Two‐Hilbert space formulations of the quantum statistical mechanics of reactive fluids: Dimer formation and decay

Thumbnail Image
Date
1986
Authors
Evans, James
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Authors
Person
Evans, James
Professor
Research Projects
Organizational Units
Organizational Unit
Ames National Laboratory

Ames National Laboratory is a government-owned, contractor-operated national laboratory of the U.S. Department of Energy (DOE), operated by and located on the campus of Iowa State University in Ames, Iowa.

For more than 70 years, the Ames National Laboratory has successfully partnered with Iowa State University, and is unique among the 17 DOE laboratories in that it is physically located on the campus of a major research university. Many of the scientists and administrators at the Laboratory also hold faculty positions at the University and the Laboratory has access to both undergraduate and graduate student talent.

Organizational Unit
Physics and Astronomy
Physics and astronomy are basic natural sciences which attempt to describe and provide an understanding of both our world and our universe. Physics serves as the underpinning of many different disciplines including the other natural sciences and technological areas.
Organizational Unit
Mathematics
Welcome to the exciting world of mathematics at Iowa State University. From cracking codes to modeling the spread of diseases, our program offers something for everyone. With a wide range of courses and research opportunities, you will have the chance to delve deep into the world of mathematics and discover your own unique talents and interests. Whether you dream of working for a top tech company, teaching at a prestigious university, or pursuing cutting-edge research, join us and discover the limitless potential of mathematics at Iowa State University!
Journal Issue
Is Version Of
Versions
Series
Department
Ames National LaboratoryPhysics and AstronomyMathematics
Abstract

A two‐Hilbert space formalism is first used to develop a general class of representations for the quantum mechanics of N‐particle reactive systems. Here the N‐particle Hilbert space HN is supplemented by a larger arrangement channel space CN of vectors with Hilbert space valued components for each N‐particle clustering, and an injection mapping of HN vectors into ‘‘physical’’ CNvectors. Such representations, for which components of the latter vectors carry an appropriate physical clustering interpretation, provide a rigorous and flexible basis for describing the statistical mechanics of reactive fluids, where atoms and molecules are treated on an equal footing (the molecular picture). Corresponding equilibrium multispecies fugacity or virial expansions follow immediately. Here we focus on analysis of the (previously derived) arrangement channel BBGKY hierarchy for a system where recombination and dissociation,as well as exchange reactions, occur. This formulation (coupled with a corresponding scattering theory) automatically suggests a reactive Boltzmannansatz which incorporates (standard) noninteracting asymptotic dynamics onlyfor two‐molecule nonreactive and reactive exchange collisions. In contrast, e.g., with three molecule recombination, two‐molecule dynamics for all three pairs is included (as required for a description of recombination via gradual stabilization of metastables). Finally we compare the resulting reduced form of appropriate channel space hierarchy equations, for a process involving dimer formation and decay, with the corresponding kinetic equations of Lowry and Snider.

Comments

This article is published as Evans, J. W. "Two‐Hilbert space formulations of the quantum statistical mechanics of reactive fluids: Dimer formation and decay." The Journal of chemical physics 85, no. 10 (1986): 5991-6003, doi:10.1063/1.451513. Posted with permission.

Description
Keywords
Citation
DOI
Copyright
Wed Jan 01 00:00:00 UTC 1986
Collections