REVIEW 4 cited by
Biorthogonal Renormalization
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Biorthogonal Renormalization
read the original abstract
The biorthogonal formalism extends conventional quantum mechanics to the non-Hermitian realm. It has, however, been pointed out that the biorthogonal inner product changes with the scaling of the eigenvectors, an ambiguity whose physical significance is still being debated. Here, we revisit this issue and argue when this choice of normalization is of physical importance. We illustrate in which settings quantities such as expectation values and transition probabilities depend on the scaling of eigenvectors, and in which settings the biorthogonal formalism remains unambiguous. To resolve the apparent scaling ambiguity, we introduce an inner product independent of the gauge choice of basis and show that its corresponding mathematical structure is consistent with quantum mechanics. Using this formalism, we identify a deeper problem relating to the physicality of Hilbert space representations, which we illustrate using the position basis. Apart from increasing the understanding of the mathematical foundations upon which many physical results rely, our findings also pave the way towards consistent comparisons between systems described by non-Hermitian Hamiltonians.
Forward citations
Cited by 4 Pith papers
-
Complex Wannier centers and drifting Wannier functions in non-Hermitian Hamiltonians
Complex Wannier centers derived from nonunitary Wilson loops in non-Hermitian Hamiltonians predict directional drift of Wannier functions and a bulk-boundary correspondence for filling anomalies and gain/loss in edge modes.
-
Generalised Entanglement Entropies from Unit-Invariant Singular Value Decomposition
Generalized entanglement entropies are constructed via left-, right-, and bi-invariant unit-invariant singular value decompositions to ensure scale invariance for non-Hermitian and rectangular operators in quantum mec...
-
Skin modes in a nonlinear Hatano-Nelson model
Families of nonlinear skin modes emerge from linear ones in the Hatano-Nelson model with Kerr nonlinearity, exhibiting enhanced localization for focusing and reduced localization for defocusing nonlinearity.
-
Perturbative Analysis of Dark State Dynamics in Weakly Anharmonic Photon-Emitter Pairs
Weak anharmonicity induces dissipation into dark states of photon-emitter pairs; first- and second-order perturbative corrections to the wavefunction are derived and applied to the master equation.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.