Lattice Green's functions in all dimensions
TL;DR: In this article, a systematic treatment of lattice Green's functions (LGF) on the d-dimensional diamond, simple cubic, body-centred cubic and face-centered cubic lattices for arbitrary dimensionality d 2 was given.
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Abstract: We give a systematic treatment of lattice Green’s functions (LGF) on the d-dimensional diamond, simple cubic, body-centred cubic and face-centred cubic lattices for arbitrary dimensionality d 2 for the first three lattices, and for 2 d 5 for the hyper-fcc lattice. We show that there is a close connection between the LGF of the d-dimensional hyper-cubic lattice and that of the (d − 1)-dimensional diamond lattice. We give constant-term formulations of LGFs for each of these lattices in all dimensions. Through a still under-developed connection with Mahler measures, we point out an unexpected connection between the coefficients of the sc, bcc and diamond LGFs and some Ramanujan-type formulae for 1/π.
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Citations
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References
•Book
An Introduction To Abstract Harmonic Analysis
Lynn H. Loomis
- 01 Jan 1953
TL;DR: An introduction to abstract harmonic analysis is one of the literary work in this world in suitable to be reading material and it will show you the amazing benefits of reading a book.
Random Walks And Random Environments
Barry D. Hughes
- 30 Mar 1995
TL;DR: Random walks and random environments provide an introduction to the problem of random walk and its applications.
1K
On the theory of cooperative phenomena in crystals
TL;DR: In this paper, the theory of cooperative phenomena in crystals is studied and the authors propose a method to solve the problem of cooperative phenomenon in crystals, which is based on the concept of cooperation.
699
•Book
Green's functions for solid state physicists
Sebastian Doniach,E H Sondheimer +1 more
- 01 Jan 1974
TL;DR: In this article, the Fenyman-Dyson expansion was used to model the Fenysdys expansion of fermions in the presence of many impurities, the theory of electrical resistance in metals, the magnetic instability of the interacting electron gas, and the X-ray and Kondo problems.
532