Systematic investigation of two-dimensional static array sums

McPhedran, RC; Botten, LC; Nicorovici, NA; Zucker, IJ

Systematic investigation of two-dimensional static array sums

McPhedran, RC Botten, LC

Nicorovici, NA Zucker, IJ

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Publication Type:: Journal Article
Citation:: Journal of Mathematical Physics, 2007, 48 (3)
Issue Date:: 2007-04-10

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Field	Value	Language
dc.contributor.author	McPhedran, RC	en_US
dc.contributor.author	Botten, LC https://orcid.org/0000-0001-6471-6954	en_US
dc.contributor.author	Nicorovici, NA	en_US
dc.contributor.author	Zucker, IJ	en_US
dc.date.issued	2007-04-10	en_US
dc.identifier.citation	Journal of Mathematical Physics, 2007, 48 (3)	en_US
dc.identifier.issn	0022-2488	en_US
dc.identifier.uri	http://hdl.handle.net/10453/3399
dc.description.abstract	We discuss general properties of doubly periodic sums over the square lattice, linking phased, Bloch-type sums in the direct lattice with displaced sums in the reciprocal lattice using the Poisson summation formula. We discuss cardinal points, where the sums reduce to a single product of Dirichlet L functions, and exhibit all cardinal points for the square lattice. We introduce a new method for evaluating lattice sums and illustrate this by solving low order systems of sums of integer order 2,3,4,5. For the last case, the analytic expressions for the sums involve complementary L functions, or alternatively L functions with complex characters. © 2007 American Institute of Physics.	en_US
dc.relation.ispartof	Journal of Mathematical Physics	en_US
dc.relation.isbasedon	10.1063/1.2472186	en_US
dc.subject.classification	Mathematical Physics	en_US
dc.title	Systematic investigation of two-dimensional static array sums	en_US
dc.type	Journal Article
utslib.citation.volume	3	en_US
utslib.citation.volume	48	en_US
utslib.for	0105 Mathematical Physics	en_US
utslib.for	01 Mathematical Sciences	en_US
utslib.for	02 Physical Sciences	en_US
dc.location.activity	ISI:000245317900020	en_US
dc.location.activity	Paris, France
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access
pubs.issue	3	en_US
pubs.publication-status	Published	en_US
pubs.volume	48	en_US

Abstract:

We discuss general properties of doubly periodic sums over the square lattice, linking phased, Bloch-type sums in the direct lattice with displaced sums in the reciprocal lattice using the Poisson summation formula. We discuss cardinal points, where the sums reduce to a single product of Dirichlet L functions, and exhibit all cardinal points for the square lattice. We introduce a new method for evaluating lattice sums and illustrate this by solving low order systems of sums of integer order 2,3,4,5. For the last case, the analytic expressions for the sums involve complementary L functions, or alternatively L functions with complex characters. © 2007 American Institute of Physics.

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http://hdl.handle.net/10453/3399