The Spectrum of a Hypoelliptic Operator with a Potential Perturbation

1975 ◽  
Vol 7 (1) ◽  
pp. 77-80
Author(s):  
M. Thompson
Keyword(s):  
Hypoelliptic Operator ◽  
Potential Perturbation

Spatial Perception During Joint Action: The "Other" as Potential Perturbation

2011 ◽  
Author(s):  
Andrew Kenning ◽  
J. Scott Jordan ◽  
Cooper Cutting ◽  
Jim Clinton ◽  
Justin Durtschi
Keyword(s):  
Joint Action ◽  
Spatial Perception ◽  
The Other ◽  
Potential Perturbation

Non-Equilibrium Green’s Functions: Variational Relations and Approximations for Particle Interactions

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Random Phase ◽  
Integration Contour ◽  
Differential Formulation ◽  
Variational Relations ◽  
Potential Perturbation ◽  
Non Equilibrium

Chapter 09 Nonequilibrium Green’s functions (NEGF), including coupled-correlated (C) single- and multi-particle Green’s functions, are defined as averages weighted with the time-development operator U(t0+τ,t0). Linear conductivity is exhibited as a two-particle equilibrium Green’s function (Kubo-type formulation). Admitting particle sources (S:η,η+) and non-conservation of number, the non-equilibrium multi-particle Green’s functions are constructed with numbers of creation and annihilation operators that may differ, and they may be derived as variational derivatives with respect to sources η,η+ of a generating functional eW=TrU(t0+τ,t0)CS/TrU(t0+τ,t0)C. (In the non-interacting case this yields the n-particle Green’s function as a permanent/determinant of single-particle Green’s functions.) These variational relations yield a symmetric set of multi-particle Green’s function equations. Cumulants and the Linked Cluster Theorem are discussed and the Random Phase Approximation (RPA) is derived variationally. Schwinger’s variational differential formulation of perturbation theories for the Green’s function, self-energy, vertex operator, and also shielded potential perturbation theory, are reviewed. The Langreth Algebra arises from analytic continuation of integration of products of Green’s functions in imaginary time to the real-time axis with time-ordering along the integration contour in the complex time plane. An account of the Generalized Kadanoff-Baym Ansatz is presented.

Wave function modification via controlled potential perturbation

1994 ◽  
Vol 305 (1-3) ◽  
pp. 317-321 ◽  
Author(s):  
K. Ensslin ◽  
H. Baum ◽  
P.F. Hopkins ◽  
A.C. Gossard
Keyword(s):  
Wave Function ◽  
Controlled Potential ◽  
Potential Perturbation

Rough estimates on the scalar heat kernel

2011 ◽  
Author(s):  
Jean-Michel Bismut
Keyword(s):  
Wave Equation ◽  
Heat Equation ◽  
Heat Kernel ◽  
Heat Kernels ◽  
Hypoelliptic Operator ◽  
Uniform Bounds ◽  
Standard Heat ◽  
Probabilistic Construction

This chapter establishes rough estimates on the heat kernel rb,tX for the scalar hypoelliptic operator AbX on X defined in the preceding chapter. By rough estimates, this chapter refers to just the uniform bounds on the heat kernel. The chapter also obtains corresponding bounds for the heat kernels associated with operators AbX and another AbX over ̂X. Moreover, it gives a probabilistic construction of the heat kernels. This chapter also explains the relation of the heat equation for the hypoelliptic Laplacian on X to the wave equation on X and proves that as b → 0, the heat kernel rb,tX converges to the standard heat kernel of X.

Thermodynamic and structural properties of liquid Al–Au alloys

2017 ◽  
Vol 31 (20) ◽  
pp. 1750134
Author(s):  
B. A. Olajire ◽  
A. A. Musari
Keyword(s):  
Gibbs Energy ◽  
Hard Sphere ◽  
Lattice Theory ◽  
Short Range ◽  
Short Range Order ◽  
Relevant Information ◽  
Liquid Alloys ◽  
Mixing Properties ◽  
Potential Perturbation ◽  
Pseudo Potential

The mixing properties of liquid Al–Au alloys with respect to the concentration of each constituent is determined using a method based on hard sphere system and pseudo-potential perturbation. These models were used to get relevant information on mixing properties of the Al–Au alloys like the Gibbs energy and the entropy of mixing. The concentration fluctuations, chemical short range order for the hard sphere mixture (quasi-lattice theory) and the activity are calculated to know the extent of order in the liquid alloys. The results revealed that there is a degree of ordering in liquid Al–Au alloy (hetero-coordinated).

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