In Situ Studies on Reaction Mechanisms in Atomic Layer Deposition

During the past decade, atomic layer deposition (ALD) has become an important thin-film deposition method in microelectronics industry, and it has also gained a lot of interest in many other areas, such as nanotechnology. The success of ALD is built on proper surface reactions. In this paper, in situ reaction mechanism studies on ALD processes are reviewed with the aim of building a general understanding on similarities and differences exhibited by various processes and process groups. Also, levels of understanding reaction mechanisms in ALD are discussed. The main methods used to study ALD chemistry in situ under typical process conditions are quadrupole mass spectrometry (QMS), quartz crystal microbalance (QCM), and infrared (IR) spectrometry. These are presented in detail in the review. Various other optical methods, ellipsometry in particular, have been used to study ALD processes too, but they provide little information about the reaction mechanisms. Competent in situ investigations solve the ALD reaction mechanism as balanced equations for the ALD half-reactions. The majority of ALD processes are exploiting ligand exchange reactions, where the ligands of the metal precursor are eliminated by bonding to the Lewis acids of the nonmetal precursors, most commonly hydrogen. These volatile byproducts are usually released during both precursor pulses, and determining their relative amounts is the important task in reaction mechanism studies of such processes. These processes are mechanistically fairly well understood, though some of these also display side-reactions to the ligand exchange reactions. There are also whole groups of processes that are using chemistry almost entirely different from the ligand exchange reactions. The most important such processes involve combustion chemistry, with oxygen, oxygen plasma, or ozone as a precursor or co-reactant. The mechanisms of these processes are complicated and less understood compared with the mechanisms of the ligand exchange reaction processes.     

A physical organic mechanistic approach to understanding the complex reaction network of hemostasis (blood clotting)

This review focuses on how the mechanistic approach of physical organic chemistry can be used to elucidate the mechanisms behind complex biochemical networks. The dynamics of biochemical reaction networks is difficult to describe by considering their individual reactions, just as the dynamics of organic reactions is difficult to describe by considering individual electrons and atomic nuclei. Physical organic chemists have developed a useful set of tools to predict the outcome of organic reactions by separating the interacting molecules into modules (functional groups), and defining general rules for how these modules interact (mechanisms). This review shows how these tools of physical organic chemistry may be used to describe reaction networks. In addition, it describes the application of these tools to develop a mechanistic understanding of the dynamics of the complex network of hemostasis, which regulates blood clotting. Copyright © 2007 John Wiley & Sons, Ltd.     

Testing the validity of the Ehrenfest theorem beyond simple static systems: Caldirola–Kanai oscillator driven by a time-dependent force

The relationship between quantum mechanics and classical mechanics is investigated by taking a Gaussian-type wave packet as a solution of the Schr o¨dinger equation for the Caldirola–Kanai oscillator driven by a sinusoidal force. For this time-dependent system, quantum properties are studied by using the invariant theory of Lewis and Riesenfeld. In particular,we analyze time behaviors of quantum expectation values of position and momentum variables and compare them to those of the counterpart classical ones. Based on this, we check whether the Ehrenfest theorem which was originally developed in static quantum systems can be extended to such time-varying systems without problems.     

Statistics of Local Value in Quantum Mechanics

Given a quantum mechanical observable and a state, one can construct a classical observable, that is, a real function on the configuration space, such that it is the optimal estimate of the quantum observable, in the sense of minimum variance. This optimal estimate turns out to be the quantum mechanical local value, which arises from several contexts such as de Broglie–Bohm's casual approach to quantum mechanics, instantaneous frequency in time–frequency analysis, Nelson's quantum fluctuations formalism, and phase-space approach to quantum mechanics. Accordingly, any observable can be decomposed into a local value part and a quantum fluctuation part, which are independent, both geometrically and statistically. Furthermore, the current density in quantum mechanics, the osmotic velocity in stochastic mechanics, and the Fisher information in classical statistical inference, arise naturally in connection with local value. In particular, Heisenberg uncertainty principle can be quantified more precisely by virtue of local value.     

Entropy and temperature of a static granular assembly: an ab initio approach

We construct a statistical framework for static assemblies of deformable grains which parallels that of equilibrium statistical mechanics but with a conservation principle based on the mechanical stress tensor. We define a state function that has all the attributes of entropy. In particular, maximizing this function leads to a well-defined granular temperature and the equivalent of the Boltzman distribution for ensembles of grain packings. Predictions of the ensemble are verified against simulated packings of frictionless, deformable disks.     

