Exact energy spectrum of a two-temperature kinetic Ising model

TL;DR

This paper derives the exact energy spectrum of a two-temperature kinetic Ising model and its dual reaction-diffusion system, revealing symmetries and explicit state vectors with implications for understanding the system's physical behavior.

Contribution

It provides the first exact calculation of the energy spectrum for a two-temperature kinetic Ising chain and its dual, including explicit state vectors and symmetry analysis.

Findings

Exact eigenvalues have a surprisingly simple form

Explicit state vectors are derived for small systems

Symmetries enable spectrum calculation and physical insights

Abstract

The exact energy spectrum is developed for a two temperature kinetic Ising spin chain, and its dual reaction diffusion system with spatially alternating pair annihilation and creation rates. Symmetries of the system pseudo-Hamiltonian that enable calculation of the spectrum are also used to derive explicit state vectors for small system sizes, and to make observations regarding state vectors in the general case. Physical consequences of the surprisingly simple form for the eigenvalues are also discussed.