arXiv subjects

Jacob T. Willson

Publications and source records attributed to Jacob T. Willson.

3 recordsLinked to original sources

arXiv2026

Maximum entropy distributions of wavefunctions at thermal equilibrium

Statistical mechanics reveals that the properties of a macroscopic physical system emerge as an average over an ensemble of statistically independent microscopic subsystems, each occupying a specific microstate. In the study of quantum systems, these microstates can be chosen to correspond to the pure state wavefunctions of individual quantum systems. However, the physical principles that govern the distribution of a pure state wavefunction ensemble, even under conditions of thermal equilibrium, are not well established. For instance, the canonical Boltzmann distribution cannot be applied to wavefunctions because they lack a definite energy. In this manuscript, we present a maximum entropy principle for the quantum wavefunction ensemble at thermal equilibrium, the so-called Scrooge ensemble. We highlight that a constraint on the energy expectation value, or even the shape of the associated eigenstate distribution, fails to yield a valid equilibrium state. We find that in addition to these constraints, one must also constrain the measurement entropy to be equal to the Rényi divergence of the ensemble with respect to the Gibbs state, indicating that the Rényi divergence may have uninvestigated physical importance to thermal equilibrium in quantum systems.

cond-mat.stat-mech↗

arXiv2023

Fast and Accurate Simulations of Partially Delocalised Charge Separation in Organic Semiconductors

Accurate computational screening of candidate materials promises to accelerate the discovery of higher-efficiency organic photovoltaics (OPVs). However, modelling charge separation in OPVs is challenging because accurate models must include disorder, polaron formation, and charge delocalisation. Delocalised kinetic Monte Carlo (dKMC) includes these three essential ingredients, but it suffers from high computational cost. Recently, we developed jumping kinetic Monte Carlo (jKMC), a computationally cheap and accurate model of delocalised charge transport that models transport over a lattice of identical, spherical polarons. Here, we extend jKMC to describe the separation of a charge-transfer state, showing that this simplified approach can reproduce the considerable improvements in charge-separation efficiencies caused by delocalisation and first seen in dKMC. The low computational cost and simplicity of jKMC allows it to be applied to parameter regimes intractable by dKMC, and ensures jKMC can be easily incorporated into any existing KMC model.

physics.chem-ph↗

arXiv2022

Jumping kinetic Monte Carlo: Fast and accurate simulations of partially delocalised charge transport in organic semiconductors

Developing devices using disordered organic semiconductors requires accurate and practical models of charge transport. In these materials, charge transport occurs through partially delocalised states in an intermediate regime between localised hopping and delocalised band conduction. Partial delocalisation can increase mobilities by orders of magnitude over conventional hopping, making it important for materials and device design. Although delocalisation, disorder, and polaron formation can be described using delocalised kinetic Monte Carlo (dKMC), it is a computationally expensive method. Here, we develop jumping kinetic Monte Carlo (jKMC), a model that approaches the accuracy of dKMC with a computational cost comparable to conventional hopping. jKMC achieves its computational performance by modelling conduction using identical spherical polarons, yielding a simple delocalisation correction to the Marcus hopping rate that allows polarons to jump over their nearest neighbours. jKMC can be used in regimes of partial delocalisation inaccessible to dKMC to show that modest delocalisation can increase mobilities by as much as two orders of magnitude.

physics.chem-ph↗