相关论文: Singular Bohr-Sommerfeld Rules for 2D Integrable S…

The classical Arnold-Liouville theorem describes the geometry of an integrable Hamiltonian system near a regular level set of the moment map. Our results describe it near a nondegenerate singular level set: a tubular neighborhood of a…

In this paper we study quasi-linear system of partial differential equations which describes the existence of the polynomial in momenta first integral of the integrable geodesic flow on 2-torus. We proved in [3] that this is a…

The paper deals with the semi-classical behaviour of quantum dynamics for a semi-classical completely integrable system with two degrees of freedom near Liouville regular torus. The phenomomenon of wave packet revivals is demonstrated in…

We study Hamiltonian reductions of the free geodesic motion on a non-compact simple Lie group using as reduction group the direct product of a maximal compact subgroup and the fixed point subgroup of an arbitrary involution commuting with…

A unified algebraic construction of the classical Smorodinsky-Winternitz systems on the ND sphere, Euclidean and hyperbolic spaces through the Lie groups SO(N+1), ISO(N), and SO(N,1) is presented. Firstly, general expressions for the…

For a class of non-selfadjoint h-pseudodifferential operators in dimension 2, we determine all eigenvalues in an h-independent domain in the complex plane and show that they are given by a Bohr-Sommerfeld quantization condition. No complete…

Classical and quantum superintegrable systems have a long history and they possess more integrals of motion than degrees of freedom. They have many attractive properties, wide applications in modern physics and connection to many domains in…

Born-Infeld nonlinear electrodynamics are considered. Main attention is given to existence of singular point at static field configuration that M.Born and L.Infeld are considered as a model of electron. It is shown that such singularities…

A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a…

We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of…

It is noted that the Schrodinger equation with any self-adjoint Hamiltonian is unitary equivalent to a set of non-interacting classical harmonic oscillators and in this sense any quantum dynamics is completely integrable. Higher order…

In the case of a one-dimensional nonsingular Hamiltonian $H$ and a singular supersymmetric partner $H_a$, the Darboux and factorization relations of supersymmetric quantum mechanics can be only formal relations. It was shown how we can…

We study the relationship between singularities of finite-dimensional integrable systems and singularities of the corresponding spectral curves. For the large class of integrable systems on matrix polynomials, which is a general framework…

Within integrable systems, the class of so called "semitoric" integrable systems in dimension four has attracted a lot of attention in recent years, especially since fundamental examples from classical and quantum mechanics have been…

We study the geodesics of the singularity free metric considered in the preceding Paper I and show that they are complete. This once again demonstrates the absence of singularity. The geodesic completeness is established in general without…

We consider a class of $N=2$ supersymmetric non--unitary theories in two--dimensional Minkowski spacetime which admit classical solitonic solutions. We show how these models can be twisted into a topological sector whose energy--momentum…

This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…

For relativistic atomic two-body systems such as the hydrogen atom, positronium, and muon-proton bound states, a two-body generalisation of the single-particle Sommerfeld fine-structure formula for the relativistic bound-state energies is…

In this paper we prove that there exists only one family of classical Hamiltonian systems of two degrees of freedom with invariant plane $\Gamma=\{q_2=p_2=0\}$ whose normal variational equation around integral curves in $\Gamma$ is…

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…