Related papers: Trace Formula for a System of Particles with Ellip…
Infinite products expansions of the Weierstrass elliptic function \ $\wp(z) = \wp(z,1,\tau)$\ and $n$-order transformations allow us to provide some modular relations.
We derive the gravitational and electrostatic self-energies of a particle at rest in the background of a cosmic dispiration (topological defect), finding that the particle may experience potential steps, well potentials or potential…
In this paper, we build up Hill-type formula for linear Hamiltonian systems with Lagrangian boundary conditions, which include standard Neumann, Dirichlet boundary conditions. Such a kind of boundary conditions comes from the brake symmetry…
We study the genuine part of the Arthur-Selberg trace formula for some nonlinear covers of connected reductive groups. As a first step towards the invariant trace formula, we express the geometric side in terms of weighted orbital…
Series of extended Epstein type provide examples of non-trivial zeta functions with important physical applications. The regular part of their analytic continuation is seen to be a convergent or an asymptotic series. Their singularity…
We generalise the formula expressing the matrix trace of a given square matrix as the integral of the numerical values of $A$ over the Euclidean sphere to the unit spheres of finite-dimensional normed spaces that have a 1-symmetric basis.…
The appearance of tracks, close to classical orbits, left by charged quantum particles propagating inside a detector, such as a cavity periodically illuminated by light pulses, is studied for a family of idealized models. In the…
We describe an algorithm for determining a minimal Weierstrass equation for hyperelliptic curves over principal ideal domains. When the curve has a rational Weierstrass point $w_0$, we also give a similar algorithm for determining the…
A research on a possibility of trapping a particle with permanent electric dipole in an electrostatic field has been conducted. For cylindrical coaxial electrodes, Keplerian orbits for some particles were revealed. The exact criterion of…
A natural generalization of Krein's theorem to a pair of commuting tuples $\left(H_1^0,H_2^0\right)$ and $\left(H_1,H_2\right)$ of bounded self-adjoint operators in a separable Hilbert space $\mathcal{H}$ with $H_j-H_j^0 = V_j\in…
The elliptically oscillating solutions in the Abelian Higgs-model are presented and the classical massive-dispersion-relation through the non-linear dynamics is discussed. The generated massive-dispersion-relation including a field value of…
Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…
We derive a trace formula for $\sum_n A_{nn}B_{nn}...\delta(E-E_n)$, where $A_{nn}$ is the diagonal matrix element of the operator $A$ in the energy basis of a chaotic system. The result takes the form of a smooth term plus periodic-orbit…
The {\it Weierstrass semigroup} of pole orders of meromorphic functions in a point $p$ of a smooth algebraic curve $C$ is a classical object of study; a celebrated problem of Hurwitz is to characterize which semigroups ${\rm S} \subset…
This work introduces non-Hermitian position-dependent mass Hamiltonians characterized by complex ladder operators and real, equidistant spectra. By imposing the Heisenberg-Weyl algebraic structure as a constraint, we derive the…
Let $q_1,q_2,...,q_N$ be the coordinates of $N$ particles on the circle, interacting with the integrable potential $\sum_{j<k}^N\wp(q_j-q_k)$, where $\wp$ is the Weierstrass elliptic function. We show that every symmetric elliptic function…
Diffractive systems are quantum-mechanical models with point-like singularities where usual semiclassical approximation breaks down. An overview of recent investigations of such systems is presented. The following examples are considered in…
In this paper we derive refined Petersson/Kuznetsov trace formulae with prescribed local ramifications. The spectral side of these formulae picks out newforms whose associated local components come from specific sub-families of…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
Our purpose is to give a generalization of Pulita exponential series. After that, we shall use these series to give an analytic expression to a Gauss sums and to a trace formula for Witt vector rings.