Related papers: The collision rate ansatz for the classical Toda l…
The discrete models of the Toda and Volterra chains are being constructed out of the continuum two-boson KP hierarchies. The main tool is the discrete symmetry preserving the Hamiltonian structure of the continuum models. The two-boson…
We construct a non-trivial $U(1)/\mathbb{Z}_q$ principal bundle on~$T^4$ from the compact $U(1)$ lattice gauge field by generalizing L\"uscher's constriction so that the cocycle condition contains $\mathbb{Z}_q$ elements (the 't~Hooft…
A simplified version of a classical problem in thermodynamics -- the adiabatic piston -- is discussed in the framework of kinetic theory. We consider the limit of gases whose relaxation time is extremely fast so that the gases contained on…
Electron-correlation effects on cohesive energy, lattice constant and bulk compressibility of rutile are calculated using an ab-initio scheme. A competition between the two groups of partially covalent Ti-O bonds is the reason that the…
A quantum $n$-particle model consisting of an open $q$-difference Toda chain with two-sided boundary interactions is placed on a finite integer lattice. The spectrum and eigenbasis are computed by establishing the equivalence with a…
A simple quantum defect model gives analytic expressions for the complex scattering length and threshold collision rates of ultracold molecules. If the probability of reaction in the short-range part of the collision is high, the model…
We consider solutions of the 2D Toda lattice hierarchy which are trigonometric functions of the ``zeroth'' time $t_0=x$. It is known that their poles move as particles of the trigonometric Ruijsenaars-Schneider model. We extend this…
We study linear closure relations for the moments' method applied to simple kinetic equations. The equations are linear collisional models (velocity jump processes) which are well suited to this type of approximation. In this simplified, 1…
In accelerator physics, the concept of impedance is popularly used to describe the interactions of charged particles inside a bunch or between bunches in a train. Standard formulations of impedance assume that the driving charge has a…
The non-equilibrium steady states of integrable models are believed to be described by the Generalized Gibbs Ensemble (GGE), which involves all local and quasi-local conserved charges of the model. In this work we investigate integrable…
We discuss the bihamiltonian geometry of the Toda lattice (periodic and open). Using some recent results on the separation of variables for bihamiltonian manifolds, we show that these systems can be explicitly integrated via the classical…
The classical approach to linking lattice dynamics properties to continuum equations of motion, the "method of long waves," is extended to include higher order terms. The additional terms account for non-local and non-linear effects. In the…
We consider the convergence of kinetic Langevin dynamics to its ergodic invariant measure, which is Gibbs distribution. Instead of the standard setup where the friction coefficient is a constant scalar, we investigate position-dependent…
We propose a conjecture on the relative twist formula of $\ell$-adic sheaves, which can be viewed as a generalization of Kato-Saito's conjecture. We verify this conjecture under some transversal assumptions. We also define a relative…
In the Hermite-expansion-based multiple-relaxation-time lattice Boltzmann (LB) model [Shan & Chen, Int. J. Mod. Phys. C, 18, 635, (2007)], a separate relaxation time is assigned to each of the tensorial moments of the collision term. Here…
In this short review we compare different ways to construct solutions of the periodic Toda lattice. We give two recipes that follow from the projection method and compare them with the algebra-geometric construction of Krichever.
When an atomic-size break junction is mechanically stretched, the total conductance of the contact remains approximately constant over a wide range of elongations, although at the same time the transmissions of the individual channels…
Causal Dynamical Triangulations (CDT) is a non-perturbative quantisation of general relativity. Ho\v{r}ava-Lifshitz gravity on the other hand modifies general relativity to allow for perturbative quan- tisation. Past work has given rise to…
It is known that there is a duality between the Davey--Stewartson type coupled systems and a class of integrable two--dimensional Toda type lattices. More precisely, the coupled systems are generalized symmetries for the lattices and the…
Quantitative estimates are derived, on the whole space, for the relative entropy between the joint law of random interacting particles and the tensorized law at the limiting systeme. The developed method combines the relative entropy method…