163 citations · 178 across the 18 of their papers we have counts for
18 papers
Robust transformations of firing patterns for neural networks
Karlis Kanders, Tom Lorimer, Yoko Uwate +2
As a promising computational paradigm, occurrence of critical states in artificial and biological neural networks has attracted wide-spread attention. An often-made explicit or imp…
Matrices, Fermi Operators and Applications
Yorick Hardy, Willi-Hans Steeb, Garreth Kemp
We consider the vector space of matrices over , Fermi operators and operators constructed from these matrices and Fermi operators. The properties of these o…
Pauli Lubanski Vector Operator, Eigenvalue Problem and Entanglement
Garreth Kemp, Willi-Hans Steeb
We study an eigenvalue problem for a spin matrix arising in the Pauli Lubanski vector operator. Entanglement of the eigenvectors and its connection with degeneracy is discussed.
Bose Operators, Coherent States, Truncation, Spin Coherent States, Lie Algebras and Spectrum
Willi-Hans Steeb, Garreth Kemp, Yorick Hardy +1
We study truncated Bose operators in finite dimensional Hilbert spaces. Spin coherent states for the truncated Bose operators and canonical coherent states for Bose operators are c…
Hierarchy of Spin Operators, Quantum Gates, Entanglement, Tensor Product and Eigenvalues
Willi-Hans Steeb, Yorick Hardy
{\bf Abstract.} We show that two hierarchies of spin Hamilton operators admit the same spectrum. Both Hamilton operators play a central role for quantum gates in particular for the…
Spin Operators, Pauli Group, Commutators, Anti-Commutators, Kronecker Product and Applications
Willi-Hans Steeb, Yorick Hardy
Pauli spin matrices, Pauli group, commutators, anti-commutators and the Kronecker product are studied. Applications to eigenvalue problems, exponential functions of such matrices,…
Boolean Functions, Quantum Gates, Hamilton Operators, Spin Systems and Computer Algebra
Yorick Hardy, Willi-Hans Steeb
We describe the construction of quantum gates (unitary operators) from boolean functions and give a number of applications. Both non-reversible and reversible boolean functions are…
Exponential of a Matrix, a Nonlinear Problem and Quantum Gates
Willi-Hans Steeb, Yorick Hardy
We describe solutions of the matrix equation , where . Applications in quantum computing are given. Both normal and nonnormal matrices are stud…
Majorana Fermions on a Lattice and a Matrix Problem
Yorick Hardy, Willi-Hans Steeb
We investigate matrix problems arising in the study of Majorana Fermions on a lattice.
Cayley transform and the Kronecker product of Hermitian matrices
Yorick Hardy, Ajda Fošner, Willi-Hans Steeb
We consider the conditions under which the Cayley transform of the Kronecker product of two Hermitian matrices can be again presented as a Kronecker product of two matrices and, if…
An Eigenvalue Problem for a Fermi System and Lie Algebras
Willi-Hans Steeb, Yorick Hardy
We study a Fermi Hamilton operator which does not commute with the number operator . The eigenvalue problem and the Schrödinger equation is solved. Entanglement is…
Exceptional Points, Nonnormal Matrices, Hierarchy of Spin Matrices and an Eigenvalue Problem
Willi-Hans Steeb, Yorick Hardy
Exceptional points of a class of non-hermitian Hamilton operators of the form are studied, where and are hermitian operat…
Spin-Hamilton Operator, Graviton-Photon Coupling and an Eigenvalue Problem
Yorick Hardy, Willi-Hans Steeb
We solve exactly the eigenvalue problem for a spin Hamilton operator describing graviton-photon coupling. Entanglement of the eigenstates are also studied. Other spin-coupled Hamil…
Hamilton Operators, Discrete Symmetries, Brute Force and SymbolicC++
Willi-Hans Steeb, Yorick Hardy
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 dis…
A Sequence of Quantum Gates
Yorick Hardy, Willi-Hans Steeb
We study a sequence of quantum gates in finite-dimensional Hilbert spaces given by the normalized eigenvectors of the unitary operators. The corresponding sequence of the Hamilton…
Spin Hamilton Operators, Symmetry Breaking, Energy Level Crossing and Entanglement
Willi-Hans Steeb, Yorick Hardy, Jacqueline de Greef
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…
Hyperdeterminant and an integrable partial differential equation
Willi-Hans Steeb
We discuss an integrable partial differential equation arising from the hyperdeterminant.
Relativistic ponderomotive force, uphill acceleration, and transition to chaos
D. Bauer, P. Mulser, W. -H. Steeb
Starting from a covariant cycle-averaged Lagrangian the relativistic oscillation center equation of motion of a point charge is deduced and analytical formulae for the ponderomotiv…