相关论文: Kowalevski's analysis of the swinging Atwood's mac…
In this paper we obtain explicit lower bounds for the radius of convergence of the Painlev\'e expansions of the Korteweg-de-Vries equation around a movable singularity manifold ${\Cal S}$ in terms of the sup norms of the arbitrary functions…
In collider-based particle physics, $invariant\ mass$ refers to the magnitude of the total-momentum 4-vector of a system of particles. An expression for the invariant mass of a 2-particle system is well known; it assumes that both the total…
The mathematical theory of integrable Painleve/Toda type systems sheds new light on the behavior of solutions to the Poisson-Boltzmann equation for the potential due to a long rod-like macroion. We investigate here the case of symmetric…
Schroedinger equations with position dependent mass which are scale invariant and admit second order integrals of motion are classified.
We consider the small mass asymptotics (Smoluchowski-Kramers approximation) for the Langevin equation with a variable friction coefficient. The limit of the solution in the classical sense does not exist in this case. We study a…
The study of the convergence of power series expansions of energy eigenvalues for anharmonic oscillators in quantum mechanics differs from general understanding, in the case of quasi-exactly solvable potentials. They provide examples of…
Recently, several authors studied small quantum systems weakly coupled to free boson or fermion fields at positive temperature. All the approaches we are aware of employ complex deformations of Liouvillians or Mourre theory (the…
Consider a rigid body having a fixed point in a superposition of two constant force fields (for example, gravitational and magnetic). Introducing the condition of Kowalevski type, O.I.Bogoyavlensky (1984) has found the first integral…
A model for planar phenomena introduced by Jackiw and Pi and described by a Lagrangian including a Chern-Simons term is considered. The associated equations of motion, among which a 2+1 gauged nonlinear Schr\"odinger equation, are rewritten…
A `covariant' field that transforms like a relativistic field operator is required to be a linear combination of `canonical' fields that transform like annihilation and creation operators and with invariant coefficients. The Invariant…
The Ermakov Pinney equation and its associated invariant are shown to arise naturally in stationary quantum mechanics when the Schrodinger equation is expressed in Bohm Madelung form and the Hamiltonian is diagonal and separable. Under…
This paper generalizes the results of [13] and then provides an interesting example. We construct a family of $W$-like maps $\{W_a\}$ with a turning fixed point having slope $s_1$ on one side and $-s_2$ on the other. Each $W_a$ has an…
Two sets of infinitely many exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials are presented. They are derived as the eigenfunctions of shape invariant and thus exactly solvable quantum mechanical…
The effective mass $\mass$ of the the Pauli-Fierz Hamiltonain with ultraviolet cutoff $\Lambda$ and the bare mass $m$ in nonrelativistic QED with spin 1/2 is investigated. Analytic properties of $\mass$ in coupling constant $e$ are shown…
In the problem of motion of the Kowalevski top on two constant fields (the A.G.Reyman - M.A.Semenov-Tian-Shansky case) the type of all critical points of the momentum map is calculated.
We consider an infinite-dimensional dynamical system with polynomial nonlinearity and additive noise given by a finite number of Wiener processes. By studying how randomness is spread by the system we develop a counterpart of Hormander's…
Cylindrically symmetric quantum mechanical systems with position dependent masses (PDM) admitting at least one second order integral of motion are classified. It is proved that there exist 68 such systems which are inequivalent. Among them…
Using methods of R.J.Tauer we exhibit an uncountable family of singular masas in the hyperfinite $\textrm{II}_1$ factor $\R$ all with Puk\'anszky invariant $\{1\}$, no pair of which are conjugate by an automorphism of $R$. This is done by…
Solutions in terms of Elliptic Functions are provided for SAM in the integrable case where the mass ration equals three. My last SAM paper (I promise). To appear in The American Journal of Physics.
The anisotropic Manev problem, which lies at the intersection of classical, quantum, and relativity physics, describes the motion of two point masses in an anisotropic space under the influence of a Newtonian force-law with a relativistic…