相关论文: Equations of Camassa--Holm type and Jacobi ellipti…
In this paper we will review a recently introduced method for solving the Hamilton-Jacobi equations by the method of Separation of Variables. This method is based on the notion of pencil of Poisson brackets and on the bihamiltonian approach…
The purpose of this note is to give a simple description of a (complete) family of functions in involution on certain hermitian symmetric spaces. This family, obtained via bi-hamiltonian approach using the Bruhat Poisson structure, is…
We construct a family of Hamiltonians whose phase diagram is guaranteed to have a single phase transition, yet the location of this phase transition is uncomputable. The Hamiltonians $H(\phi)$ describe qudits on a two-dimensional square…
We prove a spectral flow formula for one-parameter families of Hamiltonian systems under homoclinic boundary conditions, which relates the spectral flow to the relative Maslov index of a pair of curves of Lagrangians induced by the stable…
A Hamiltonian path (a Hamiltonian cycle) in a graph is a path (a cycle, respectively) that traverses all of its vertices. The problems of deciding their existence in an input graph are well-known to be NP-complete, in fact, they belong to…
The pure-quantum self-consistent harmonic approximation (PQSCHA) permits to study a quantum system by means of an effective classical Hamiltonian - depending on quantum coupling and temperature - and classical-like expressions for the…
The theory of isospectral flows comprises a large class of continuous dynamical systems, particularly integrable systems and Lie--Poisson systems. Their discretization is a classical problem in numerical analysis. Preserving the spectra in…
We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly…
We investigate a singular perturbation for Hamilton-Jacobi equations in an open subset of two dimensional Euclidean space, where the set is determined through a Hamiltonian function and the Hamilton-Jacobi equations are the dynamic…
Symplectic invariants introduced in math-ph/0702045 can be computed for an arbitrary spectral curve. For some examples of spectral curves, those invariants can solve loop equations of matrix integrals, and many problems of enumerative…
Whenever an It\^o-Wentsel type of formula holds for composition of flows of a certain differential dynamics, there exists locally a decomposition of the corresponding flow according to complementary distributions (or foliations, in the case…
We have studied a quantum Hamiltonian that models an array of ultrasmall Josephson junctions with short range Josephson couplings, $E_J$, and charging energies, $E_C$, due to the small capacitance of the junctions. We derive a new effective…
The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting $\W$-algebra is a…
Topological constraints play a key role in the self-organizing processes that create structures in macro systems. In fact, if all possible degrees of freedom are actualized on equal footing without constraint, the state of "equipartition"…
The closed string model in the background gravity field is considered as the bi-Hamiltonian system in assumption that string model is the integrable model for particular kind of the background fields. The dual nonlocal Poisson brackets, de…
It is shown how to construct an infinite number of families of quasi-bi-Hamiltonian (QBH) systems by means of the constrained flows of soliton equations. Three explicit QBH structures are presented for the first three families of the…
Motivated by optimal control problems and differential games for functional differential equations of retarded type, the paper deals with a Cauchy problem for a path-dependent Hamilton--Jacobi equation with a right-end boundary condition.…
We study the entanglement Hamiltonian of two disjoint blocks in the harmonic chain on the line and in its ground state. In the regime of large mass, the non vanishing terms are only the on-site and the nearest-neighbour ones. Analytic…
We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS$_{3}$ algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions. The analysis…
This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a "junction", that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison…