Pauli Master Equation Research Articles

Charge and spin thermoelectric transport in benzene-based molecular nano-junctions: a quantum many-body study.

Within the Coulomb blockade regime, our study delves into the charge, spin, and thermoelectric transport characteristics of a benzene-based molecular nano-junction using the Pauli master equation and linear response theory. The charge- and spin-transport studies show strong negative differential conductance features in the current-voltage (I-V) characteristics for the ortho and meta connections of electrodes on either side. Contrarily, the para-connection displays Coulomb staircase behavior. By exploring spin current behavior in the presence of spin-polarized electrodes or an external Zeeman field, we establish a methodology that facilitates precise control over the specific spin flow. Various charge and spin thermoelectric transport coefficients have been studied with varying chemical potentials. We focus on spin-polarized conductance, the Seebeck coefficient, and the figure of merit. By adjusting electrode polarization or employing an external magnetic field, we achieve an impressive peak value for the spin thermoelectric figure of merit, approximately 4.10. This outcome underscores the strategic value of harnessing both spin-polarized electrodes and external magnetic fields within the domain of spin caloritronics.

Carrier Screening Controls Transport in Conjugated Polymers at High Doping Concentrations.

Transport properties of doped conjugated polymers (CPs) have been widely analyzed with the Gaussian disorder model (GDM) in conjunction with hopping transport between localized states. These models reveal that even in highly doped CPs, a majority of carriers are still localized because dielectric permittivity of CPs is well below that of inorganic materials, making Coulomb interactions between carriers and dopant counterions much more pronounced. However, previous studies within the GDM did not consider the role of screening the dielectric interactions by carriers. Here we implement carrier screening in the Debye-Hückel formalism in our calculations of dopant-induced energetic disorder, which modifies the Gaussian density of states (DOS). Then we solve the Pauli master equation using Miller-Abrahams hopping rates with states from the resulting screened DOS to obtain conductivity and Seebeck coefficient across a broad range of carrier concentrations and compare them to measurements. Our results show that screening has significant impact on the shape of the DOS and consequently on carrier transport, particularly at high doping. We prove that the slope of Seebeck coefficient versus electric conductivity, which was previously thought to be universal, is impacted by screening and decreases for systems with small dopant-carrier separation, explaining our measurements. We also show that thermoelectric power factor is underestimated by a factor of ∼10 at higher doping concentrations if screening is neglected. We conclude that carrier screening plays a crucial role in curtailing dopant-induced energetic disorder, particularly at high carrier concentrations.

Exploring plasmonic effect on exciton transport: A theoretical insight from macroscopic quantum electrodynamics.

Exciton transport in extended molecular systems and how to manipulate such transport in a complex environment are essential to many energy and optical-related applications. We investigate the mechanism of plasmon-coupled exciton transport by using the Pauli master equation approach, combined with kinetic rates derived from macroscopic quantum electrodynamics. Through our theoretical framework, we demonstrate that the presence of a silver nanorod induces significant frequency dependence in the ability of transporting exciton through a molecule chain, indicated by the exciton diffusion coefficient, due to the dispersive nature of the silver dielectric response. Compared with the same system in vacuum, great enhancement (up to a factor of 103) in the diffusion coefficient can be achieved by coupling the resonance energy transfer process to localized surface plasmon polariton modes of the nanorod. Furthermore, our analysis reveals that the diffusion coefficients with the nearest-neighbor coupling approximation are ∼10 times smaller than the results obtained beyond this approximation, emphasizing the significance of long-range coupling in exciton transport influenced by plasmonic nanostructures. This study not only paves the way for exploring practical approaches to study plasmon-coupled exciton transport but also provides crucial insights for the design of innovative plasmon-assisted photovoltaic applications.

Protein charge transfer far from equilibrium: a theoretical perspective.

Potential differences for protein-assisted electron transfer across lipid bilayers or in bio-nano setups can amount to several 100 mV; they lie far outside the range of linear response theory. We describe these situations by Pauli-master equations that are based on Marcus theory of charge transfer between self-trapped electrons and that obey Kirchhoff's current law. In addition, we take on-site blockade effects and a full non-linear response of the local potentials into account. We present analytical and numerical current-potential curves and electron populations for multi-site model systems and biological electron transfer chains. Based on these, we provide empirical rules for electron populations and chemical potentials along the chain. The Pauli-master mean-field results are validated by kinetic Monte Carlo simulations. We briefly discuss the biochemical and evolutionary aspects of our findings.

