scholarly journals ON THE "UNIVERSAL" N=2 SUPERSYMMETRY OF CLASSICAL MECHANICS

2001 ◽  
Vol 16 (15) ◽  
pp. 2709-2746 ◽  
Author(s):  
E. DEOTTO ◽  
E. GOZZI
Keyword(s):  
Classical Mechanics ◽  
Functional Approach ◽  
Constant Energy ◽  
Geometrical Features ◽  
Energy Surfaces

In this paper we continue the study of the geometrical features of a functional approach to classical mechanics proposed some time ago. In particular, we try to shed some light on a N = 2 "universal" supersymmetry which seems to have an interesting interplay with the concept of ergodicity of the system. To study the geometry better we make this susy local and clarify pedagogically several issues present in the literature. Secondly, in order to prepare the ground for a better understanding of its relation to ergodicity, we study the system on constant energy surfaces. We find that the procedure of constraining the system on these surfaces injects in it some local Grassmannian invariances and reduces the N = 2 global susy to an N = 1.

Chemical Reactions In Condensed Phases

2006 ◽  
Author(s):  
Abraham Nitzan
Keyword(s):  
Chemical Reactions ◽  
Condensed Phase ◽  
Chemical Change ◽  
Classical Mechanics ◽  
Chemical System ◽  
Condensed Phases ◽  
Molecular Configuration ◽  
Middle Stage ◽  
Condensed Phase Reactions ◽  
Energy Surfaces

Understanding chemical reactions in condensed phases is essentially the understanding of solvent effects on chemical processes. Such effects appear in many ways. Some stem from equilibrium properties, for example, solvation energies and free energy surfaces. Others result from dynamical phenomena: solvent effect on diffusion of reactants toward each other, dynamical cage effects, solvent-induced energy accumulation and relaxation, and suppression of dynamical change in molecular configuration by solvent induced friction. In attempting to sort out these different effects it is useful to note that a chemical reaction proceeds by two principal dynamical processes that appear in three stages. In the first and last stages the reactants are brought together and products are separated from each other. In the middle stage the assembled chemical system undergoes the structural/chemical change. In a condensed phase the first and last stages involve diffusion, sometimes (e.g. when the species involved are charged) in a force field. The middle stage often involves the crossing of a potential barrier. When the barrier is high the latter process is rate-determining. In unimolecular reactions the species that undergoes the chemical change is already assembled and only the barrier crossing process is relevant. On the other hand, in bi-molecular reactions with low barrier (of order kBT or less), the rate may be dominated by the diffusion process that brings the reactants together. It is therefore meaningful to discuss these two ingredients of chemical rate processes separately. Most of the discussion in this chapter is based on a classical mechanics description of chemical reactions. Such classical pictures are relevant to many condensed phase reactions at and above room temperature and, as we shall see, can be generalized when needed to take into account the discrete nature of molecular states. In some situations quantum effects dominate and need to be treated explicitly. This is the case, for example, when tunneling is a rate determining process. Another important class is nonadiabatic reactions, where the rate determining process is hopping (curve crossing) between two electronic states. Such reactions are discussed in Chapter 16.

Calculation of Constant-Energy Surfaces for Copper by the Korringa-Kohn-Rostoker Method

1967 ◽  
Vol 161 (3) ◽  
pp. 656-664 ◽  
Author(s):  
J. S. Faulkner ◽  
Harold L. Davis ◽  
H. W. Joy
Keyword(s):  
Constant Energy ◽  
Energy Surfaces

STATES OF A FEW HOLES IN A t-J MODEL

1991 ◽  
Vol 05 (09) ◽  
pp. 1401-1417 ◽  
Author(s):  
DANIEL C. MATTIS ◽  
HUA CHEN
Keyword(s):  
Ground State ◽  
Green Functions ◽  
Constant Energy ◽  
One Dimensional ◽  
Energy Surfaces

The interaction of a few holes with the magnons and with each other in the t-J model, is formulated in k-space. At small J/t, each hole is accompanied by a cloud of <n> ≈ 1.4(t/J)1/3 magnons (spin reversals), on average. We obtain, and in some cases, solve formal expressions for the ground state eigenfunctions, eigenvalues, and Green functions. The constant energy surfaces are quasi-one-dimensional.

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