Spin-Hamilton operator, graviton-photon coupling and an eigenvalue problem

- Hardy, Yorick, Steeb, Willi-Hans

**Authors:**Hardy, Yorick , Steeb, Willi-Hans**Date:**2012-09-28**Subjects:**Spin-Hamilton operator , Graviton-photon coupling , Eigenvalues**Type:**Article**Identifier:**uj:5973 , http://hdl.handle.net/10210/8418**Description:**We solve exactly the eigenvalue problem for a spin Hamilton operator describing graviton-photon coupling. Entanglement of the eigenstates are also studied.**Full Text:**

**Authors:**Hardy, Yorick , Steeb, Willi-Hans**Date:**2012-09-28**Subjects:**Spin-Hamilton operator , Graviton-photon coupling , Eigenvalues**Type:**Article**Identifier:**uj:5973 , http://hdl.handle.net/10210/8418**Description:**We solve exactly the eigenvalue problem for a spin Hamilton operator describing graviton-photon coupling. Entanglement of the eigenstates are also studied.**Full Text:**

Cayley transform and the Kronecker product of Hermitian matrices

- Hardy, Yorick, Fošner, Ajda, Steeb, Willi-Hans

**Authors:**Hardy, Yorick , Fošner, Ajda , Steeb, Willi-Hans**Date:**2013-05-05**Subjects:**Hermitian matrices , Cayley transform , Kronecker product**Type:**Article**Identifier:**uj:5976 , http://hdl.handle.net/10210/8441**Description:**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 so, if it is a product of the Cayley transforms of the two Hermitian matrices.**Full Text:**

**Authors:**Hardy, Yorick , Fošner, Ajda , Steeb, Willi-Hans**Date:**2013-05-05**Subjects:**Hermitian matrices , Cayley transform , Kronecker product**Type:**Article**Identifier:**uj:5976 , http://hdl.handle.net/10210/8441**Description:**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 so, if it is a product of the Cayley transforms of the two Hermitian matrices.**Full Text:**

A sequence of quantum gates

- Steeb, Willi-Hans, Hardy, Yorick

**Authors:**Steeb, Willi-Hans , Hardy, Yorick**Date:**2012-02-10**Subjects:**Hilbert spaces , Hamilton operators , Cayley transform , Quantum gates**Type:**Article**Identifier:**uj:5978 , http://hdl.handle.net/10210/8443**Description:**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 operators is also given. From the Hamilton operators we construct another hierarchy of quantum gates via the Cayley transform.**Full Text:**

**Authors:**Steeb, Willi-Hans , Hardy, Yorick**Date:**2012-02-10**Subjects:**Hilbert spaces , Hamilton operators , Cayley transform , Quantum gates**Type:**Article**Identifier:**uj:5978 , http://hdl.handle.net/10210/8443**Description:**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 operators is also given. From the Hamilton operators we construct another hierarchy of quantum gates via the Cayley transform.**Full Text:**

Hamilton operators, discrete symmetries, brute force and symbolicC++

- Steeb, Willi-Hans, Hardy, Yorick

**Authors:**Steeb, Willi-Hans , Hardy, Yorick**Date:**2012-08-23**Subjects:**Hamilton operators , Spin-Hamilton operators , Quantum theory**Type:**Article**Identifier:**uj:5974 , http://hdl.handle.net/10210/8419**Description:**To find the discrete symmetries of a Hamilton operator ˆH 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.**Full Text:**

**Authors:**Steeb, Willi-Hans , Hardy, Yorick**Date:**2012-08-23**Subjects:**Hamilton operators , Spin-Hamilton operators , Quantum theory**Type:**Article**Identifier:**uj:5974 , http://hdl.handle.net/10210/8419**Description:**To find the discrete symmetries of a Hamilton operator ˆH 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.**Full Text:**

Exceptional points, nonnormal matrices, hierarchy of spin matrices and an eigenvalue problem

