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Fractals, 2000
For a regular harmonic structure on a post-critically finite (p.c.f.) self-similar fractal, the Dirichlet problem for the Laplacian can be solved by integrating against an explicitly given Green's function. We give a recursive formula for computing the values of the Green's function near the diagonal, and use it to give sharp estimates for the decay ...
Kigami, Jun +2 more
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For a regular harmonic structure on a post-critically finite (p.c.f.) self-similar fractal, the Dirichlet problem for the Laplacian can be solved by integrating against an explicitly given Green's function. We give a recursive formula for computing the values of the Green's function near the diagonal, and use it to give sharp estimates for the decay ...
Kigami, Jun +2 more
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Journal of Mathematical Physics, 1964
A one-parameter integral representation is given for the momentum space Green's function of the nonrelativistic Coulomb problem.
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A one-parameter integral representation is given for the momentum space Green's function of the nonrelativistic Coulomb problem.
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Physics Today, 2003
In 1828, an English miller from Nottingham published a mathematical essay that generated little response. George Green’s analysis, however, has since found applications in areas ranging from classical electrostatics to modern quantum field theory.
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In 1828, an English miller from Nottingham published a mathematical essay that generated little response. George Green’s analysis, however, has since found applications in areas ranging from classical electrostatics to modern quantum field theory.
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Journal of Mathematical Physics, 1987
The local Green’s function is used in many physical problems. In this paper, the properties of the local Green’s function are studied, and it is proved that the N×N local Green’s function can represent the results of the full N1×N1 Green’s function, where N is small (or at least finite) and N1 is large (or infinite). The accuracy of cutting the general
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The local Green’s function is used in many physical problems. In this paper, the properties of the local Green’s function are studied, and it is proved that the N×N local Green’s function can represent the results of the full N1×N1 Green’s function, where N is small (or at least finite) and N1 is large (or infinite). The accuracy of cutting the general
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GREEN FUNCTIONS AND COHOMOLOGY
Mathematics of the USSR-Izvestiya, 1986Complex Green functions for the Laplace operator on the background of general Yang-Mills fields are interpreted in terms of cohomology in the space of complex light lines by means of the Penrose-Ward transformation.
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Construction of green's function in terms of green's function of lower dimension
Journal of Applied Mathematics and Mechanics, 1968The problem under consideration is the construction of Green's functions for \(m\)-th order linear partial differential operators with constant coefficients in \(n\)-dimensional space in terms of the Green's function in \((n-1)\)-dimensional hyperplanes. In the end the results are applied to 3-dimensional problems in anisotropic elasticity.
Indenbom, V. L., Orlov, S. S.
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Journal of Mathematical Physics, 1997
Green’s functions are valuable analytical tools for solving a myriad of boundary-value problems in mathematical physics. Here, Green’s functions of the Laplacian and biharmonic operators are derived for a three-dimensional toroidal domain. In some sense, the former result may be regarded as “standard,” but the latter is most certainly not.
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Green’s functions are valuable analytical tools for solving a myriad of boundary-value problems in mathematical physics. Here, Green’s functions of the Laplacian and biharmonic operators are derived for a three-dimensional toroidal domain. In some sense, the former result may be regarded as “standard,” but the latter is most certainly not.
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Partition function from the Green function
Journal of Physics A: Mathematical and General, 1984The partition function in quantum statistical mechanics can be expressed as an energy integral of exp(- beta E) times the discontinuity of the Green function. A Monte Carlo approach for its evaluation which is not based on path integral representation is suggested. The fermion problem is avoided in the sense that all integrands are positive.
Avishai, Y., Richert, J.
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Correlation Functions as Hydrodynamic Green's Functions
Physical Review, 1968A formal solution for the thermodynamic variables describing a system in a nonequilibrium state is given in terms of space- and time-dependent correlation functions. The solution during the hydrodynamic stage is also given by the Green's function solution to the hydrodynamic equations. The correlation functions contain information, not contained in the
Dufty, J. W., McLennan, J. A.
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Green’s functions in WKB approximation
Journal of Mathematical Physics, 1991A systematic technique based on a variational principle is developed for obtaining WKB Green’s functions for a non-Hermitian set of inhomogeneous, nonstationary differential equations in a space of arbitrary dimensions. A key element in this technique involves the use of the Van Vleck determinant for the amplitudes of WKB functions.
Pfirsch, D., Sudan, R.
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