Real-time path integral approach to nonequilibrium many-body quantum system

A real-time path integral Monte Carlo approach is developed to study the dynamics in a many-body quantum system until reaching a nonequilibrium stationary state. The approach is based on augmenting an exact reduced equation for the evolution of the system in the interaction picture which is amenable to an efficient path integral (worldline) Monte Carlo approach. Results obtained for a model of inelastic tunneling spectroscopy reveal the applicability of the approach to a wide range of physically important regimes, including high (classical) and low (quantum) temperatures, and weak (perturbative) and strong electron-phonon couplings.Comment: 5 pages, 2 figure

A Stochastic Approach for Investigation Ultrafast Phenomena in Semiconductors

2002 Mathematics Subject Classification: 65C05In this paper a stochastic approach is proposed for investigation the ultrafast evolution of electrons interacting with phonons in the presence of an applied electric field. The quantum-kinetic equation describing the above ultrafast phenomena contains polynomial non-linearity which allows to use the link between non-stationary iterative processes and the branching stochastic processes. The considered stochastic approach relies on the numerical Monte Carlo (MC) theory as applied to the integral form of the quantum-kinetic equation and estimates the electron energy distribution using statistical averages over long evolution times. The numerical tests were performed for GaAs material parameters. The numerical results for the electron energy distribution function in the case of a non-linear electron quantum transport is compared with the obtained results in the linear case.Supported by Center of Excellence BIS-21 grant ICA1-2000-70016 and by the NSF of Bulgaria under Grants # I 811/98 and # MM 902/99

Development of Hybrid Deterministic-Statistical Models for Irradiation Influenced Microstructural Evolution.

Ion irradiation holds promise as a cost-effective approach to developing structured nano--porous and nano--fiberous semiconductors. Irradiation of certain semiconductors leads to the development of these structures, with exception of the much desired silicon. Hybrid deterministic-statistical models were developed to better understand the dominating mechanisms during structuring. This dissertation focuses on the application of hybrid models to two different radiation damage behavior: (1) precipitate evolution in a binary two-phase system and (2) void nucleation induced nano--porous structuring. Phenomenological equations defining the deterministic behavior were formulated by considering the expected kinetic and phenomenological behavior. The statistical component of the models is based on the Potts Monte Carlo (PMC) method. It has been demonstrated that hybrid models efficiently simulate microstructural evolution, while retaining the correct kinetics and physics. The main achievement was the development of computational methods to simulate radiation induced microstructural evolution and highlight which processes and materials properties could be essential for nano--structuring. Radiation influenced precipitate evolution was modeled by coupling a set of non-linear partial differential equations to the PMC model. The simulations considered the effects of dose rate and interfacial energy. Precipitate growth becomes retarded with increased damage due to diffusion of the radiation defects countering capillarity driven precipitate growth. The effects of grain boundaries (GB) as sinks was studied by simulating precipitate growth in an irradiated bi-crystalline matrix. Qualitative comparison to experimental results suggest that precipitate coverage of the GB is due to kinetic considerations and increased interfacial energy effects. Void nucleation induced nano--porous/fiberous structuring was modeled by coupling rate theory equations, kinetic Monte Carlo swelling algorithm and the PMC model. Point defect (PD) diffusivities were parameterized to study their influence on nano--structuring. The model showed that PD kinetic considerations are able to describe the formation of nano--porous structures. As defects diffuse faster, void nucleation becomes limited due to the fast removal of the defects. It was shown that as the diffusivities' ratio diverges from unity, the microstructures become statistically similar and uniform. Consequently, the computational results suggest that nano--pore structuring require interstitials that are much faster than the slow diffusing vacancies, which accumulate and cluster into voids.PhDNuclear Engineering and Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111424/1/efrainhr_1.pd

