Thermodynamics of a subensemble of a canonical ensemble

Two approaches to describe the thermodynamics of a subsystem that interacts with a thermal bath are considered. Within the first approach, the mean system energy $E_{S}$ is identified with the expectation value of the system Hamiltonian, which is evaluated with respect to the overall (system+bath) equilibrium distribution. Within the second approach, the system partition function $Z_{S}$ is considered as the fundamental quantity, which is postulated to be the ratio of the overall (system+bath) and the bath partition functions, and the standard thermodynamic relation $E_{S}=-d(\ln Z_{S})/d\beta$ is used to obtain the mean system energy. % ($\beta\equiv 1/(k_{B}T)$, $k_{B}$ is the Boltzmann constant, %and $T$ is the temperature). Employing both classical and quantum mechanical treatments, the advantages and shortcomings of the two approaches are analyzed in detail for various different systems. It is shown that already within classical mechanics both approaches predict significantly different results for thermodynamic quantities provided the system-bath interaction is not bilinear or the system of interest consists of more than a single particle. Based on the results, it is concluded that the first approach is superior

A model for dynamical solvent control of molecular junction electronic properties

Experimental measurements of electron transport properties of molecular junctions are often performed in solvents. Solvent-molecule coupling and physical properties of the solvent can be used as the external stimulus to control electric current through a molecule. In this paper, we propose a model, which includes dynamical effects of solvent-molecule interaction in the non-equilibrium Green's function calculations of electric current. The solvent is considered as a macroscopic dipole moment that reorients stochastically and interacts with the electrons tunnelling through the molecular junction. The Keldysh-Kadanoff-Baym equations for electronic Green's functions are solved in time-domain with subsequent averaging over random realisations of rotational variables using Furutsu-Novikov method for exact closure of infinite hierarchy of stochastic correlation functions. The developed theory requires the use of wide-band approximation as well as classical treatment of solvent degrees of freedom. The theory is applied to a model molecular junction. It is demonstrated that not only electrostatic interaction between molecular junction and solvent but also solvent viscosity can be used to control electrical properties of the junction. Aligning of the rotating dipole moment breaks particle-hole symmetry of the transmission favouring either hole or electron transport channels depending upon the aligning potential

Hierarchical Equations-of-Motion Method for Momentum System-Bath Coupling

[Image: see text] For a broad class of quantum models of practical interest, we demonstrate that the Hamiltonian of the system nonlinearly coupled to a harmonic bath through the system and bath coordinates can be equivalently mapped into the Hamiltonian of the system bilinearly coupled to the bath through the system and bath momenta. We show that the Hamiltonian with bilinear system–bath momentum coupling can be treated by the hierarchical equations-of-motion (HEOM) method and present the corresponding proof-of-principle simulations. The developed methodology creates the opportunity to scrutinize a new family of nonlinear quantum systems by the numerically accurate HEOM method

Dissipative Landau-Zener transitions in a three-level bow-tie model: accurate dynamics with the Davydov multi-D2 Ansatz

We investigate Landau-Zener (LZ) transitions in the three-level bow-tie model (3L-BTM) in a dissipative environment by using the numerically accurate method of multiple Davydov D2 Ansatze. We first consider the 3L-TBM coupled to a single harmonic mode, study evolutions of the transition probabilities for selected values of the model parameters, and interpret the obtained results with the aid of the energy diagram method. We then explore the 3L-TBM coupled to a boson bath. Our simulations demonstrate that sub-Ohmic, Ohmic and super-Ohmic boson baths have substantially different influences on the 3L-BTM dynamics, which cannot be grasped by the standard phenomenological Markovian single-rate descriptions. We also describe novel bath-induced phenomena which are absent in two-level LZ systems.Comment: 11 pages, 7 figure

Exciton Dynamics and Time-Resolved Fluorescence in Nanocavity-Integrated Monolayers of Transition-Metal Dichalcogenides

We have developed an ab-initio-based fully-quantum numerically-accurate methodology for the simulation of the exciton dynamics and time- and frequency-resolved fluorescence spectra of the cavity-controlled two-dimensional materials at finite temperature and applied this methodology to the single-layer WSe2 system. This allowed us to establish dynamical and spectroscopic signatures of the polaronic and polaritonic effects as well as uncover their characteristic timescales in the relevant range of temperatures

First-passage time theory of activated rate chemical processes in electronic molecular junctions

Confined nanoscale spaces, electric fields and tunneling currents make the molecular electronic junction an experimental device for the discovery of new, out-of-equilibrium chemical reactions. Reaction-rate theory for current-activated chemical reactions is developed by combining a Keldysh nonequilibrium Green's functions treatment of electrons, Fokker-Planck description of the reaction coordinate, and Kramers' first-passage time calculations. The NEGF provide an adiabatic potential as well as a diffusion coefficient and temperature with local dependence on the reaction coordinate. Van Kampen's Fokker-Planck equation, which describes a Brownian particle moving in an external potential in an inhomogeneous medium with a position-dependent friction and diffusion coefficient, is used to obtain an analytic expression for the first-passage time. The theory is applied to several transport scenarios: a molecular junction with a single, reaction coordinate dependent molecular orbital, and a model diatomic molecular junction. We demonstrate the natural emergence of Landauer's blowtorch effect as a result of the interplay between the configuration dependent viscosity and diffusion coefficients. The resultant localized heating in conjunction with the bond-deformation due to current-induced forces are shown to be the determining factors when considering chemical reaction rates; each of which result from highly tunable parameters within the system