Related papers: Representation of a complex Green function on a re…
We demonstrate that any function $f$ from a finite set $Y$ to itself can be represented linearly. Specifically, we prove the existence of an injective map $j$ from $Y$ into a modular ring $\mathbb{Z}/m\mathbb{Z}$ and a constant $a \in…
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a…
Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on regression problems, without routinely incorporating…
In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…
We develop the rudiments of a finite-dimensional representation theory of groups over idempotent semifields by considering linear actions on tropical linear spaces. This can be considered a tropical representation theory, a characteristic…
I propose to use Hamiltonians which contain two-dimensional and three-dimensional kinetic terms for the description of two-dimensional systems in physics. As a model system the evolution of three-dimensional wavefunctions in the presence of…
For a linear non-Hermitian system, I demonstrate that a Hamiltonian can be constructed such that the non-Hermitian equations can be expressed exactly in the form of Hamilton's canonical equations. This is first shown for discrete systems…
Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in…
Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. Criteria are given which characterize existence of a fine or coarse moduli space classifying, up to isomorphism, the representations of $\Lambda$ with fixed…
We use a simple system, the electron configuration in a Hydrogen-like atom, to demonstrate the importance of using a complete basis set to provide a proper quantum mechanical description. We first start with what might be considered a…
We develop a resonance theory to describe the evolution of open systems with time-dependent dynamics. Our approach is based on piecewise constant Hamiltonians: we represent the evolution on each constant bit using a recently developed…
In this article, we prove a representation theorem that any generic line arrangement in the plane over an ordered field which has global cyclicity can be represented isomorphically by a line arrangement with a given set of distinct slopes…
The group theoretical treatment of bound and scattering state problems is extended to include band structure. We show that one can realize Hamiltonians with periodic potentials as dynamical symmetries, where representation theory provides…
As physical systems, qubits must evolve from input to output state. We describe a simple scheme in which the effect of a quantum gate is described by the action of an effective Hamiltonian acting for some characteristic time. This model…
Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of…
To be able to solve operator equations numerically a discretization of those operators is necessary. In the Galerkin approach bases are used to achieve discretized versions of operators. In a more general set-up, frames can be used to…
Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and…
For the rational, elliptic and trigonometric r-matrices, we exhibit the links between three "levels" of Poisson spaces: (a) Some finite-dimensional spaces of matrix-valued holomorphic functions on the complex line; (b) Spaces of spectral…
The basis of the identity representation of a polyhedral group is able to describe functions with symmetries of a platonic solid, i.e., 3-D objects which geometrically obey the cubic symmetries. However, to describe the dynamic of assembles…
Some positive answers to the problem of endowing a dynamical system with a Hamiltonian formulation are presented within the class of Poisson structures in a geometric framework. We address this problem on orientable manifolds and by using…