Optical and Transport Properties of Disordered Materials by Computer Simulation

This work is a summary of a study on optical and transport properties of disordered materials. Since disorder plays an important role in various optoelectronic phenomena, a suitable theoretical description of clutter effects is crucial for the development of electronic devices such as transistors, memory, light emitting diodes, and solar cells. This work addresses some of the problems associated with the recombination of excitons in disordered materials. Furthermore, the mechanism of release of carriers from traps and the concept of effective temperature for hopping transport, with special emphasis on the Kinetic Monte Carlo Method (KMC), are considered

Photocatalytic Degradation of Phenolic Compounds in Water: Irradiation and Kinetic Modeling

Scaling up a photoreactor requires both knowledge of optical properties of the slurry medium and an established kinetic model. Measuring the scattering and absorption coefficients of particles suspended in water involves the use of specialized optical equipment, as well as the partial solution of the radiative transfer equation (RTE). In addition, modeling of the radiation field in photoreactors with complicated geometries offers special challenges. On the other hand, most of the kinetic models (KM) for phenol photodegradation reported in the literature were obtained for a single organic chemical species only. In fact, neglecting all the intermediate species generated during the photoreaction, is a common oversimplification that limits the KM application. As a result, once the radiation and kinetic models fully established, energy efficiencies can be obtained. In this PhD dissertation, the photocatalytic degradation of phenol over four different TiO2 catalysts is studied. It is proven that phenol yields hydroquinone, catechol, benzoquinone, and acetic and formic acids as main intermediate species. The radiation field inside photocatalytic reactors is predicted by solving the RTE. From the solution of the RTE, the local volumetric rate of energy absorption (LVREA) is also calculated. The radiation field inside an annular photoreactor is simulated using the Monte Carlo (MC) method for different TiO2 suspensions in water. All simulations are performed by using both the spectral distribution, and the wavelength-averaged scattering and absorption coefficients. The Henyey-Greenstein phase function is adopted to represent forward, isotropic and backward scattering modes. It is assumed that the UV lamp reflects the back-scattered photons by the slurried medium. It is proven, photo-absorption rates, using MC simulations and spectral distribution of the optical coefficients, agree closely with experimental observations from a macroscopic balance (MB). It is also found that the scattering mode of the probability density function, is not a critical factor for a consistent representation of the radiation field. When solving the RTE, two optical parameters are needed: (1) the absorption and scattering coefficients, and (2) the phase function. In this research work, the MC method, along with an optimization technique, is shown to be effective in predicting the wavelength-averaged absorption and scattering coefficients for different TiO2 powders. To accomplish this, the LVREA and the transmitted radiation (Pt) in the photoreactor are determined by using a MB. The optimized coefficients are calculated ensuring that they comply with a number of physical constrains, falling in between bounds established via independent criteria. The optimization technique is demonstrated by finding the absorption and scattering coefficients for different semiconductors that best fit the experimental values from the MB. The objective function in this optimization is given by the least-squared error for the LVREA. A photocatalyst is synthesized and its optical properties determined by the proposed method. This approach is a general and promising one; not being restricted to reactors of concentric geometry, specific semiconductors and/or particular photocatalytic reactor unit scale. Based on the proposed intermediate reactions, a phenomenological based unified kinetic model is proposed for describing the obtained experimental observations in phenol photodegradation. This Langmuir-Hinshelwood (L-H) kinetic model is based on a “Series-Parallel” reaction network. This reaction model is found to be applicable to the various TiO2 photocatalyst in the present study. This unified kinetic network is based on the identified and quantified chemical species in the photoconversion of phenol and its intermediates. In order to minimize the number of optimized parameters, the adsorption constants of the different intermediate species on the different catalysts configuration, are obtained experimentally. It is shown that the unified kinetic model requires a number of significant assumptions to be effective; avoiding overparametization. As a result, the unified kinetic model is adapted for each specific TiO2 photocatalyst under study.These different models adequately describe the experimental results. It is shown that this approach results in good and objective parameter estimates in the L-H kinetic model, which is typically applied to photocatalytic reactors. Finally, two efficiency factors, the quantum yield and the photochemical and thermodynamic efficiency factor, are obtained, in this PhD dissertation. These factors are based on the kinetic model proposed and the radiation being absorbed by the photocatalyst particles. The efficiency calculations consider stoichiometric relationships involving observable chemical species and OH· groups. The obtained efficiency factors point toward a high degree of photon utilization and, as a result, the value of photocatalysis and Photo-CREC-Water reactors for the conversion of organic pollutants in water is confirmed

