Related papers: The collision rate ansatz for the classical Toda l…
Boundary conditions compatible with classical integrability are studied both directly, using an approach based on the explicit construction of conserved quantities, and indirectly by first developing a generalisation of the Lax pair idea.…
We consider an electron model of superconductivity on a three-dimensional lattice where there are on-site attractive Hubbard interaction and long-range repulsive Coulomb interaction. It is claimed that fully gapped $s$-wave…
We consider the classical Prandtl-Tomlinson model of a particle moving on a corrugated potential, pulled by a spring. In the usual situation in which pulling acts at constant velocity $\dot\gamma$, the model displays an average friction…
We study an initial value problem for the Toda lattice with almost periodic initial data. We consider initial data for which the associated Jacobi operator is absolutely continuous and has a spectrum satisfying a Craig-type condition, and…
We consider an elastic-plastic medium whose motion equations are isomorphic to Maxwell's equations. Electrical charges are modeled by pressure centers of the medium. The electric interaction is shown to be concerned with the conservation…
We study stability of higher-derivative dynamics from the viewpoint of more general correspondence between symmetries and conservation laws established by the Lagrange anchor. We show that classical and quantum stability may be provided if…
The average of the ratio of powers of the spectral determinants of the Dirac operator in the $\epsilon$-regime of QCD is shown to satisfy a Toda lattice equation. The quenched limit of this Toda lattice equation is obtained using the…
The main purpose of the paper is to demonstrate that condition of invariance with respect to the Legendre transformations allows effectively isolate the class of integrable difference equations on the triangular lattice, which can be…
The identity of classical motion is established for two physically different models, one of which is the relativistic particle with torsion, whose action contains higher derivatives and which is the effective system for the statistically…
We report on a lattice computation of the second moment of the pion matrix element of the twist-2 non-singlet operator corresponding to the average momentum of parton densities. We apply a fully non-perturbatively evaluated running…
Coulomb collisions in plasmas are typically modeled using the Boltzmann collision operator, or its variants, which apply to weakly magnetized plasmas in which the typical gyroradius of particles significantly exceeds the Debye length.…
We analyze the physical mechanisms leading either to synchronization or to the formation of spatio-temporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we…
We derive the classical dynamics of massless charged particles in a rigorous way from first principles. Since due to ultraviolet divergences this dynamics does not follow from an action principle, we rely on a) Maxwell's equations, b)…
We develop a theory of static friction by modeling the homogeneous surfaces of contact as being composed of a regular array of compressible elastic smooth microscopic inclines. Static friction is thought of as the resistance due to having…
We establish a correspondence between classical $A_n^{(1)}$ affine Toda field theories and $A_n$ Bethe Ansatz systems. We show that the connection coefficients relating specific solutions of the associated classical linear problem satisfy…
The Toda lattice is a nonlinear but integrable system. Here we study the thermalization problem in one-dimensional, perturbed Toda lattices in the thermodynamic limit. We show that the thermalization time, $T_{eq}$, follows a universal law;…
We obtained the global persistence exponent $\theta_g$ for a continuous spin model on the simple cubic lattice with double-exchange interaction by using two different methods. First, we estimated the exponent $\theta_g$ by following the…
We study the dynamical response to small distortions of a lattice about its uniform state, drifting through a dissipative medium due to an external force, and show, analytically and numerically, that the fluctuations, both transverse and…
We investigate the coupled dynamics of charge and energy in interacting lattice models with dipole conservation. We formulate a generic hydrodynamic theory for this combination of fractonic constraints and numerically verify its…
We derive a simple consistency relation from the running of the tensor-to-scalar ratio. This new relation is first order in the slow-roll approximation. While for single field models we can obtain what can be found by using other…