Quantum Mechanics and Stochastic Mechanics for Compatible Observables at Different Times

Bohm mechanics and Nelson stochastic mechanics are confronted with quantum mechanics in the presence of noninteracting subsystems. In both cases, it is shown that correlations at different times of compatible position observables on stationary states agree with quantum mechanics only in the case of product wave functions. By appropriate Bell-like inequalities it is shown that no classical theory, in particular no stochastic process, can reproduce the quantum mechanical correlations of position variables of noninteracting systems at different times.     

Micro- and nano-mechanics in China: A brief review of recent progress and perspectives

The past three decades have witnessed the explosion of nanoscience and technology, where notable research efforts have been made in synthesizing nanomaterials and controlling nanostructures of bulk materials. The uncovered mechanical behaviors of structures and materials with reduced sizes and dimensions pose open questions to the community of mechanicians, which expand the framework of continuum mechanics by advancing the theory, as well as modeling and experimental tools. Researchers in China have been actively involved into this exciting area, making remarkable contributions to the understanding of nanoscale mechanical processes, the development of multi-scale, multi-field modeling and experimental techniques to resolve the processing-microstructures-properties relationship of materials, and the interdisciplinary studies that broaden the subjects of mechanics. This article reviews selected progress made by this community, with the aim to clarify the key concepts, methods and applications of micro- and nano-mechanics, and to outline the perspectives in this fast-evolving field.     

Foundations of quantum mechanics: The Langevin equations for QM

Stochastic derivations of the Schrödinger equation are always developed on very general and abstract grounds. Thus, one is never enlightened which specific stochastic process corresponds to some particular quantum mechanical system, that is, given the physical system—expressed by the potential function, which fluctuation structure one should impose on a Langevin equation in order to arrive at results identical to those comming from the solutions of the Schrödinger equation. We show, from first principles, how to write the Langevin stochastic equations for any particular quantum system. We also show the relation between these Langevin equations and those proposed by Bohm in 1952. We present numerical simulations of the Langevin equations for some quantum mechanical problems and compare them with the usual analytic solutions to show the adequacy of our approach. The model also allows us to address important topics on the interpretation of quantum mechanics.     

Parallelization strategies for an implicit Newton-based reactive flow solver

The solution of reactive flows using fully implicit methods on distributed memory machines is investigated in detail. Three different parallel implementations of Newton's method are described and tested on the solution of two-dimensional laminar axisymmetric coflow diffusion flames. Each implementation has different computational requirements, both in the amount of communication among the processes and in the computational overhead due to the calculation of physical quantities at the interfaces between subdomains. An effective trade-off is established between communications and calculations so that the most communication-intensive implementation results in computational speedup only if the network is sufficiently fast.

Benchmark results are presented for a variety of chemical mechanisms, grid decomposition techniques, and hardware. Parallelization efficiencies of about 80% and speedups of 20–100 are reported for most test cases. The method developed here is well suited for complex chemistry problems with very large mechanisms; in particular, the numerical solution of a laminar axisymmetric JP-8/air coflow diffusion flame with a 222-species mechanism is made possible using this approach.     

The underlying Brownian motion of nonrelativistic quantum mechanics

Nonrelativistic quantum mechanics can be derived from real Markov diffusion processes by extending the concept of probability measure to the complex domain. This appears as the only natural way of introducing formally classical probabilistic concepts into quantum mechanics. To every quantum state there is a corresponding complex Fokker-Planck equation. The particle drift is conditioned by an auxiliary equation which is obtained through stochastic energy conservation; the logarithmic transform of this equation is the Schrödinger equation. To every quantum mechanical operator there is a stochastic process; the replacement of operators by processes leads to all the well-known results of quantum mechanics, using stochastic calculus instead of formal quantum rules. Comparison is made with the classical stochastic approaches and the Feynman path integral formulation.     

Foundations of the quantum statistics of systems in equilibrium: A measuretheoretic approach

The fundamental equations of equilibrium quantum statistical mechanics are derived in the context of a measure-theoretic approach to the quantum mechanical ergodic problem. The method employed is an extension, to quantum mechanical systems, of the techniques developed by R. M. Lewis for establishing the foundations of classical statistical mechanics. The existence of a complete set of commuting observables is assumed, but no reference is made a priori to probability or statistical ensembles. Expressions for infinite-time averages in the microcanonical, canonical, and grand canonical ensembles are developed which reduce to conventional quantum statistical mechanics for systems in equilibrium when the total energy is the only conserved quantity. No attempt is made to extend the formalism at this time to deal with the difficult problem of the approach to equilibrium.     