Quantum Chaos, Random Matrices, and Irreversibility in Interacting Many-Body Quantum Systems.

The Pauli master equation describes the statistical equilibration of a closed quantum system. Simplifying and generalizing an approach developed in two previous papers, we present a derivation of that equation using concepts developed in quantum chaos and random-matrix theory. We assume that the system consists of subsystems with strong internal mixing. We can then model the system as an ensemble of random matrices. Equilibration results from averaging over the ensemble. The direction of the arrow of time is determined by an (ever-so-small) coupling to the outside world. The master equation holds for sufficiently large times if the average level densities in all subsystems are sufficiently smooth. These conditions are quantified in the text, and leading-order correction terms are given.

Computational modeling of charge hopping dynamics along a disordered one-dimensional wire with energy gradients in quantum environments.

This computational study investigates the effects of energy gradients on charge hopping dynamics along a one-dimensional chain of discrete sites coupled to quantum bath, which is modeled at the level of Pauli master equation (PME). This study also assesses the performance of different approximations for the hopping rates. Three different methods for solving the PME, a fourth order Runge-Kutta method, numerical diagonalization of the rate matrix followed by analytic propagation, and kinetic Monte Carlo simulation method, are tested and confirmed to produce virtually identical values of time dependent mean square displacement, diffusion constant, and mobility. Five different rate expressions, exact numerical evaluation of Fermi's Golden Rule (FGR) rate, stationary phase interpolation (SPI) approximation, semiclassical approximation, classical Marcus rate, and Miller-Abrahams rate, are tested to help understand the effects of approximations in representing quantum environments in the presence of energy gradients. The results based on direct numerical evaluation of FGR rate exhibit transition from diffusive to non-diffusive behavior with the increase in the gradient and show that the charge transport in the quantum bath is more sensitive to the magnitude of the gradient and the disorder than in the classical bath. Among all the four approximations for the hopping rates, the SPI approximation is confirmed to work best overall. A comparison of two different methods to calculate the mobility identifies drift motion of the population distribution as the major source of non-diffusive behavior and provides more reliable information on the contribution of quantum bath.

Structures and exciton dynamics of aggregated lutein and zeaxanthin in aqueous media

We carried out comprehensively experimental and theoretical studies of the aggregates of lutein and zeaxanthin. The experimental absorption, Circular Dichroism (CD) spectra of these aggregates are measured in aqueous ethanol media with different concentrations of water at temperature range of 20–65 °C. Comparing with the broad absorption of monomers around 450 nm, the sharp peaks of absorption band ca. at 369 and 384 nm of lutein evidence two tightly packed H–aggregates, exhibiting non-vibrational bands of monomer. Zeaxanthin tends to form H–type at 20 °C and J–type at 65 °C, based on the absorption spectral shifts. The helical structures of these aggregates are proved by CD spectra with classic excitonic bisignate line-shape due to Cotton effect. Combining with Frenkel exciton model and line-shape spectral theory, the theoretical simulations of experimental absorption and CD spectra are carried out to investigate the helical details of these aggregates. The calculated distance ranges from 0.57 to 0.66 nm with the overlay angle of 10° for all H–types of helical aggregates, which is coherent to the value of nearest distance (~0.65 nm) of lutein and zeaxanthin dimers optimized by Gaussian program. Furthermore, with the help of Pauli master equation, we studied theoretically the dynamics and diffusion of Frenkel exciton in the one-dimensional carotenoid aggregates, using the parameters obtained from the fit of the absorption spectra. As compared with loosely packed J–aggregate, the exciton of tightly structured H–aggregate experiences a faster relaxation within 10 ps from highest excited state to lowest one along with the exciton traveling on the aggregate chain to be trapped. We propose a pattern of gradient diagonal disorder that can localize the exciton at the segment of certain molecules on the aggregate chain. The study involved would be helpful and valuable to understand energy absorption, transfer and trapping in antenna system.

