Perturbations of integrable systems and Dyson-Mehta integrals
نویسنده
چکیده
We show that the existence of algebraic forms of quantum, exactly-solvable, completely-integrable A−B−C−D and G2, F4, E6,7,8 Olshanetsky-Perelomov Hamiltonians allow to develop the algebraic perturbation theory, where corrections are computed by pure linear algebra means. A Lie-algebraic classification of such perturbations is given. In particular, this scheme admits an explicit study of anharmonic many-body problems. The approach also allows to calculate the ratio of a certain generalized Dyson-Mehta integrals algebraically, which are interested by themselves.
منابع مشابه
ON CONVERGENCE THEOREMS FOR FUZZY HENSTOCK INTEGRALS
The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...
متن کاملGENERALIZED FUZZY VALUED $theta$-Choquet INTEGRALS AND THEIR DOUBLE-NULL ASYMPTOTIC ADDITIVITY
The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...
متن کاملA PDE approach to finite time approximations in Ergodic Theory
For dynamical systems defined by vector fields over a compact invariant set, we introduce a new class of approximated first integrals based on finite-time averages and satisfying an explicit first order partial differential equation. Referring to the PDE framework, we detect their viscosity robustness with respect to stochastic perturbations of the vector field. We formulate this approximating ...
متن کاملMatrix integrals and several integrable differential-difference systems
In this paper, the relations between three special forms of matrix integrals and their associated integrable differential-difference systems are considered. It turns out that these matrix integrals with special β = 2 and 1, 4 satisfy the differential-difference KP equation, the two-dimensional Toda lattice, the semi-discrete Toda equation and their Pfaffianized systems, respectively.
متن کاملOn Limit Cycles Appearing by Polynomial Perturbation of Darbouxian Integrable Systems
We prove an existential finiteness result for integrals of rational 1-forms over the level curves of Darbouxian integrals. 1. Limit cycles born by perturbation of integrable systems 1.1. Poincaré–Pontryagin integral. Limit cycles (isolated periodic trajectories) of polynomial planar vector fields can be produced by perturbing integrable systems which have nested continuous families of non-isola...
متن کامل