optics (GO) is widely used for modeling waves in various areas of physics. However, GO fails at caustics, which significantly limits its…
We apply a recently introduced reduction procedure based on the embedding of non-crystallographic Coxeter groups into crystallographic ones to Calogero-Moser systems. For rational potentials the familiar generalized Calogero Hamiltonian is…
Diffusion, as described by Fick's laws, governs the spreading of particles, information, data, and even financial fluctuations. However, due to its parabolic structure, the diffusion equation leads to an unphysical prediction: any localized…
In \cite{kri02}, I. M. Krichever invented the space of matrices parametrizing the cotangent bundle of moduli space of stable vector bundles over a compact Riemann surface, which is named as the Hitchin system after the investigation…
A substantial number of algorithms exists for the simulation of moving particles suspended in fluids. However, finding the best method to address a particular physical problem is often highly non-trivial and depends on the properties of the…
We study invariant manifolds of measure-valued solutions of the partial differential equation for geodesic flow of a pressureless fluid. These solutions describe interaction dynamics on lower-dimensional support sets; for example, curves,…
To acquire the ability to numerically study the rheology of particulate two-phase flows that lack scale separation, we present a general method to average or coarse-grain the equations of motion of a mixture of a continuous fluid of…
We describe a new hybrid N-body/hydrodynamical code based on the particle-mesh (PM) method and the piecewise-parabolic method (PPM) for use in solving problems related to the evolution of large-scale structure, galaxy clusters, and…
It is shown that the deformed Calogero-Moser-Sutherland (CMS) operators can be described as the restrictions on certain affine subvarieties (called generalised discriminants) of the usual CMS operators for infinite number of particles. The…
Quantum liquids in two dimensions represent interesting dynamical quantum systems for several reasons, among them the possibility of the existence of infinite hidden symmetries, such as conformal symmetry or the symmetry associated with…