Master-Equation Study of Quantum Transport in Realistic Semiconductor Devices Including Electron-Phonon and Surface-Roughness Scattering

In conventional theoretical methods for studying dissipative quantum transport, numerical complexity forces us to ignore important nonlocal effects, or to restrict attention to very small or one-dimensional systems. The authors present an efficient method, based on the Pauli master equation, that treats dissipative quantum transport while explicitly taking into account the nonlocal and inelastic nature of the scattering processes. Applying the method to a realistic semiconductor device reveals that, even at the nanoscale, electronic transport is predominantly dissipative, and demonstrates quantitatively that scattering due to interface roughness has a drastic impact on device performance.

Ultrafast Dynamics of Tripyrrindiones in Solution Mediated by Hydrogen-Bonding Interactions.

The optical properties and ultrafast dynamics of hexaethyl tripyrrin-1,14-dione (H3TD1) are tuned by hydrogen-bonding interactions between the solute and the solvent. In solvents with low hydrogen-bonding affinity, H3TD1 preferentially forms hydrogen-bonded dimers, whereas in solvents that can either donate or accept hydrogen bonds H3TD1 is present as a monomer. The distinction between dimer and monomer determines the dynamics of the system, with faster internal conversion observed in the dimer form. The ultrafast dynamics were characterized using time-correlated single photon counting, fluorescence upconversion, and transient absorption measurements. The time-resolved dynamics of both the monomer and dimer in solution were modeled using a Pauli master equation treatment for a three level system. The solvent-dependent optical properties were measured using steady-state absorption and fluorescence. This data was then used to calculate the quantum yield and extinction coefficients.

In Russian

Stochastic non-equilibrium processes can serve as a driving force for a Brownian motor. In this case, the simplest description of an induced directional motion is carried out under the approximation of small changes in potential energy of a particle compared to the thermal energy (the high-temperature or low-energy approximation). Within this approximation, characteristics of the stochastic process are included into the final analytical expressions for the average velocity of a Brownian motor only through lower correlation functions. The purpose of this article is to obtain these correlation functions for Markov stochastic processes of a general form. The Pauli master equation has been considered, which describes the kinetics of an N states system in terms of given transition rate constants. The general solution of this equation, expressed in terms of the eigenvalues and eigenfunctions of the transition rate matrix, has been specified for the cases of dichotomous fluctuations (N = 2) and fluctuations of transitions from the ground state into two symmetric excited ones (N = 3). To study the influence of a type of a correlation function on the average velocity of a Brownian motor, a spatially harmonic controlled signal is considered, with which the average motor velocity is proportional to the second-order correlation function. The introduction of the additional state allowed us to obtain a bell-shaped frequency dependence of the average motor velocity, with the maximum and the width of the bell easily controllable by the transition rate constants and with the diffusion coefficient which depends on temperature, a particle size, and medium viscosity. Dichotomous process, which is a particular case of the model considered, is characterized by the highest values of the average velocity. A three-level model is preferable in case of a narrower width of the bell-shaped frequency dependence is required.

Photoinduced Anomalous Coulomb Blockade and the Role of Triplet States in Electron Transport through an Irradiated Molecular Transistor.

In this study, we explore photoinduced electron transport through a molecule weakly coupled to two electrodes by combining first-principles quantum chemistry calculations with a Pauli master equation approach that accounts for many-electron states. In the incoherent limit, we demonstrate that energy-level alignment of triplet and charged states plays a crucial role, even when the rate of intersystem crossing is much smaller than the rate of fluorescence. Furthermore, the field intensity dependence and an upper bound to the photoinduced electric current can be analytically derived in our model. Under an optical field, the conductance spectra (charge stability diagrams) exhibit unusual Coulomb diamonds, which are associated with molecular excited states, and their widths can be expressed in terms of energies of the molecular electronic states. This study offers new directions for exploring optoelectronic response in nanoelectronics.

QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices

QmeQ is an open-source Python package for numerical modeling of transport through quantum dot devices with strong electron–electron interactions using various approximate master equation approaches. The package provides a framework for calculating stationary particle or energy currents driven by differences in chemical potentials or temperatures between the leads which are tunnel coupled to the quantum dots. The electronic structures of the quantum dots are described by their single-particle states and the Coulomb matrix elements between the states. When transport is treated perturbatively to lowest order in the tunneling couplings, the possible approaches are Pauli (classical), first-order Redfield, and first-order von Neumann master equations, and a particular form of the Lindblad equation. When all processes involving two-particle excitations in the leads are of interest, the second-order von Neumann approach can be applied. All these approaches are implemented in QmeQ. We here give an overview of the basic structure of the package, give examples of transport calculations, and outline the range of applicability of the different approximate approaches. Program summaryProgram Title:QmeQProgram Files doi:http://dx.doi.org/10.17632/8687mrhgg9.1Licensing provisions: BSD 2-ClauseProgramming language:PythonExternal libraries:NumPy, SciPy, CythonNature of problem: Calculation of stationary state currents through quantum dots tunnel coupled to leads.Solution method: Exact diagonalization of the quantum dot Hamiltonian for a given set of single particle states and Coulomb matrix elements. Numerical solution of the stationary-state master equation for a given approximate approach.Restrictions: Depending on the approximate approach the temperature needs to be sufficiently large compared to the coupling strength for the approach to be valid.

Kinetics of nanosize ferroelectrics

We analyze theoretically the finite-temperature polarization dynamic in displacive-type ferroelectrics. In particular we consider the thermally-activated switching time of a single-domain ferroelectric polarization studied by means of the Landau-Khalatnikov equation, extended as to capture thermal fluctuations. The results are compared with the switching time formula that follows from the analytical solution of Pauli master equations. In a second step we focus on the phase diagram of a prototypical ferroelectric as described by the temperature-dependent Landau-Devonshire model including thermal fluctuations. Our simulations show the emergence of phase instability at reduced sizes which we attribute to thermal fluctuations in the order parameter in the respective phase. We conclude that, along with the temperature-dependent potential coefficients, thermal fluctuations should be taken into account to achieve a comprehensive description of the thermal behavior of reduced-size ferroelectrics. To endorse our conclusions, we simulated the electric-field activated switching time for a multi-domain system and compared the results to the predictions of well-established models such as the Kolmogorov-Avrami-Ishibashi.

Splitting nodes and linking channels: A method for assembling biocircuits from stochastic elementary units

Akin to electric circuits, we construct biocircuits that are manipulated by cutting and assembling channels through which stochastic information flows. This diagrammatic manipulation allows us to create a method which constructs networks by joining building blocks selected so that (a) they cover only basic processes; (b) it is scalable to large networks; (c) the mean and variance-covariance from the Pauli master equation form a closed system; and (d) given the initial probability distribution, no special boundary conditions are necessary to solve the master equation. The method aims to help with both designing new synthetic signaling pathways and quantifying naturally existing regulatory networks.

Symmetric and antisymmetric forms of the Pauli master equation.

When applied to matter and antimatter states, the Pauli master equation (PME) may have two forms: time-symmetric, which is conventional, and time-antisymmetric, which is suggested in the present work. The symmetric and antisymmetric forms correspond to symmetric and antisymmetric extensions of thermodynamics from matter to antimatter — this is demonstrated by proving the corresponding H-theorem. The two forms are based on the thermodynamic similarity of matter and antimatter and differ only in the directions of thermodynamic time for matter and antimatter (the same in the time-symmetric case and the opposite in the time-antisymmetric case). We demonstrate that, while the symmetric form of PME predicts an equibalance between matter and antimatter, the antisymmetric form of PME favours full conversion of antimatter into matter. At this stage, it is impossible to make an experimentally justified choice in favour of the symmetric or antisymmetric versions of thermodynamics since we have no experience of thermodynamic properties of macroscopic objects made of antimatter, but experiments of this kind may become possible in the future.

Transport in serial spinful multiple-dot systems: The role of electron-electron interactions and coherences.

