{"id":1818,"date":"2014-05-01T22:00:16","date_gmt":"2014-05-01T22:00:16","guid":{"rendered":"http:\/\/casgroups.case.edu\/physics-senior-projects\/?p=1818"},"modified":"2017-01-24T21:08:17","modified_gmt":"2017-01-24T21:08:17","slug":"optimization-of-the-static-first-hyperpolarizibility-of-many-non-interacting-fermions","status":"publish","type":"post","link":"https:\/\/casgroups.case.edu\/physics-senior-projects\/optimization-of-the-static-first-hyperpolarizibility-of-many-non-interacting-fermions\/","title":{"rendered":"Optimization of the Static First Hyperpolarizibility of Many Non-Interacting Fermions"},"content":{"rendered":"

Edwin Bernardoni with Rolfe Petschek<\/h3>\n

Optimization of the Static First Hyperpolarizibility of Many Non-Interacting Fermions <\/i><\/h3>\n
\n\t\t\t\t
\n\t\t\t\t\t

\n\t\t\t\t\t\t\u201dPoster\u201d<\/a>\n\t\t\t\t\t<\/h4>\n\t\t\t\t<\/div>\n\t\t\t\t
\n\t\t\t\t\t
\n

\"Bill's<\/p>\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n

Large non-linear electronic polarizabilities would be advantageous for a variety of devices and have been intensely studied for around three decades. This project will examine theoretical limits on the static first non-linear electronic susceptibility of a material, \u03b2, known as the hyperpolarizability. Numerical optimizations for a single fermion in a one-dimensional potential strongly suggest that in this case the actual limit is about 70% of the analytically proven limit, and the same result obtains for multiple fermions when there is a strong attraction between them.\u00a0 <\/span>We will investigate the results for non-interacting fermions, which seem a better model for actual electrons, which repel each-other, and expect a yet lower limit.\u00a0 <\/span>Prior work in our group suggests in one dimension this ratio decreases with increasing number of non-interacting particles.\u00a0 <\/span>We complete this work for segmented linear potentials, examine other model potentials specifically as finite sums of hermite polynomials and investigate the possibility that an analytic result can be obtained.\u00a0 <\/span>Time permitting we will investigate the limits for multiple non-interacting electrons for the static second hyperpolarizability gamma.<\/p>\n

Paper<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Edwin Bernardoni with Rolfe Petschek
\nOptimization of the Static First Hyperpolarizibility of Many Non-Interacting Fermions <\/i><\/p>\n

Large non-linear electronic polarizabilities would be advantageous for a variety of devices and have been intensely studied for around three decades. This project will examine theoretical limits on the static first non-linear electronic susceptibility of a material, \u03b2, known as the hyperpolarizability. Numerical optimizations for a single fermion in a one-dimensional potential strongly suggest that in this case the actual limit is about 70% of the analytically proven limit, and the same result obtains for multiple fermions when there is a strong attraction between them.\u00a0<\/p>\n

Continue reading… Optimization of the Static First Hyperpolarizibility of Many Non-Interacting Fermions<\/span><\/a><\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[44,1,38,5,11,4],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/posts\/1818"}],"collection":[{"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/comments?post=1818"}],"version-history":[{"count":5,"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/posts\/1818\/revisions"}],"predecessor-version":[{"id":3019,"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/posts\/1818\/revisions\/3019"}],"wp:attachment":[{"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/media?parent=1818"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/categories?post=1818"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/tags?post=1818"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}