A Class of Completely Integrable Quantum Systems Associated with Classical Root Systems
نویسندگان
چکیده
We classify the completely integrable systems associated with classical root systems whose potential functions are meromorphic at an infinite point.
منابع مشابه
Completely Integrable Systems Associated with Classical Root Systems
We explicitly construct sufficient integrals of completely integrable quantum and classical systems associated with classical root systems, which include Calogero-Moser-Sutherland models, Inozemtsev models and Toda finite lattices with boundary conditions. We also discuss the classification of the completely integrable systems.
متن کاملA systematic construction of completely integrable Hamiltonians from coalgebras
A universal algorithm to construct N -particle (classical and quantum) completely integrable Hamiltonian systems from representations of coalgebras with Casimir element is presented. In particular, this construction shows that quantum deformations can be interpreted as generating structures for integrable deformations of Hamiltonian systems with coalgebra symmetry. In order to illustrate this g...
متن کاملQuantum vs Classical Integrability in Calogero-Moser Systems
Calogero-Moser systems are classical and quantum integrable multi-particle dynamics defined for any root system ∆. The quantum Calogero systems having 1/q2 potential and a confining q2 potential and the Sutherland systems with 1/ sin q potentials have “integer” energy spectra characterised by the root system ∆. Various quantities of the corresponding classical systems, e.g. minimum energy, freq...
متن کاملRelationships between Darboux Integrability and Limit Cycles for a Class of Able Equations
We consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i. Inside this class of polynomial differential equation we consider a subclass of Darboux integrable systems. Moreover, under additional conditions we proved such Darboux integrable systems can have at most 1 limit cycle.
متن کاملQuantum & Classical Eigenfunctions in Calogero & Sutherland Systems
An interesting observation was reported by Corrigan-Sasaki that all the frequencies of small oscillations around equilibrium are “quantised” for Calogero and Sutherland (C-S) systems, typical integrable multi-particle dynamics. We present an analytic proof by applying recent results of Loris-Sasaki. Explicit forms of ‘classical’ and quantum eigenfunctions are presented for C-S systems based on ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005