- Steeb, Willi-Hans, Hardy, Yorick

**Authors:**Steeb, Willi-Hans , Hardy, Yorick**Date:**2013-02-08**Subjects:**Hamilton operators , Spin matrices , Eigenvalues**Type:**Article**Identifier:**uj:5979 , http://hdl.handle.net/10210/8444**Description:**Exceptional points are studied for non-hermitian Hamilton operators given by a hierarchy of spin-operators.**Full Text:**

**Authors:**Steeb, Willi-Hans , Hardy, Yorick**Date:**2013-02-08**Subjects:**Hamilton operators , Spin matrices , Eigenvalues**Type:**Article**Identifier:**uj:5979 , http://hdl.handle.net/10210/8444**Description:**Exceptional points are studied for non-hermitian Hamilton operators given by a hierarchy of spin-operators.**Full Text:**

Vector product and an integrable dynamical system

- Steeb, Willi-Hans, Tanski, Igor, Hardy, Yorick

**Authors:**Steeb, Willi-Hans , Tanski, Igor , Hardy, Yorick**Date:**2011**Subjects:**Vector product , Nambu mechanics , Differential equations , Integrals**Type:**Article**Identifier:**uj:5808 , ISSN 0253-6102 , http://hdl.handle.net/10210/7816**Description:**We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals. The connection with Nambu mechanics is established. The extension to higher dimensions is also discussed.**Full Text:**

**Authors:**Steeb, Willi-Hans , Tanski, Igor , Hardy, Yorick**Date:**2011**Subjects:**Vector product , Nambu mechanics , Differential equations , Integrals**Type:**Article**Identifier:**uj:5808 , ISSN 0253-6102 , http://hdl.handle.net/10210/7816**Description:**We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals. The connection with Nambu mechanics is established. The extension to higher dimensions is also discussed.**Full Text:**

Spin Hamilton operators, symmetry breaking, energy level crossing and entanglement

- Steeb, Willi-Hans, Hardy, Yorick, De Greef, Jacqueline

**Authors:**Steeb, Willi-Hans , Hardy, Yorick , De Greef, Jacqueline**Date:**2012-01-27**Subjects:**Hilbert spaces , Hamilton operators , Spin matrices , Eigenvalues**Type:**Article**Identifier:**uj:5975 , http://hdl.handle.net/10210/8440**Description:**© Willi-Hans Steeb, Yorick Hardy and Jacqueline de Greef, 2012 Available online: http://arxiv.org/abs/1110.4204v2 , 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.**Full Text:**

**Authors:**Steeb, Willi-Hans , Hardy, Yorick , De Greef, Jacqueline**Date:**2012-01-27**Subjects:**Hilbert spaces , Hamilton operators , Spin matrices , Eigenvalues**Type:**Article**Identifier:**uj:5975 , http://hdl.handle.net/10210/8440**Description:**© Willi-Hans Steeb, Yorick Hardy and Jacqueline de Greef, 2012 Available online: http://arxiv.org/abs/1110.4204v2 , 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.**Full Text:**

An eigenvalue problem for a fermi system and lie algebras

- Steeb, Willi-Hans, Hardy, Yorick

**Authors:**Steeb, Willi-Hans , Hardy, Yorick**Date:**2013-04-15**Subjects:**Schrodinger equation , Eigenvalues , Lie algebras , Hamilton operators , Fermi Hamilton operators**Type:**Article**Identifier:**uj:5977 , http://hdl.handle.net/10210/8442**Description:**Please refer to full text to view abstract**Full Text:**

**Authors:**Steeb, Willi-Hans , Hardy, Yorick**Date:**2013-04-15**Subjects:**Schrodinger equation , Eigenvalues , Lie algebras , Hamilton operators , Fermi Hamilton operators**Type:**Article**Identifier:**uj:5977 , http://hdl.handle.net/10210/8442**Description:**Please refer to full text to view abstract**Full Text:**

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