Ab initio atomistic thermodynamics and statistical mechanics of surface properties and functions

Previous and present "academic" research aiming at atomic scale understanding is mainly concerned with the study of individual molecular processes possibly underlying materials science applications. Appealing properties of an individual process are then frequently discussed in terms of their direct importance for the envisioned material function, or reciprocally, the function of materials is somehow believed to be understandable by essentially one prominent elementary process only. What is often overlooked in this approach is that in macroscopic systems of technological relevance typically a large number of distinct atomic scale processes take place. Which of them are decisive for observable system properties and functions is then not only determined by the detailed individual properties of each process alone, but in many, if not most cases also the interplay of all processes, i.e. how they act together, plays a crucial role. For a "predictive materials science modeling with microscopic understanding", a description that treats the statistical interplay of a large number of microscopically well-described elementary processes must therefore be applied. Modern electronic structure theory methods such as DFT have become a standard tool for the accurate description of individual molecular processes. Here, we discuss the present status of emerging methodologies which attempt to achieve a (hopefully seamless) match of DFT with concepts from statistical mechanics or thermodynamics, in order to also address the interplay of the various molecular processes. The new quality of, and the novel insights that can be gained by, such techniques is illustrated by how they allow the description of crystal surfaces in contact with realistic gas-phase environments.Comment: 24 pages including 17 figures, related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Transport phenomena in quantum wells and wires in presence of disorder and interactions

Present-day electronics employ circuits of smaller and smaller dimensions, and today the length scales are so small that the laws of physics which rule micro-cosmos, quantum mechanics, become directly important. This thesis reports on theoretical work on electron transport in different nanostructures. We have studied semiconductor quantum wells, layered materials where each layer can be only a few atomic layers thick, and transport in thin atomic wires. The layered materials have been studied semi-classically by means the so-called Bolzmann equation and Monte-Carlo techniques. The works on layered materials focused on effects of resonant scattering mechanisms on the electron transport and the feasibility to use semiconductor super- lattices for generating terahertz (THz)radiation. The quantum wires were modeled by 1D Hubbard chains connected to semi-infinite leads and were treated fully quantum-mechanically via the time-dependent density- functional theory (TDDFT). Our TDDFT treatment appears to be able to capture complex features due to competition between correlation and disorder. The merits of the coherent-potential approximation are also analyzed for contacted chains. In total, four papers are included in the thesis. In paper I, Monte Carlo simulations of transport in various two- dimensional semiconductor hetero-structures, in particular in cases where accurately calculated scattering probabilities are needed. In paper II, we present result for electron transport in į-doped Si/SiGe quantum wells at different temperatures and field strengths. In paper III, we develop a Monte-Carlo technique to handle electron transport between quantum-well layers when an electric field is applied along the growth direction. We use this method to study scattering- assisted transport under strong fields in the Wannier-Stark regime. In paper IV, finally, the static and dynamical behavior of 1D Hubbard chains are investigated. The focus is on how the interplay of interactions and disorder affects the localization of fermions in Hubbard chains contacted to semi-infinite leads

Auxiliary master equation for nonequilibrium dual-fermion approach

We introduce auxiliary quantum master equation - dual fermion approach (QME-DF) and argue that it presents a convenient way to describe steady-states of correlated impurity systems. The combined scheme yields an expansion around a reference much closer to the true nonequilibrium state than in the original dual fermion formulation. In steady-state situations, the scheme is numerically cheaper and allows to avoid long time propagation of previous considerations. Anderson impurity is used as a test model. The QME-DF simulations are compared with numerically exact tdDMRG results.Comment: 8 pages, 4 figure