4,255 research outputs found

    Semiclassical theory of vibrational energy relaxation

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    A theory of vibrational energy relaxation based on a semiclassical treatment of the quantum master equation is presented. Using new results on the semiclassical expansion of dipole matrix elements, we show that in the classical limit the master equation reduces to the Zwanzig energy diffusion equation. The leading quantum corrections are determined and discussed for the harmonic and Morse potentials.Comment: See also at http://vesta.physik.uni-freiburg.de/www/dqs/sfb.htm

    Supermembranes and M(atrix) Theory

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    In these lectures, we review the D=11 supermembrane and supersymmetric matrix models at an introductory level. We also discuss some more recent developments in connection with non-perturbative string theory.Comment: 46 pages, 4 figures, Lectures given by H. Nicolai at the Trieste Spring School on Non-Perturbative Aspects of String Theory and Supersymmetric Gauge Theories, 23 - 31 March 199

    Has the Chinese Housing Boom Truly Impacted the U.S. Stock Market? Investigating the Potential Relationship Between China\u27s Housing Price Dynamics and the U.S. Stock Market

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    In this paper, we review the effect that the boom of China\u27s housing prices has had on the U.S. stock market and the potential connection between the two markets. Looking at it more in-depth, the U.S. stock market focus is on the S&P 500 and the eleven sectors of the stock market (Industrial, Healthcare, Real Estate, Utilities, Materials, Industrials, Information Technology, Financials, Consumer Discretionary, Consumer Staples, and Communication Services) while the housing prices are dictated by the residential housing price index within China. Given the relatively recent disaster in September 2021 regarding the Evergrande Group and their potential for failure, the connection between the two markets has come more into focus now than in recent history. The Evergrande Group crisis combined with the housing boom has potentially created a bubble primed to burst and has set the stage for a collapse. Using data from April 2005 to October 2021 and running OLS regressions, I conclude that there should be a significant linear positive relationship between the housing prices of China and the U.S. stock market. If this turns out to be a positive relationship, investors should be wary of the potential effects the housing market would have on their portfolio if it were to continue to boom or abruptly burst

    Techniques for treating non-Gaussian random processes

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    A brief survey of constrained mechanics and variational problems in terms of differential forms

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    There has been considerable interest recently in constrained mechanics and variational problems. This is in part due to applied interests (such as 'non-holonomic mechanics in robotics') and in other part due to the fact that several schools of 'pure' mathematics have found that this classical subject is of importance for what they are trying to do. I have made various attempts at developing these subjects since my Lincoln lab days of the late 1950's. In this Chapter, I will sketch a Unified point of view, using Cartan's approach with differential forms. This has the advantage from the C-O-R viewpoint being developed in this Volume that the extension from 'smooth' to 'generalized' data is very systematic and algebraic. (I will only deal with the 'smooth' point of view in this Chapter; I will develop the 'generalized function' material at a later point.) The material presented briefly here about Variational Calculus and Constrained Mechanics can be found in more detail in my books, 'Differential Geometry and the Calculus of Variations', 'Lie Algebras and Quantum Mechanics', and 'Geometry, Physics and Systems'
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