6533b85ffe1ef96bd12c286d

RESEARCH PRODUCT

A chain of solvable non-Hermitian Hamiltonians constructed by a series of metric operators

Naomichi HatanoFabio Bagarello

subject

HamiltoniansQuantum PhysicsPure mathematicsSeries (mathematics)010308 nuclear & particles physicsFOS: Physical sciencesGeneral Physics and AstronomyMathematical Physics (math-ph)01 natural sciencesHermitian matrixSet (abstract data type)symbols.namesakeSimilarity mapsIsospectralChain (algebraic topology)0103 physical sciencesMetric (mathematics)symbolsQuantum Physics (quant-ph)010306 general physicsHamiltonian (quantum mechanics)Settore MAT/07 - Fisica MatematicaMathematical PhysicsEigenvalues and eigenvectorsMathematics

description

We show how, given a non-Hermitian Hamiltonian $H$, we can generate new non-Hermitian operators sequentially, producing a virtually infinite chain of non-Hermitian Hamiltonians which are isospectral to $H$ and $H^\dagger$ and whose eigenvectors we can easily deduce in an almost automatic way; no ingredients are necessary other than $H$ and its eigensystem. To set off the chain and keep it running, we use, for the first time in our knowledge, a series of maps all connected to different metric operators. We show how the procedure works in several physically relevant systems. In particular, we apply our method to various versions of the Hatano-Nelson model and to some PT-symmetric Hamiltonians.

https://doi.org/10.1016/j.aop.2021.168511