Balanced ternary formalism of second quantization
Yao Yao
TL;DR
This work develops a balanced ternary (qutrit) formalism to unify electron, hole, and CT exciton dynamics within a single unitary framework, addressing nonconserving charge processes in disordered organic materials. It constructs a chain of qutrits and defines CT exciton bosons (a_dag) and y-excitons (b_dag_y), enabling thermodynamic treatments via canonical and complementary coherent states and a stabilizer-based description that connects to external environments. Key contributions include a concrete operator construction for CT excitons, a mechanistic account of exciton-driven current and fission, and a spinful extension that reveals ferromagnetic orderings and magnetoresistance phenomena rooted in exciton entanglement, all without relying on a conventional hopping Hamiltonian. The framework provides a bridge between quantum thermodynamics and quantum simulations, offering a flexible platform for studying exciton transport, nonconserving processes, and emergent magnetic behavior in rigid-backbone organic systems, with potential impact on energy harvesting and spintronic applications.
Abstract
We construct a second-quantized representation with a structure of balanced ternary formalism, which involves three substances in organic molecular materials, namely electron, hole and charge-transfer exciton, into a uniform framework. The quantum thermodynamic of excitons is investigated in a closed and compact manner, benefitting from the interplay of the three substances. In order to be friendly with quantum simulations, the interactions among them are all described with unitary transformations. Significantly, the nonconserving dynamics of particle numbers, such as the generation of charge current and the exciton fission in organic semiconductors, is consistently expressed by this unitary formalism on the basis of bosonic coherent states. The spin degree of freedom is further taken into account, and an exotic molecular ferromagnetic ordering is induced in a specific configuration of excitons. This balanced ternary formalism establishes a solid bridge to connect thermodynamics and quantum simulations.