Routes of Transport in the Path Integral Lindblad Dynamics through State-to-State Analysis

TL;DR

The paper tackles the challenge of characterizing transport routes in open quantum systems under non-equilibrium conditions, where both a non-Markovian solvent bath and empirical pumping or draining processes influence dynamics. It introduces the Lindblad state-to-state (PILD) formalism, combining numerically exact path-integral bath treatment with Markovian Lindblad jumps to decompose population flows into Hamiltonian transport and Lindbladian transport, and provides a state-to-state expression for $P_{l\leftarrow r}(t)$ with a locality constraint on elementary jumps. The authors validate the approach by showing consistency with a prior non-Hermitian state-to-state method in lossy setups, and apply it to pumped and pump-and-drain excitonic aggregates to reveal explicit transport routes and steady-state currents, including size-dependent currents in dimers and trimers. The framework is solver-agnostic and scalable, enabling detailed mechanistic insight into transport in complex molecular networks with pumping and loss, and offering a versatile platform for exploring a broader class of empirical processes in quantum transport.

Abstract

Analyzing routes of transport for open quantum systems with non-equilibrium initial conditions is extremely challenging. The state-to-state approach [A. Bose, and P.L. Walters, J. Chem. Theory Comput. 2023, 19, 15, 4828-4836] has proven to be a useful method for understanding transport mechanisms in quantum systems interacting with dissipative thermal baths, and has been recently extended to non-Hermitian systems to account for empirical loss. These non-Hermitian descriptions are, however, not capable of describing empirical processes of more general nature, including but not limited to a variety of pumping processes. We extend the state-to-state analysis to account for Lindbladian descriptions of generic dissipative, pumping and decohering processes acting on a system which is exchanging energy with a thermal bath. This Lindblad state-to-state method can elucidate routes of transport in systems coupled to a bath and additionally acted upon by Lindblad jump operators. The method is demonstrated using examples of excitonic aggregates subject to incoherent pumping and draining processes. Using this new state-to-state formalism, we demonstrate the establishment of steady-state excitonic currents across molecular aggregates, yielding a different first-principles approach to quantifying the same.

Figures (12)

• Figure 1: Population, $P_\alpha(t)$, of different states $\ket{\alpha}$ in a polaritonic trimer with an initial excitation $\rho_\text{sys}(0)=\dyad{1}$. (Markers: non-Hermitian state-to-state results sharmaNonHermitianState2025; Lines: Lindblad state-to-state results)
• Figure 2: State-to-state analysis of excitation flows into different sites of the lossy polaritonic trimer. (Lines: Lindblad state-to-state result; Markers: non-Hermitian state-to-state results sharmaNonHermitianState2025; Orange: $P_{*\leftarrow 1}(t)$, Green: $P_{*\leftarrow 2}(t)$, Red: $P_{*\leftarrow 3}(t)$ and Purple: $P_{*\leftarrow c}(t)$. Terms of the type $P_{\alpha\leftarrow\alpha}(t)$ are not depicted here.)
• Figure 3: Site-specific excitation loss, $\mathcal{L}_{j}(t)$, from the polaritonic trimer. Lines: Lindblad state-to-state, Markers: non-Hermitian method from Ref. sharmaNonHermitianState2025.
• Figure 4: Population, $P_\alpha(t)$, of different states $\ket{\alpha}$ in the excitonic dimer initially in the ground state, $\rho_\text{sys}(0)=\dyad{gg}$, with excitation being pumped into monomer 1 with a time-constant of $T_\mathrm{pump}=300\fs$.
• Figure 5: State-to-state analysis of excitation flows into the diabatic states of the excitonic dimer when pumped with $T_\mathrm{pump}=300\fs$. (Blue: $P_{*\leftarrow gg}(t)$, Orange: $P_{*\leftarrow eg}(t)$, Green: $P_{*\leftarrow ge}(t)$ and Red: $P_{*\leftarrow ee}(t)$. Black indicates multiple overlapping curves with legends marked as discs of corresponding colors.)