Exact Results for the Tavis-Cummings and H$\ddot{\mathbf{u}}$ckel Hamiltonians with Diagonal Disorder

Abstract

We present an exact method to calculate the electronic states of one electron Hamiltonians with diagonal disorder. We show that the disorder averaged one particle Green's function can be calculated directly, using a deterministic complex (non-Hermitian) Hamiltonian. For this, we assume that the molecular states have a Cauchy (Lorentz) distribution and use the supersymmetric method which has already been used in problems of solid state physics. Using the method we find exact solutions to the states of $N$ molecules, confined to a microcavity, for any value of $N$. Our analysis shows that the width of the polaritonic states as a function of $N$ depend on the nature of disorder, and hence can be used to probe the way molecular energy levels are distributed. We also show how one can find exact results for H$\ddot{u}$ckel type Hamiltonians with on-site, Cauchy disorder and demonstrate its use.

References in corpus (6)

• Theory of Nanoscale Organic Cavities: The Essential Role of Vibration-Photon Dressed States
• Catalysis by Dark States in Vibropolaritonic Chemistry
• Polaritonic normal modes in Transition State Theory
• Unusual Dynamical Properties of Disordered Polaritons in Micocavities
• Effects of disorder on polaritonic and dark states in a cavity using the disordered Tavis-Cummings model
• Disordered ensembles of strongly coupled single-molecule plasmonic picocavities as nonlinear optical metamaterials

Cited by in corpus (4)

• Polariton Localization and Dispersion Properties of Disordered Quantum Emitters in Multimode Microcavities
• Effects of disorder on polaritonic and dark states in a cavity using the disordered Tavis-Cummings model
• Vibrational polariton transport in disordered media
• Extracting accurate light-matter couplings from disordered polaritons