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Open Quantum Systems Decoherence Quantum Simulation

Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

arXiv
Authors: Francisco M Fernández

Year

2015

Paper ID

27270

Status

Preprint

Abstract Read

~2 min

Abstract Words

94

Citations

N/A

Abstract

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.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • 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.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1509.04267 [2] arXiv https://arxiv.org/abs/1509.04267 [3] Publisher https://arxiv.org/abs/1509.04267

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