Modlar toplama yöntemi ile sonsuz silindirdeki kuantum boşluk enerjisi
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Tarih
2006
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info:eu-repo/semantics/openAccess
Özet
Bu çalışmada a yarıçaplı iletken sonsuz bir silindir için elektromagnetik alanın kuantum boşluk enerjisi tartışıldı. Casimir enerjisinin anlaşılmasını kolaylaştırmak için bir örnek verildi. Bu örnekte tek boyutta iki levha arasında kütlesiz skaler alanın periyodik sınır şartları ile kuantum boşluk enerjisi ele alındı. Daha sonra Casimir enerjisi için genel bir integral gösterimi ele alındı. Sonraki bölümde silindirik koordinatlarda Maxwell denklemleri çözülerek frekanslar bulundu.Elektromagnetik dalga hızının v olduğu ve elektromagnetik alanın özelliklerinin ε1μ1 = ε 2 μ 2 = v â 2 koşuluna uyduğu varsayıldı ve ε 1 , μ1 sırasıyla silindirin permitivi ve permabilitesi, ε 2 , μ 2 silindirin permitivi ve permabilitesidir. Bu koşullar sağlandığında silindirin içindeki ve dışındaki modlar arasındaki ıraksamalar Zeta fonksiyonu tekniği kullanılarak ortadan kaldırıldı.Son olarak ξ 2 = (ε 1 â ε 2 ) 2 /(ε 1 + ε 2 ) 2 ξ 2 << 1 ve ξ 2 = 1 olduğundaki durumlar göz önüne alınarak silindiriksel olmak üzere kabuğun Casimir enerjisi hesaplandı.
The quantum vacuum energy of the electromagnetic field for a conducting cylinder of radius a was discussed. An example was given in order to make understanding of Casimir Energy easier. In this example, periodic boundary condition of massless scalar field Ï (t , x) and quantum vacuum energy were studied. Afterwards, a general integral representation for the Casimir energy was studied. In the next step, Maxwell equations were solved in cylindrical coordinates and frequencies were obtained. It was assumed that the electromagnetic characteristics were suitable for the condition ε 1 μ1 = ε 2 μ 2 = v â 2 where v is the speed of the electromagnetic wave and, the permittivity and permeability of the cylinder material are (ε 1 , μ1 ) and of the surroundings are (ε 2 , μ 2 ) .When these conditions were created the divergences between the modes inside and outside the cylinder were eliminated by using Zeta function technique. Finally, Casimir energy of cylindrical shell was calculated considering the cases ξ 2 = (ε 1 â ε 2 ) 2 /(ε 1 + ε 2 ) 2 and ξ 2 << 1 and ξ 2 = 1 .
The quantum vacuum energy of the electromagnetic field for a conducting cylinder of radius a was discussed. An example was given in order to make understanding of Casimir Energy easier. In this example, periodic boundary condition of massless scalar field Ï (t , x) and quantum vacuum energy were studied. Afterwards, a general integral representation for the Casimir energy was studied. In the next step, Maxwell equations were solved in cylindrical coordinates and frequencies were obtained. It was assumed that the electromagnetic characteristics were suitable for the condition ε 1 μ1 = ε 2 μ 2 = v â 2 where v is the speed of the electromagnetic wave and, the permittivity and permeability of the cylinder material are (ε 1 , μ1 ) and of the surroundings are (ε 2 , μ 2 ) .When these conditions were created the divergences between the modes inside and outside the cylinder were eliminated by using Zeta function technique. Finally, Casimir energy of cylindrical shell was calculated considering the cases ξ 2 = (ε 1 â ε 2 ) 2 /(ε 1 + ε 2 ) 2 and ξ 2 << 1 and ξ 2 = 1 .
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