Related papers: Optimized hierarchical equations of motion for Dru…
To advance hierarchial equations of motion as a standard theory for quantum dissipative dynamics, we put forward a mixed Heisenberg--Schrodinger scheme with block-matrix implementation on efficient evaluation of nonlinear optical response…
We theoretically investigate an electron transfer (ET) process in a dissipative environment by means of two-dimensional (2D) correlation spectroscopy. We extend the reduced hierarchy equations of motion approach to include both overdamped…
A nonperturbative theory is developed, aiming at an exact and efficient evaluation of a general quantum system interacting with arbitrary bath environment at any temperature and in the presence of arbitrary time-dependent external fields.…
The hierarchical equations of motion (HEOM) for a generalized quantum dissipative system is rigorously constructed in the frameworks of two different stochastic dynamical descriptions, i.e., the non-Markovian quantum state diffusion…
We present a formulation of proper orthogonal decomposition (POD) producing a velocity-temperature basis optimized with respect to an $H^1$ dissipation norm. This decomposition is applied, along with a conventional POD optimized with…
We propose a nonperturbative quantum dissipation theory, in term of hierarchical quantum master equation. It may be used with a great degree of confidence to various dynamics systems in condensed phases. The theoretical development is…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
We present an algorithm for the approximation of a finite horizon optimal control problem for advection-diffusion equations. The method is based on the coupling between an adaptive POD representation of the solution and a Dynamic…
For the multi-mode Dicke model in a transport setting that exhibits collective boson transmissions, we construct the equation of motion for the cumulant generating function. Approximating the exact system of equations at the level of…
Traditionally, systems governed by linear Partial Differential Equations (PDEs) are spatially discretized to exploit their algebraic structure and reduce the computational effort for controlling them. Due to beneficial insights of the PDEs,…
Well--defined criteria are proposed for assessing the accuracy of quantum master equations whose memory functions are approximated by Pad\'e resummation of the first two moments in the electronic coupling. These criteria partition the…
In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…
A recently developed approach to the thermodynamics of open quantum systems, on the basis of the principle of minimal dissipation, is applied to the spin-boson model. Employing a numerically exact quantum dynamical treatment based on the…
We outline a reduction scheme for a class of Brownian dynamics which leads to meaningful corrections to the Smoluchowski equation in the overdamped regime. The mobility coefficient of the reduced dynamics is obtained by exploiting the…
Correlated driving-and-dissipation equation (CODDE) is an optimized complete second-order quantum dissipation approach, which is originally concerned with the reduced system dynamics only. However, one can actually extract the hybridized…
We consider integrated circuits with semiconductors modeled by modified nodal analysis and drift-diffusion equations. The drift-diffusion equations are discretized in space using mixed finite element method. This discretization yields a…
A hierarchical equations of motion formalism for a quantum dissipation system in a grand canonical bath ensemble surrounding is constructed, on the basis of the calculus-on-path-integral algorithm, together with the parametrization of…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…