Pith. sign in

REVIEW 1 cited by

Birth and death processes and quantum spin chains

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

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

arxiv 1205.4689 v2 pith:Y2LNEX2M submitted 2012-05-21 quant-ph

Alberto F. Grünbaum , Luc Vinet , Alexei Zhedanov This is my paper · ORCID
classification quant-ph
keywords spinbirthdeathprocesseschainsprobabilityquantumtransition
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

This papers underscores the intimate connection between the quantum walks generated by certain spin chain Hamiltonians and classical birth and death processes. It is observed that transition amplitudes between single excitation states of the spin chains have an expression in terms of orthogonal polynomials which is analogous to the Karlin-McGregor representation formula of the transition probability functions for classes of birth and death processes. As an application, we present a characterization of spin systems for which the probability to return to the point of origin at some time is 1 or almost 1.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Exactly solvable multicomponent spinless fermions

    hep-th 2025-02 conditional novelty 5.0 of 10

    Four exactly solvable multicomponent spinless fermion models are constructed from multivariate Krawtchouk, Meixner, and two Rahman-like polynomial families.

Pith tools