Quantum dots are nanoscopic systems, where carriers are confined in all three spatial directions. Such nanoscopic systems are suitable for fundamental studies of quantum mechanics and are candidates for applications such as quantum information processing. It was also proposed that linear arrangements of quantum dots could be used as quantum cascade laser. In this work we study the impact of electron-electron interactions on transport in a spinful serial triple quantum dot system weakly coupled to two leads. We find that due to electron-electron scattering processes the transport is enabled beyond the common single-particle transmission channels. This shows that the scenario in the serial quantum dots intrinsically deviates from layered structures such as quantum cascade lasers, where the presence of well-defined single-particle resonances between neighboring levels are crucial for device operation. Additionally, we check the validity of the Pauli master equation by comparing it with the first-order von Neumann approach. Here we demonstrate that coherences are of relevance if the energy spacing of the eigenstates is smaller than the lead transition rate multiplied by ħ.

Numerical simulations of the role of a ferroelectric polymer interfacial layer in organic solar cells.

A Pauli master equation method is adopted for the simulation of polymer bulk heterojunction (BHJ) solar cells with vinylidene fluoride-trifluoroethylene copolymer (P(VDF-TrFE)) films as interfacial layers. According to previous reports, using highly crystalline P(VDF-TrFE) films as interfacial layers can highly enhance the efficiency of polymer BHJ solar cells, and possible mechanisms for the enhancement by two different groups were given as the dipole induced permanent internal electric field or simply the electrode improvement which implied that the origin is the barrier lowering effect. The correlation between the appearance of S-shaped current density-voltage (J-V) characteristics and the energy barrier is studied first, and then further results indicate that the previous electrode improvement model provides a consistent explanation for the origin of performance enhancement due to the insertion of polarized P(VDF-TrFE) interfacial layers. Moreover, the phenomenon of an increase of the internal electric field observed before can be attributed to better contact conditions which help reduce the bimolecular recombination rate. Comparatively speaking, the electrode improvement model can give a more rational explanation for the origin of performance enhancement experimentally found. In contrast, the dipole induced permanent internal electric field model was not complete enough.

Influence of extraction barrier on the loss process of photogenerated charge carrier in polymer bulk heterojunction solar cells

Based on a full device model adopting three-dimensional Pauli master equation approach, the charge carrier loss process due to poor extraction channels between electrode and active layer in polymer bulk heterojunction( BHJ) solar cells was studied. The influence of barrier height on device performance was simulated to reveal the importance of electrode improvement. It was found that relatively large extraction barrier height(over 0.40 eV) can lead to the significant diminishing of the overall charge collection efficiency, since bimolecular recombination rate would increase to a high level due to enhanced space charge accumulation effect near electrodes. In contrast, the percentage of charge carrier annihilated due to geminate recombination did not change significantly with barrier height variation. Our simulation results may provide the basis for a more accurate model and potential direction of polymer BHJ solar cells improvement.

Performance Optimization and Instability Study in Ring Cavity Quantum Cascade Lasers

An optimization study of quantum cascade lasers (QCLs) considering the laser instability condition is performed. To model current transport, the Pauli master equation is solved using a Monte Carlo approach. The effects of saturable absorber and pumping strength on the instability threshold are investigated. A particle swarm optimization algorithm is applied to increase the laser optical gain. A large optical gain below the instability threshold is achieved for optimized QCL designs. To analyze the optimized structure, a numerical calculation based on the Maxwell-Bloch equations is performed. The results indicate side-mode instabilities due to Risken-Nummedal-Graham-Haken-like instability.

The Influence of Morphology on the Charge Transport in Two-Phase Disordered Organic Systems

ABSTRACTIn this work we use a three-dimensional Pauli master equation to investigate the charge carrier mobility of a two-phase system, which can mimic donor-acceptor and amorphous-crystalline bulk heterojunctions. Our approach can be separated into two parts: the morphology generation and the charge transport modeling in the generated blend. The morphology part is based on a Monte Carlo simulation of binary mixtures (donor/acceptor). The second part is carried out by numerically solving the steady-state Pauli master equation. By taking the energetic disorder of each phase, their energy offset and domain morphology into consideration, we show that the carrier mobility can have a significant different behavior when compared to a one-phase system. When the energy offset is non-zero, we show that the mobility electric field dependence switches from negative to positive at a threshold field proportional to the energy offset. Additionally, the influence of morphology, through the domain size and the interfacial roughness parameters, on the transport was also investigated.