Statistical Average of a Product of Phase Sums Arising in the Study of Disordered Lattice. II
This recurrence formula, derived in a previous paper [J. Math. Phys. 10, 2263 (1969)] to evaluate 〈S(k 1)S(k 2) ⋯ S(kn )〉,is extended here, for the case when k 1 + k 2 + ⋯ + kn = 0 but no other partial sum of the set k 1, k 2, ⋯, kn is zero. The average is of O(N) as compared to the O(1) when k 1 +...
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| Veröffentlicht in: | Journal of mathematical physics 1970-04, Vol.11 (4), p.1279-1282, Article 1279 |
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| container_title | Journal of mathematical physics |
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| creator | Sah, Priyamvada |
| description | This recurrence formula, derived in a previous paper [J. Math. Phys. 10, 2263 (1969)] to evaluate 〈S(k
1)S(k
2) ⋯ S(kn
)〉,is extended here, for the case when k
1 + k
2 + ⋯ + kn
= 0 but no other partial sum of the set k
1, k
2, ⋯, kn
is zero. The average is of O(N) as compared to the O(1) when k
1 + k
2 + ⋯ + kn
≠ 0. Formulas are then proposed for the situations when more than one partial sum of the set vanish. 〈S(k)S(−k)〉 is considered for a parabolic probability distribution s(r) with a cutoff which shows striking similarity with x‐ray diffraction pattern of liquids. |
| doi_str_mv | 10.1063/1.1665256 |
| format | Article |
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1)S(k
2) ⋯ S(kn
)〉,is extended here, for the case when k
1 + k
2 + ⋯ + kn
= 0 but no other partial sum of the set k
1, k
2, ⋯, kn
is zero. The average is of O(N) as compared to the O(1) when k
1 + k
2 + ⋯ + kn
≠ 0. Formulas are then proposed for the situations when more than one partial sum of the set vanish. 〈S(k)S(−k)〉 is considered for a parabolic probability distribution s(r) with a cutoff which shows striking similarity with x‐ray diffraction pattern of liquids.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.1665256</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><ispartof>Journal of mathematical physics, 1970-04, Vol.11 (4), p.1279-1282, Article 1279</ispartof><rights>The American Institute of Physics</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c214t-c38d0e9f4090830a2d1aeeb0e854f86b95bede200b01af9f7a841591b266fe723</citedby><cites>FETCH-LOGICAL-c214t-c38d0e9f4090830a2d1aeeb0e854f86b95bede200b01af9f7a841591b266fe723</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/1.1665256$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>314,776,780,1553,27901,27902,76133</link.rule.ids></links><search><creatorcontrib>Sah, Priyamvada</creatorcontrib><title>Statistical Average of a Product of Phase Sums Arising in the Study of Disordered Lattice. II</title><title>Journal of mathematical physics</title><description>This recurrence formula, derived in a previous paper [J. Math. Phys. 10, 2263 (1969)] to evaluate 〈S(k
1)S(k
2) ⋯ S(kn
)〉,is extended here, for the case when k
1 + k
2 + ⋯ + kn
= 0 but no other partial sum of the set k
1, k
2, ⋯, kn
is zero. The average is of O(N) as compared to the O(1) when k
1 + k
2 + ⋯ + kn
≠ 0. Formulas are then proposed for the situations when more than one partial sum of the set vanish. 〈S(k)S(−k)〉 is considered for a parabolic probability distribution s(r) with a cutoff which shows striking similarity with x‐ray diffraction pattern of liquids.</description><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1970</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEURYMoWKsL_0G2CjN9yWTSzLLUr0LBQnUpQ2by0kbaTknSQv-9HVoVVFw97uPcs7iEXDNIGcisx1ImZc5zeUI6DFSR9GWuTkkHgPOEC6XOyUUI7wCMKSE65G0adXQhulov6GCLXs-QNpZqOvGN2dSxDZO5Dkinm2WgA--CW82oW9E43__ixuxa5M6Fxhv0aOhYx70OUzoaXZIzqxcBr463S14f7l-GT8n4-XE0HIyTmjMRkzpTBrCwAgpQGWhumEasAFUurJJVkVdokANUwLQtbF8rwfKCVVxKi32edcnNwVv7JgSPtlx7t9R-VzIo211KVh532bO9H2zt2g2aVfTaLf5s3B4a4ZP80m8b_w2Wa2P_g3-bPwD2jYAO</recordid><startdate>197004</startdate><enddate>197004</enddate><creator>Sah, Priyamvada</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>197004</creationdate><title>Statistical Average of a Product of Phase Sums Arising in the Study of Disordered Lattice. II</title><author>Sah, Priyamvada</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c214t-c38d0e9f4090830a2d1aeeb0e854f86b95bede200b01af9f7a841591b266fe723</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1970</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sah, Priyamvada</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sah, Priyamvada</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Statistical Average of a Product of Phase Sums Arising in the Study of Disordered Lattice. II</atitle><jtitle>Journal of mathematical physics</jtitle><date>1970-04</date><risdate>1970</risdate><volume>11</volume><issue>4</issue><spage>1279</spage><epage>1282</epage><pages>1279-1282</pages><artnum>1279</artnum><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>This recurrence formula, derived in a previous paper [J. Math. Phys. 10, 2263 (1969)] to evaluate 〈S(k
1)S(k
2) ⋯ S(kn
)〉,is extended here, for the case when k
1 + k
2 + ⋯ + kn
= 0 but no other partial sum of the set k
1, k
2, ⋯, kn
is zero. The average is of O(N) as compared to the O(1) when k
1 + k
2 + ⋯ + kn
≠ 0. Formulas are then proposed for the situations when more than one partial sum of the set vanish. 〈S(k)S(−k)〉 is considered for a parabolic probability distribution s(r) with a cutoff which shows striking similarity with x‐ray diffraction pattern of liquids.</abstract><doi>10.1063/1.1665256</doi><tpages>4</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0022-2488 |
| ispartof | Journal of mathematical physics, 1970-04, Vol.11 (4), p.1279-1282, Article 1279 |
| issn | 0022-2488 1089-7658 |
| language | eng |
| recordid | cdi_scitation_primary_10_1063_1_1665256 |
| source | AIP Digital Archive |
| title | Statistical Average of a Product of Phase Sums Arising in the Study of Disordered Lattice. II |
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