Effective Hamiltonian for a non-unitary quantum walk

Authors

Francis N. C. Paraan ⋅ PH National Institute of Physics, University of the Philippines Diliman
Sven T. Sorupia ⋅ PH National Institute of Physics, University of the Philippines Diliman
Gene M. M. Itable ⋅ PH National Institute of Physics, University of the Philippines Diliman

Abstract

We construct an effective Hamiltonian for the non-unitary evolution operator of a multi-step quantum walk with a mechanism for gain and loss. This Hamiltonian is expressed in the basis of the identity and Pauli operators to make its spectrum easy to calculate and its symmetries evident. The parametrization we use allows for an efficient evaluation of the phase boundary where the PT-symmetry of the model is known to be spontaneously broken and shows that the effective Hamiltonian, although non-Hermitian, is real.

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Issue

2022: Proceedings of the 40th Samahang Pisika ng Pilipinas Physics Conference

Physics 2.0.2022: Renormalizing uncertainties with Physics
19-21 October 2022, Legazpi City

Please visit the SPP2022 activity webpage for more information on this year's Physics Congress.

Article ID

SPP-2022-PB-10

Section

Poster Session B (Complex Systems, Simulations, and Theoretical Physics)

Published

2022-09-16

How to Cite

[1]

FNC Paraan, ST Sorupia, and GMM Itable, Effective Hamiltonian for a non-unitary quantum walk, Proceedings of the Samahang Pisika ng Pilipinas 40, SPP-2022-PB-10 (2022). URL: https://proceedings.spp-online.org/article/view/SPP-2022-PB-10.