Casimir Momentum in Complex Media?
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1 Casr Moentu n Coplex Meda? Bart an Tggelen Grenoble Collaborators: Geert Rkken (LNCMI Grenoble/Toulouse Sébasten Kawka (Ph.D Grenoble ENS Psa Jaes Babngton (postdoc( ANR Grenoble Costas Soukouls 6 years, June
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4 Moentu fro Nothng B E ε,μ,g,g hω, k' hω, k hω, k
5 ω det ε c D H Fresnel dsperson law p B-ansotropc Meda ( ω = ε( ω E( ω χ( ω B( ω * ( ω = χ ( ω E μ( ω B( ω ( Φ p = ε pl pp n nl ω χ c ω c ( ε p ( ε p χ * = ( ω ω gδ j χ = j Rotatory power χ ( ω = ( ε j ε jl Fzeau effect c l χ j ( ( ω = g E B B E Magneto-electrc electrc brefrngence j j k y E x B k x
6 phenoenologcal contnuu theory T t j ρ = 8π 4π c E B = T ( E B δ ( E E B B j 4π j j cut-off n X-ray X? E B c c d d k k 4 c hωk g( ω E B = g E 4 B π c hω k [ ε ( ω ] c hω = ρ cas Inertal ass of quantu acuu? Photonc oentu n delectrc eda? classcal «Abraha» contrbuton already controersal UV catastrophe of acuu energy? Lorentz narance of quantu acuu? Inerta of quantu acuu?
7 UV catastrophe n sonolunescence (> 94 Schwnger (99 ΔE(bubble = d 4 ha ωc c r d k hωk (bubble MeV ε n water d k hωk (water no bubble cut-off n the UV? ( ε ΔE c ( bubble = 56π. ev a
8 The UV catastrophe s real ω ε ( ω = ω P ρ cas = h ω p dωω c ω = Free electron g ME (ω/n agnetc dpole Electrc quadruole g ME = h = dωω g( ω E B c Pcas = Rzzo etal,, -9, 9, Babngton & BAT,,
9 Casr oentu,, f nfnte, s Lorentz narant L c ( E, B, = ρc ( E B ν ( E B ( E B ν Fluctuaton- Dsspaton E = B = E( r, ω E * j E B E B ( r', ω' ( ω ( ω B-ansotropc Lorentz-narant acuu = hω IG ( r, r', ω πδ( ω ω' j E* H = 4π Zero energy flow K l ωc h dω dω ρ( ω, Ω c (π 4π = ω E* B 4 = νk E B 4π nfnte oentu densty Lorentz scalar
10 Classcal Abraha oentu n crossed EM felds B E (t ε (Walker Nature, 976 ρ P B = constant = 4 ( t = t B ( ε πa E( && r && r = qe( t qr& = qe( t qr& E (t B B f ( r B f ( r - r, = R ± ( a x R& qx B = constant = && x = qe( t qr& B ω x q / R & = E( t B ω
11 Ex: Helu α ( E=45 V/; B= T =. ρ =.7 kg/ g =.7 4 C (roo T /VT /V (6.6a abr = α( EB p n / sec Classcal abraha force π h = geb. n / sec 4 ρλ c hc =.58 ( ε geb a. n / sec Fegel 4 regula Fegel QED wth cut-off. n Regularzaton of acuu energy n a= c (Mlton, 4 at QED = abr α log π e.8n / sec QED haronc oscllator (Kawka,,
12 p = α( E B dp/dt dt=abraha force Acoustc pressure ( ω = P α( E B ω cosωt n L P V= 8 n/sec-.8 Fegel : n/sec p/(eb E=45 V/; B= T; f= 7.6 khz Experent: : Geert Rkken α(
13 Casr oentu: /4 QED of haronc oscllator n crossed felds e -e E B A = B r φ = E r H = ( p ea ( r ea( r ( p ea ( r ea( r ee r μω r hω ( * a a
14 Casr oentu: /4 QED of haronc oscllator n crossed felds E e -e B Conjugate oenta knetc oentu Pseudo- oentu s consered p p = = ea ea ( r ( r K ˆ = p p eb r = Pkn eb r [ K, H ] =
15 pc p p dp M = = = / 4 ( α π δ δ δμ δ δ Casr Casr oentu oentu: /4 /4 QED of QED of haronc haronc oscllator oscllator n n crossed crossed felds felds E B ( * ( ( ˆ = a a e e e k r B A r A r K h K K B E B E = Ψ Ψ ω μ δ μω δ e e M M K e e -e
16 Casr oentu: 4/4 QED of haronc oscllator n crossed felds E e -e B K 4 = α( E B α 6π = α( E B dp p 4 α log π / p p ( c / h p / p ( c / h p K α hω ( E Bα α μc K : % QED correcton to Abraha force K :. % QED correcton Kawka & Van Tggelen,, EPL
17 A quantu acuu force F= g db/dt dt? ε ε ε Chral geoetry ε B geoetry wth electrc polarzabltes 4πc γ α( ω, σ = ω ω ω σvb γω Faraday Rotaton B = H dr E B = dr E H =
18 A quantu acuu force F= g db/dt dt? µ χ dr E H = µ µ µ ( ω, σ χ( B Chral geoetry wth agnetc polarzabltes ω ω ω σvb γω = Faraday Rotaton d r E B = gb Na Tetraeder L= n g/ = n/sec/t
19 oentu of quantu acuu to shed new lght on the controersal nature of zero-pont energy Congratulatons Costas! Corsca, 6
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