Casimir surface forces on dielectric media in spherical geometry

Brevik, Iver; Skurdal, I; Sollie, R.

doi:10.1088/0305-4470/27/20/021

Cited by 37 publications

(54 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As a matter of fact, the Casimir interaction between two concentric spheres in D ¼ 3 dimensions has been considered in [56][57][58]. For scalar fields or spinor fields in general D dimensions, the zero temperature Casimir effect on two concentric spherical shells has been studied in [59][60][61][62][63][64].…”

Section: Introductionmentioning

confidence: 99%

Casimir interaction of concentric spheres at finite temperature

Teo

2011

Phys. Rev. D

View full text Add to dashboard Cite

We consider the finite temperature Casimir effect between two concentric spheres due to the vacuum fluctuations of the electromagnetic field in the $(D+1)$-dimensional Minkowski spacetime. Different combinations of perfectly conducting and infinitely permeable boundary conditions are imposed on the spheres. The asymptotic expansions of the Casimir free energies when the dimensionless parameter $\vep$, the ratio of the distance between the spheres to the radius of the smaller sphere, is small are derived in both the high temperature region and the low temperature region. It is shown that the leading terms agree with those obtained using the proximity force approximation, which are of order $T\vep^{1-D}$ in the high temperature region and of order $\vep^{-D}$ in the low temperature region. Some universal structures are observed in the next two correction terms. The leading terms of the thermal corrections in the low temperature region are also derived. They are found to be finite when $\vep\rightarrow 0^+$, and are of order $T^{D+1}$.Comment: 19 pages, version accepted by Phys. Rev.

show abstract

Section: Introductionmentioning

confidence: 99%

Casimir interaction of concentric spheres at finite temperature

Teo

2011

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…[21] the analysis of the divergencies, which appear in calculation of the Casimir energy of a dielectric ball, has been carried out by determining the relevant heat kernel coefficients. The role of dispersion in this problem is now under study also [8,19,[22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Zero-Point Energy of a Dilute Dielectric Ball in the Mode Summation Method

2001

View full text Add to dashboard Cite

A bstractIn the (" 1 " 2 ) 2 {approxi m ati on the C asi m i renergy ofa di l ute di el ectri c bal l i s deri ved usi ng a si m pl e and cl ear m ethod of the m ode sum m ati on. T he addi ti on theorem for the B esselfuncti ons enabl es one to present i n a cl osed form the sum over the angul ar m om entum before the i ntegrati on over the i m agi nary frequenci es. T he l i near i n (" 1 " 2 ) contri buti on i nto the vacuum energy i s rem oved by an appropri ate subtracti on. T he rol e of the contact term s used i n other approaches to thi s probl em i s el uci dated. 12. 20. D s,03. 70. + k,78. 60. M q,42. 50. Lc Typeset usi ng R EV T E X I. IN T R O D U C T IO NT he progress i n cal cul ati on ofthe C asi m i r energy i s rather sl ow . In hi s pi oneer paper [ 1]i n 1948 H .B.G .C asi m i r cal cul ated the vacuum el ectrom agneti c energy for the m ost si m pl e boundary condi ti ons,for two paral l elperfectl y conducti ng pl ates pl aced i n vacuum . D i el ectri c properti esofthe m edi a separated by pl ane boundari esdo notadd new m athem ati caldi cul ti es [ 2] . H owever the rst resul t on the cal cul ati on ofthe C asi m i r energy for the non-at boundari es was obtai ned onl y i n 1968. By com puter cal cul ati ons,l asted 3 years, T .H .Boyer found the C asi m i r energy ofa perfectl y conducti ng spheri calshel l [ 3] . A ccount ofdi el ectri c and m agneti c properti es ofthe m edi a i n cal cul ati ons ofthe vacuum energy for non at i nterface l eads to new pri nci paldi cul ti es or,m ore preci sel y,to a new structure of di vergenci es.T he cal cul ati on ofthe C asi m i r energy i n a speci alcase,w hen both the m ateri alm edi a have the sam e vel oci ty ofl i ght,proves to be,from the m athem ati calstand poi nt,exactl y the sam e as for perfectl y conducti ng shel l s pl aced i n vacuum and havi ng the shape ofthe i nterface between these m edi a [ 4{14] .T he rst attem pt to cal cul ate the C asi m i r energy ofa di el ectri c com pact bal lhas been undertaken by K .A .M i l ton i n 1980 [ 15] .A nd onl y justrecentl y thevacuum el ectrom agneti c energy ofa di l ute di el ectri c bal lwas found 1 [ 16{20] . T he l i ght vel oci ty i s di sconti nuous on the surface of such a bal l . In R ef.[ 21]the anal ysi s of the di vergenci es, w hi ch appear i n cal cul ati on ofthe C asi m i r energy ofa di el ectri c bal l ,has been carri ed out by determ i ni ng the rel evant heat kernelcoe ci ents. T he rol e of di spersi on i n thi s probl em i s now under study al so [ 8, 19, 22{25] .U nder these ci rcum stances i t i s of a i ndubi tabl e i nterest to devel op new m ethods for cal cul ati ng the vacuum energy fornon-atboundari esw i th al l owance forthe m ateri alcharacteri sti cs ofthe m edi a. It i s thi s ai m that i s pursued i n the present paper.Practi cal l y al lthe cal cul ati ons ofthe C asi m i r energy for the boundari es w i th spheri cal orcyl i ndri calsym m etri es use the uni form asym ptoti c expansi on forthe Besselfuncti ons. In pl ace ofthi s we are em pl oyi...

show abstract

“…Within this context, the present paper tries to further the study of the C function associated with the Bessel equation [7-91. One of the initial motivations for considering this function was the Casimir effect due to the presence of spherical boundaries. Problems of this nature have attracted the theorist's attention for quite a long time (from [lo] to many up-to-date related topics, e.g., [11,12]), and have been the object of several different approaches, such as Green function methods, multiple scattering expansions, etc., most of them reviewed in [13]. In this work, our particular C-function technique enables us to calculate the finite part of the Casimir energy due to auantum fluctuations of a free massless scalar field existing inside a spherical domain and satisfying Dirichlet boundary conditions on its surface.…”

Section: Introductionmentioning

confidence: 99%