21 research outputs found
Hydrodynamic limit and large deviations of reaction-diffusion master equations
We derive the hydrodynamic limit of a reaction-diffusion master equation, that combines an exclusion process with a reversible chemical master equation expression for the reaction rates. The crucial assumption is that the associated macroscopic reaction network has a detailed balance equilibrium. The hydrodynamic limit is given by a system of reaction-diffusion equations with a modified mass action law for the reaction rates. We provide the upper bound for large deviations of the empirical measure from the hydrodynamic limit
Hybrid quantum-classical modeling of quantum dot devices
The design of electrically driven quantum dot devices for quantum optical
applications asks for modeling approaches combining classical device physics
with quantum mechanics. We connect the well-established fields of
semi-classical semiconductor transport theory and the theory of open quantum
systems to meet this requirement. By coupling the van Roosbroeck system with a
quantum master equation in Lindblad form, we introduce a new hybrid
quantum-classical modeling approach, which provides a comprehensive description
of quantum dot devices on multiple scales: It enables the calculation of
quantum optical figures of merit and the spatially resolved simulation of the
current flow in realistic semiconductor device geometries in a unified way. We
construct the interface between both theories in such a way, that the resulting
hybrid system obeys the fundamental axioms of (non-)equilibrium thermodynamics.
We show that our approach guarantees the conservation of charge, consistency
with the thermodynamic equilibrium and the second law of thermodynamics. The
feasibility of the approach is demonstrated by numerical simulations of an
electrically driven single-photon source based on a single quantum dot in the
stationary and transient operation regime
Convergence to equilibrium in energy-reaction-diffusion systems using vector-valued functional inequalities
We discuss how the recently developed energy-dissipation methods for reactiondi usion systems can be generalized to the non-isothermal case. For this we use concave entropies in terms of the densities of the species and the internal energy, where the importance is that the equilibrium densities may depend on the internal energy. Using the log-Sobolev estimate and variants for lower-order entropies as well as estimates for the entropy production of the nonlinear reactions we give two methods to estimate the relative entropy by the total entropy production, namely a somewhat restrictive convexity method, which provides explicit decay rates, and a very general, but weaker compactness method
An entropic gradient structure for Lindblad equations and GENERIC for quantum systems coupled to macroscopic models
We show that all Lindblad operators (i.e. generators of quantum
semigroups) on a finite-dimensional Hilbert space satisfying the detailed
balance condition with respect to the thermal equilibrium state can be
written as a gradient system with respect to the relative entropy. We discuss
also thermodynamically consistent couplings to macroscopic systems, either as
damped Hamiltonian systems with constant temperature or as GENERIC systems
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Hybrid quantum-classical modeling of quantum dot devices
The design of electrically driven quantum dot devices for quantum
optical applications asks for modeling approaches combining classical device
physics with quantum mechanics. We connect the well-established fields of
semi-classical semiconductor transport theory and the theory of open quantum
systems to meet this requirement. By coupling the van Roosbroeck system with
a quantum master equation in Lindblad form, we obtain a new hybrid
quantum-classical modeling approach, which enables a comprehensive
description of quantum dot devices on multiple scales: It allows the
calculation of quantum optical figures of merit and the spatially resolved
simulation of the current flow in realistic semiconductor device geometries
in a unified way. We construct the interface between both theories in such a
way, that the resulting hybrid system obeys the fundamental axioms of
(non-)equilibrium thermodynamics. We show that our approach guarantees the
conservation of charge, consistency with the thermodynamic equilibrium and
the second law of thermodynamics. The feasibility of the approach is
demonstrated by numerical simulations of an electrically driven single-photon
source based on a single quantum dot in the stationary and transient
operation regime
Mathematical modeling of semiconductors: From quantum mechanics to devices
We discuss recent progress in the mathematical modeling of semiconductor devices. The central result of this paper is a combined quantum-classical model that self-consistently couples van Roosbroeck's drift-diffusion system for classical charge transport with a Lindblad-type quantum master equation. The coupling is shown to obey fundamental principles of non-equilibrium thermodynamics. The appealing thermodynamic properties are shown to arise from the underlying mathematical structure of a damped Hamitlonian system, which is an isothermal version of so-called GENERIC systems. The evolution is governed by a Hamiltonian part and a gradient part involving a Poisson operator and an Onsager operator as geoemtric structures, respectively. Both parts are driven by the conjugate forces given in terms of the derivatives of a suitable free energy
Complex Intramolecular Mechanics of G-actin - An Elastic Network Study
Systematic numerical investigations of conformational motions in single actin
molecules were performed by employing a simple elastic-network (EN) model of
this protein. Similar to previous investigations for myosin, we found that
G-actin essentially behaves as a strain sensor, responding by well-defined
domain motions to mechanical perturbations. Several sensitive residues within
the nucleotide-binding pocket (NBP) could be identified, such that the
perturbation of any of them can induce characteristic flattening of actin
molecules and closing of the cleft between their two mobile domains. Extending
the EN model by introduction of a set of breakable links which become
effective only when two domains approach one another, it was observed that
G-actin can possess a metastable state corresponding to a closed conformation
and that a transition to this state can be induced by appropriate
perturbations in the NBP region. The ligands were roughly modeled as a single
particle (ADP) or a dimer (ATP), which were placed inside the NBP and
connected by elastic links to the neighbors. Our approximate analysis suggests
that, when ATP is present, it stabilizes the closed conformation of actin.
This may play an important role in the explanation why, in the presence of
ATP, the polymerization process is highly accelerated
Multi-dimensional modeling and simulation of semiconductor nanophotonic devices
Self-consistent modeling and multi-dimensional simulation of semiconductor nanophotonic devices is an important tool in the development of future integrated light sources and quantum devices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically explore their optimization potential. The efficient implementation of multi-dimensional numerical simulations for computer-aided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in device-scale modeling of quantum dot based single-photon sources and laser diodes by self-consistently coupling the optical Maxwell equations with semiclassical carrier transport models using semi-classical and fully quantum mechanical descriptions of the optically active region, respectively. For the simulation of realistic devices with complex, multi-dimensional geometries, we have developed a novel hp-adaptive finite element approach for the optical Maxwell equations, using mixed meshes adapted to the multi-scale properties of the photonic structures. For electrically driven devices, we introduced novel discretization and parameter-embedding techniques to solve the drift-diffusion system for strongly degenerate semiconductors at cryogenic temperature. Our methodical advances are demonstrated on various applications, including vertical-cavity surface-emitting lasers, grating couplers and single-photon sources
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Convergence to equilibrium in energy-reaction-diffusion systems using vector-valued functional inequalities : dedicated to Peter Markowich on the occasion of his sixtieth birthday
We discuss how the recently developed energy-dissipation methods for
reaction-diffusion systems can be generalized to the non-isothermal case. For
this we use concave entropies in terms of the densities of the species and
the internal energy, with the important feature, that the equilibrium
densities may depend on the internal energy. Using the log-Sobolev estimate
and variants for lower-order entropies as well as estimates for the entropy
production of the nonlinear reactions we give two methods to estimate the
relative entropy by the total entropy production, namely a somewhat
restrictive convexity method, which provides explicit decay rates, and a very
general, but weaker compactness method