Supersymmetry in quantum mechanics

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable. In this lecture I review the theoretical formulation of supersymmetric quantum mechanics and discuss many of its applications. I show that the well-known exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials and shape invariance. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics is discussed and multi-soliton solutions of the KdV equation are constructed. Further, it is pointed out that the connection between the solutions of the Dirac equation and the Schrödinger equation is exactly same as between the solutions of the MKdV and the KdV equations.     

Quantum Transfer Energy and Nonlocal Correlation in a Dimer with Time-Dependent Coupling Effect

The presence of coherence phenomenon due to the interference of probability amplitude terms, is one of the most important features of quantum mechanics theory. Recent experiments show the presence of quantum processes whose coherence provided over suddenly large interval-time. In particular, photosynthetic mechanisms in light-harvesting complexes provide oscillatory behaviors in quantum mechanics due to quantum coherence. In this work, we investigate the coherent quantum transfer energy for a single-excitation and nonlocal correlation in a dimer system modelled by a two-level atom system with and without time-dependent coupling effect. We analyze and explore the required conditions that are feasible with real experimental realization for optimal transfer of quantum energy and generation of nonlocal quantum correlation. We show that the enhancement of the probability for a single-excitation transfer energy is greatly benefits from the combination of the energy detuning and time-dependent coupling effect. We investigate the presence of quantum correlations in the dimer using the entanglement of formation. We also find that the entanglement between the donor and acceptor is very sensitive to the physical parameters and it can be generated during the coherent energy transfer. On the other hand, we study the dynamical behavior of the quantum variance when performing a measurement on an observable of the density matrix operator. Finally, an interesting relationship between the transfer probability, entanglement and quantum variance is explored during the time evolution in terms of the physical parameters.     

Chemical vapor deposition of diamond

In the recent decade a multitude of diamond thin film production methods has been developed, generally based on chemical vapor deposition processes from thermally or plasma activated gas phases. Diagnostic studies, growth experiments and numerical kinetic investigations have in recent years lead to an improved understanding of the prerequisites of continuous diamond growth and of the chemical processes involved. While the mechanism of carbon incorporation into the diamond surface is not yet known completely, the gas-phase species which are essential in a diamond-growth atmosphere can be narrowed to a small number, whose role in the gas-phase chemistry is quite well known.     

Poincaré canonical momenta and nambu mechanics

We show that if certain Poincaré-like integrals are conserved, then to each configuration coordinate of a system an entity can be associated that is an acceptable generalization of the notion of canonical momentum: In the particular case of standard mechanics, the canonical momenta are retrieved. Under certain general restrictions, the Poincaré momenta make sense for either mechanical or general systems for which we do not have (or are not aware of) entities (like the Lagrangian) that are generally used to define the momentum. The Poincaré momentum may also make sense for systems whose characteristics are difficult, or impossible, to reconcile with the notion of the usual canonical momentum. It is also relevant for certain cases where a Lagrangian exists, but it leads to a mixture of physical and unphysical entities. In particular, we show that while physical canonical momenta do not generally exist in the new Nambu mechanics (because of the dimensionality of state vector space), the Poincaré momenta exist, they are physical, and have the properties we could have expected for the mechanics.     

Coexistent effects in quantum mechanics

Effects are defined in this paper as observable changes in the state of a macrosystem, which are caused by interaction with a microsystem. These effects are the starting point of Ludwig's axiomatic foundation of quantum theory. In this theory the concept of commensurability is developed by considering effects which can be caused together, by one single microsystem. Such effects are called coexistent. It is shown that in ordinary quantum mechanics the formal definition of coexistence and the corresponding postulates given by Ludwig are consistent with the dynamics of interaction processes leading to effects.Part of a work supported by the Deutsche Forschungsgemeinschaft.     

Nonlinearity of Quantum Mechanics and Solution of the Problem of Wave Function Collapse

The problem of the wave function collapse(a problem of measurement in quantum mechanics) is considered.It is shown that it can be solved based on quantum mechanics and does not require any additional assumptions or new theories. The particle creation and annihilation processes, which are described based on quantum field theory, play a key role in the measurement processes. Superposition principle is not valid for the system of equations of quantum field theory for particles and fields, because this system is a non-linear. As a result of the creation(annihilation) of a particle,an additional uncertainty arises, which "smears" the interference pattern. The imposition of such a large number of uncertainties in the repetitive measurements leads to the classical behavior of particles. The decoherence theory also implies the creation and annihilation of particles, and this processes are the consequence of non-linearity of quantum mechanics. In this case, the term "collapse of the wave function" becomes a consequence of the other statements of quantum mechanics instead of a separate postulate of quantum mechanics.