相关论文: Solvability of $F_4$ quantum integrable systems

Following the basic principles stated by Painlev\'e, we first revisit the process of selecting the admissible time-independent Hamiltonians $H=(p_1^2+p_2^2)/2+V(q_1,q_2)$ whose some integer power $q_j^{n_j}(t)$ of the general solution is a…

Certain aspects of the integrability/solvability of the Calogero-Sutherland-Moser systems and the Ruijsenaars-Schneider-van Diejen systems with rational and trigonometric potentials are reviewed. The equilibrium positions of classical…

We show that, in general, averaging at simple resonances a real--analytic, nearly--integrable Hamiltonian, one obtains a one--dimensional system with a cosine--like potential; ``in general'' means for a generic class of holomorphic…

We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it regular quantum graphs}. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are…

In recent years, progress toward the classification of superintegrable systems with higher order integrals of motion has been made. In particular, a complete classification of all exotic potentials with a third or a fourth order integrals,…

We study the autonomous systems of quadratic differential equations of the form $\dot{x}_i(t)=\mathbf{x}(t)^T \mathbf{A}_i \mathbf{x}(t) + \mathbf{v}_i^T \mathbf{x}(t)$ with $\mathbf{x}(t) = (x_1(t),x_2(t),\dots,x_i(t),\dots)$ which, in…

The quantum integrability of a class of massive perturbations of the parafermionic conformal field theories associated to compact Lie groups is established by showing that they have quantum conserved densities of scale dimension 2 and 3.…

Numerical evidence for a cosmological version of the Bartnik-McKinnon family of particle-like solutions of the Einstein-Yang-Mills system is presented. Our solutions are also static, but space has the topology of a three-sphere. By…

We present a procedure to solve the Schroedinger equation of two interacting electrons in a quantum dot in the presence of an external magnetic field within the context of quasi-exactly-solvable spectral problems. We show that the…

A countable class of integrable dynamical systems, with four dimensional phase space and conserved quantities in involution (H\_n,I\_n) are exhibited. For $n=1$ we recover Neumann sytem on T*S^2. All these systems are also integrable at the…

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…

Thought experiments about the physical nature of set theoretical counterexamples to the axiom of choice motivate the investigation of peculiar constructions, e.g. an infinite dimensional Hilbert space with a modular quantum logic. Applying…

We consider the Lie-algebraic notion of commutant in the setting of Poisson algebra. This provides a framework for deforming Hamiltonian differential equations. By taking a subalgebra of the algebra of integrals, and considering the set of…

We present a new class of quantum field theories which are exactly solvable. The theories are generated by introducing Pauli-Villars fermionic and bosonic fields with masses degenerate with the physical positive metric fields. An algorithm…

We study the problem of computing the isolated regular solutions of a system \((f_1,\ldots,f_n)\) of \(n\) polynomial equations in \(n\) variables \((X_1, \dots, X_n)\) over a field of characteristic zero \(k\). We focus on systems with a…

The Kowalevski top in two constant fields is known as the unique profound example of an integrable Hamiltonian system with three degrees of freedom not reducible to a family of systems in fewer dimensions. As the first approach to…

We prove homological stability for both general linear groups of modules over a ring with finite stable rank and unitary groups of quadratic modules over a ring with finite unitary stable rank. In particular, we do not assume the modules…

A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…

In this paper we present the theorem on Lie integrability by quadratures for time-independent Hamiltonian systems on symplectic and contact manifolds, and for time-dependent Hamiltonian systems on cosymplectic and cocontact manifolds. We…

We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…