1,159 research outputs found
Hyperdeterminant and an integrable partial differential equation
We discuss an integrable partial differential equation arising from the
hyperdeterminant
Hamilton Operators, Discrete Symmetries, Brute Force and SymbolicC++
To find the discrete symmetries of a Hamilton operator is of central
importance in quantum theory. Here we describe and implement a brute force
method to determine the discrete symmetries given by permutation matrices for
Hamilton operators acting in a finite-dimensional Hilbert space. Spin and Fermi
systems are considered as examples. A computer algebra implementation in
SymbolicC++ is provided
Nonlinear dynamical systems and classical orthogonal polynomials
It is demonstrated that nonlinear dynamical systems with analytic
nonlinearities can be brought down to the abstract Schr\"odinger equation in
Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion
of solutions to the Schr\"odinger equation in the particular occupation number
representation are expressed by means of the classical orthogonal polynomials.
The introduced formalism amounts a generalization of the classical methods for
linearization of nonlinear differential equations such as the Carleman
embedding technique and Koopman approach.Comment: 21 pages latex, uses revte
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