On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation

• URL: http://arxiv.org/abs/2109.14540v5
• Date: Mon, 13 Jun 2022 14:09:39 GMT
• Title: On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation
• Authors: Francisco M. Fern\'andez
• Abstract summary: We show that some non-Hermitian Hamiltonian operators with tridiagonal matrix representation may be quasi Hermitian or similar to Hermitian operators. In the class of Hamiltonian operators discussed here the transformation is given by a Hermitian, positive-definite, diagonal operator.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that some non-Hermitian Hamiltonian operators with tridiagonal matrix representation may be quasi Hermitian or similar to Hermitian operators. In the class of Hamiltonian operators discussed here the transformation is given by a Hermitian, positive-definite, diagonal operator. We show that there is an important difference between open boundary conditions and periodic ones. We illustrate the theoretical results by means of two simple, widely used, models.

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