Related papers: Explicit Form of the Evolution Operator for the Fo…
Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables,…
The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of…
A distributed computing approach to solve the curse of dimensionality, caused by the complex quantum system modeling, is discussed. With the help of Cannon's algorithm, the distributed computing transformation of numerical method for…
The operator product expansion in four-dimensional superconformal field theory is discussed. The OPE takes a particularly simple form for chiral operators, in $N=1$ and $N=2$, and for analytic operators, in $N=2$ and $N=4$. It is argued…
We define the harmonic evolution of states of a graph by iterative application of the harmonic operator (Laplacian over $Z_2$). This provides graphs with a new geometric context and leads to a new tool to analyze them. The digraphs of…
We study the problem of convergence to equilibrium for evolution equations associated to general quadratic operators. Quadratic operators are non-selfadjoint differential operators with complex-valued quadratic symbols. Under appropriate…
In this note we obtain the solutions of four $q$-functional equations and express the solutions in $q$-operator forms. These equations give sufficient conditions for $q$-operator methods.
By introducing thermal entangled state representation which can map master equations of density operator in quantum statistics as state vector evolution equations and using dissipative interaction picture we solve the master equation of J-C…
An evolution equation, arising in the study of the Dynamical Systems Method (DSM) for solving equations with monotone operators, is studied in this paper. The evolution equation is a continuous analog of the regularized Newton method for…
We give an explicit description of the mutation class of quivers of type D.
No bracket determines the evolution operator in covariant (polysymplectic and multisymplectic) Hamiltonian field theory.
We establish an explicit formula for the Half-Wave maps equation for rational functions with simple poles. The Lax pair provides a description of the evolution of the poles. By considering a half-spin formulation, we use linear algebra to…
We present a general, systematic, and efficient method for decomposing any given exponential operator of bosonic mode operators, describing an arbitrary multi-mode Hamiltonian evolution, into a set of universal unitary gates. Although our…
We prove a determinant formula for the standard integral form of a lattice vertex operator algebra.
Here we propose an evolutionary algorithm that self modifies its operators at the same time that candidate solutions are evolved. This tackles convergence and lack of diversity issues, leading to better solutions. Operators are represented…
In this short note, we give an algorithm to get an explicit expression of the Luroth invariant in terms of the Dixmier-Ohno invariants. We also get the explicit factorized expression on the locus of Ciani quartics in terms of the…
There is a widespread belief in the quantum physical community, and in textbooks used to teach Quantum Mechanics, that it is a difficult task to apply the time evolution operator Exp{-itH/h} on an initial wave function. That is to say,…
The Weitzenb\"ock curvature operators are the curvature terms of order zero that appear in the well known classical Weitzenb\"ock formula. In this paper, we use the formalism of double forms to prove a simple formula for this operators and…
A method for constructing evolution equations admitting a master symmetry is proposed. Several examples illustrating the method are presented. It is also noted that for certain evolution equations master symmetries can be useful for…
A new Active Flux method for the multi-dimensional Euler equations is based on an additive operator splitting into acoustics and advection. The acoustic operator is solved in a locally linearized manner by using the exact evolution…