51 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
Spin Hamilton Operators, Symmetry Breaking, Energy Level Crossing and Entanglement
We study finite-dimensional product Hilbert spaces, coupled spin systems,
entanglement and energy level crossing. The Hamilton operators are based on the
Pauli group. We show that swapping the interacting term can lead from
unentangled eigenstates to entangled eigenstates and from an energy spectrum
with energy level crossing to avoided energy level crossing
- …