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International Journal of Quantum Chemistry

Some theoretical problems in chemistry and physics

Erkki Brändas

Published Jan 1, 2006• 7 citations
Publisher

Abstract

Abstract Recently the need for incorporating so‐called Jordan blocks in the theoretical formulation of dynamical processes in Nature has been confronted and challenged. In addition, quantum mechanics has evolved from the very theoretical to the highly technological prompting the establishment of the new field of quantum technology. Initial studies in an extended time‐irreversible picture seem to indicate a possible map of degenerate Jordan forms onto the description of complex natural phenomena. Jordan blocks appear logically in the generalized dynamical picture. A compelling interpretation is microscopic self‐organization (MSO). Not only have the manifestation of quantum thermal correlations, and the emergence of generic time scales been established, but the present viewpoint also appears to throw new light on the age‐old problem of quantum mechanics versus relativity. A simple resonance model is presented that bears out the problems and possibilities. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

DOI
10.1002/qua.21110

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Abstract Recently the need for incorporating so‐called Jordan blocks in the theoretical formulation of dynamical processes in Nature has been confronted and challenged. In addition, quantum mechanics has evolved from the very theoretical to the highly technological prompting the establishment of the new field of quantum technology. Initial studies in an extended time‐irreversible picture seem to indicate a possible map of degenerate Jordan forms onto the description of complex natural phenomena. Jordan blocks appear logically in the generalized dynamical picture. A compelling interpretation is microscopic self‐organization (MSO). Not only have the manifestation of quantum thermal correlations, and the emergence of generic time scales been established, but the present viewpoint also appears to throw new light on the age‐old problem of quantum mechanics versus relativity. A simple resonance model is presented that bears out the problems and possibilities. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006
The old dilemma of quantum mechanics versus the theory of relativity is reconsidered via a first principles relativistically invariant theory. By analytic extension of quantum mechanics into the complex plane one may (i) include dynamical features such as time‐ and length‐scales and (ii) examine the possibility and flexibility of so‐called general Jordan block formations. The present viewpoint asks for a new perspective on the age‐old problem of quantum mechanics versus the theory of relativity. To bring these ideas together, we will establish the relation with the Klein‐Gordon‐Dirac relativistic theory and confirm some dynamical features of both the special and the general relativity theory.
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Abstract Quantum mechanical and classical aspects are of equal importance in chemistry, and theoretical chemistry must be able to deal with this situation. Classical quantities with which a chemist has to deal include, for example, the temperature and the chemical potential of a substance, and chirality, knot‐type and tertiary structures of molecules. Classical concepts of this type are no more consequences of traditional quantum chemistry than is the theory of complex chemical processes (for example adsorption, heterogeneous catalysis) and macroscopic systems. Algebraic quantum mechanics affords a general framework for the discussion of classical quantities and large systems. There are other independent approaches for the theoretical treatment of chemical problems; these can be summarized by using the keywords “fractals”, “chaotic motion”, “quasicrystals” and “knot theory”. The relationships between these four research topics and their connection with algebraic quantum mechanics, as well as their importance for theoretical chemistry, were discussed at a NATO Workshop in 1987 (see Ref. [1]). In an extended theoretical chemistry, the notion of “molecules” will not play a role as central as it does in quantum chemistry. In the theory of large systems in particular, the introduction of complementary approaches appears to be appropriate; the term “molecule” as used by the chemist does not appear either in the description of disordered systems by means of fractals or in the thermodynamic limit of algebraic statistical mechanics.
Abstract A challenging problem facing physicists is the compatibility of irreversibility, as expressed by the second law of thermodynamics, with ordinary quantum mechanics. We present a solution through an extension of the latter. The presence of self‐energy processes (already found in quantum electrodynamics) is fully exploited to get an extension of a reversible formalism. They enable the widening of the dynamics by the introduction of specific auxiliary variables, leading to the recognition of such processes. A projection technique modeled on the one introduced long ago by the Brussels group defines a subdynamics that is shown to contain entirely the starting formulation (it corresponds to a restricted class of initial conditions, namely, the reversible one). A new kinetic description is obtained in which, for example, collision processes for privileged components arise from the original interaction. A very simple model and its generalizations are considered. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
It is indicated that quantum mechanics contains provision for treatment of “organization” and dynamical structure which is more appropriate than that normally employed. This description makes use of observables, to superselection operators, which are stable to fluctuations and perturbations of the system. It is suggested that they may account for structure in a biological system, produced by the “pumping” of collective modes by the environment. It is noted that certain forms of structure may be incompatible, within the same system.
Current experiments on semiconductor devices using femtosecond lasers provide new theoretical challenges for the description of charge carrier dynamics. Among the new features of such experiments are states driven very far from equilibrium and probes on time scales short compared to scattering and other characteristic material relaxation times. Standard many-body methods must be modified and extended to accommodate these features. We propose that the quantum hierarchy for reduced density operators is an ideal formulation of such initial value problems and describe how the dominant effects of exchange and charge correlations can be accounted for in a simple and physically transparent closure of the hierarchy of equations. The transformations, approximations, and interpretation can be accomplished independent of any particular matrix representation. Decomposition into kinetic equations for band occupation densities and polarization densities follows in a straightforward way after the many-body problem has been brought under control. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 929–940, 1997