INIFTA   05425
INSTITUTO DE INVESTIGACIONES FISICO-QUIMICAS TEORICAS Y APLICADAS
Unidad Ejecutora - UE
artículos
Título:
Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation
Autor/es:
FRANCISCO MARCELO FERNÁNDEZ
Revista:
ANNALS OF PHYSICS (NEW YORK)
Editorial:
ACADEMIC PRESS INC ELSEVIER SCIENCE
Referencias:
Lugar: Amsterdam; Año: 2016 vol. 369 p. 168 - 176
ISSN:
0003-4916
Resumen:
We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit.