casimir momentum in complex media? bart van tiggelen
DESCRIPTION
Casimir Momentum in Complex Media? Bart van Tiggelen. Grenoble. Collaborators: Geert Rikken (LNCMI Grenoble/Toulouse) Sébastien Kawka (Ph.D Grenoble ENS Pisa ) James Babington (postdoc ANR Grenoble). Costas Soukoulis 60 years, June 2011. Momentum from Nothing. B 0. E 0. ε , μ ,g. - PowerPoint PPT PresentationTRANSCRIPT
Casimir Momentum in Complex Casimir Momentum in Complex Media?Media?
Bart van TiggelenBart van Tiggelen
Collaborators:Collaborators:
• Geert Rikken (LNCMI Grenoble/Toulouse)Geert Rikken (LNCMI Grenoble/Toulouse)• Sébastien Kawka (Ph.D Grenoble Sébastien Kawka (Ph.D Grenoble ENS Pisa) ENS Pisa)•James Babington (postdoc ANR Grenoble)James Babington (postdoc ANR Grenoble)
Costas Soukoulis 60 years, June 2011Costas Soukoulis 60 years, June 2011
Grenoble
Momentum from NothingMomentum from Nothing
εε,,μμ,g,g
k, k,', kE0
B0
0
v)1(
cl
ijlij
BEχH
BχED
*
ε
0000jijiij EBBEg
Magneto-electric birefringenceMagneto-electric birefringence
0*det00
220
2
χpεpεχpp
ccp
c
lnmlinmpiΦ p
Fresnel dispersion lawFresnel dispersion law
kx
Bi-anisotropic MediaBi-anisotropic Media
Fizeau effectFizeau effect
ky
vv
ijij gi
EE0 0 x Bx B00
Rotatory powerRotatory power
1010-15-151010-8-8
1010-2-2
0
3
0
003
0
12
11
2
11
00
cd
c
gdc
k
k
vk
BEk
BE
0040
3
4
3
2BE g
cc
cut-off in X-ray ?cut-off in X-ray ?
phenomenological continuum theoryphenomenological continuum theory
Photonic momentum in dielectric media? Photonic momentum in dielectric media? classical « Abraham » contribution already controversialclassical « Abraham » contribution already controversialUV catastrophe of vacuum energy ?UV catastrophe of vacuum energy ?Lorentz invariance of quantum vacuum?Lorentz invariance of quantum vacuum?Inertia of quantum vacuum? Inertia of quantum vacuum?
jijiijij
t
BBEET
c
4
1
8
1
4
1
220
0
0
BE
TBEv
vcasi
Inertial mass of quantum vacuum?Inertial mass of quantum vacuum?
)bubble nowater (
2
1)in water bubble(
2
1)bubble( 333
kk kkr dddE
MeV101
130
43
c
a c
Schwinger (1993)Schwinger (1993)
UV catastrophe in sonoluminescence
(> 1934)
cut-off in the UV ?cut-off in the UV ?
eV001.0
1
1536
23)bubble( 0
2
a
cE
2
2
1)( P
2
23
030
p
casi dc
++
Free electronFree electron
Electric quadruoleElectric quadruole
Rizzo etal, 2003-2009, Babington & BAvT, 2011Rizzo etal, 2003-2009, Babington & BAvT, 2011
03
030
)( BEP 0 gdccasi
ggME ME = 10= 10-17--17-- -
1010-11-11
The UV catastrophe is realThe UV catastrophe is real
magnetic dipolemagnetic dipole
gME(ω)/n
2222222
22 )(
2)(2)(
2
11),,( BEBEBEv
vBE
ccL
BBB
EEE
0
0
003
40
4
*0 BE
BE
K
004
*0
HE
),()2(
1lim 040
21
3
ddK
c
c
Zero energy flowZero energy flow infinite momentum densityinfinite momentum density
Lorentz Lorentz scalarscalar
Bi-anisotropic Bi-anisotropic Lorentz-invariant vacuumLorentz-invariant vacuum
)'(2),',(Im20)','(),(0 2* rrrr ijji GEE Fluctuation-Fluctuation-DissipationDissipation
Casimir momentum, if infinite, is Lorentz invariantCasimir momentum, if infinite, is Lorentz invariant
BB00
εεEE00(t)(t) vv
003 )(
3
41)( BEv tatm 0constant BPv
++ --
EE00(t)(t)
BB00vv
)()(
)()(
1222
1211
rqtqm
rqtqm
fBrEr
fBrEr
02)(2
0constant220
xBREx
BxR
mqtqm
qm
0020
2
)(/
2 BER tmq
m
)(2
12,1 xaRr
Classical Abraham momentum in crossed EM fieldsClassical Abraham momentum in crossed EM fields
(Walker Nature, 1976)(Walker Nature, 1976)
sec/nm32
)0(vabr
pm
EB
sec/nm02.04
v4Feigel gEB
h
c
sec/nm0.0
10158.0v 20
gEBa
cregula
sec/nm08.0log3
4vv abr
e
atQED m
m
Classical abraham Classical abraham forceforce
Feigel QED with cut-off Feigel QED with cut-off 0.1 nm0.1 nm
Regularization of Regularization of vacuum energy in a=10 cmvacuum energy in a=10 cm
(Milton, 2000)(Milton, 2000)
QED harmonic oscillatorQED harmonic oscillator(Kawka, 2010)(Kawka, 2010)
E=450 V/mm; B=1 T
m/VT10017.0
)T(roomkg/m17.0
)6.16(/VCm1022.00
22
3
30
240
g
a
Ex: HeliumEx: Helium
BEp )0( LntBEPP cos)0(0
AcousticAcousticpressurepressure
dp/dt=Abraham forcedp/dt=Abraham force
Experiment: Geert RikkenExperiment: Geert Rikken αα(0)(0)
p/(EB) p/(EB)
E=450 V/mm;E=450 V/mm; B=1 T; B=1 T; f= 7.6 kHz f= 7.6 kHz
V= 8 nm/sec+- 0.8V= 8 nm/sec+- 0.8Feigel : 2 nm/secFeigel : 2 nm/sec
rErBA 000 2
1
221
20210
22202
2
21101
1
2
1
)()(2
1)()(
2
1
rrE
rArAprArAp
e
eem
eem
H
Casimir momentum: Casimir momentum: 1/41/4
QED of harmonic oscillator in crossed fieldsQED of harmonic oscillator in crossed fields
EE00
BB00
+e+e -e-e
21* iii
i
aa
)(
)(
20212
10111
rAvp
rAvp
em
em
Casimir momentum: Casimir momentum: 2/42/4
QED of harmonic oscillator in crossed fieldsQED of harmonic oscillator in crossed fields
0],[ HK
rBPrBppK 021021 2
1ˆ ee kin
Pseudo-Pseudo- momentum is conservedmomentum is conserved
Conjugate momentaConjugate momenta ≠ ≠ kinetic momentumkinetic momentum
EE00
BB00
+e+e -e-e
pcmp
pdpm
mm
mmmmM
ii
2/3
4)(
2021
2121
Casimir momentum: Casimir momentum: 3/43/4
QED of harmonic oscillator in crossed fieldsQED of harmonic oscillator in crossed fields
EE00
BB00
21*)()(ˆ
210212211 iiii
aaeeemm krBrArAvvK
210020
2
0020
2
00
1KKBEBEvv
eeMMK
+e+e -e-e
220
002 )0( c
BEK
Casimir momentum: Casimir momentum: 4/44/4
QED of harmonic oscillator in crossed fieldsQED of harmonic oscillator in crossed fields
2
1
12
1200
12
22
012
12001
log3
4)0(
/2//2/6
4)0(
m
m
mm
mm
cmpp
p
cmpp
pdp
mm
mm
BE
BEK
KK1 1 : 2 % QED correction to Abraham force: 2 % QED correction to Abraham forceKK22: 0.01 % QED correction : 0.01 % QED correction
Kawka & Van Tiggelen, EPL 2010Kawka & Van Tiggelen, EPL 2010
EE00
BB00
+e+e -e-e
BB00
Faraday RotationFaraday Rotation
A quantum vacuum force F= g dB/dt ?A quantum vacuum force F= g dB/dt ?
0
20
220
204
,
iVBi
c
Chiral geometry with electric polarizabilitiesChiral geometry with electric polarizabilities
00000 HErBErHB dd
εε
εεεε
εε
BB00
Faraday RotationFaraday Rotation
A quantum vacuum force F= g dB/dt ?A quantum vacuum force F= g dB/dt ?
iVBi
20
2
200,
000 HErd
Chiral geometry with magnetic polarizabilitiesChiral geometry with magnetic polarizabilities
000 BBEr gd Na Na TetraederTetraeder L=10 nm L=10 nm g/m = 1 nm/sec/T g/m = 1 nm/sec/T
µµµµµµ
µµ
momentum of quantum vacuum tomomentum of quantum vacuum toshed new light on the controversial shed new light on the controversial
nature of zero-point energynature of zero-point energy
Corsica,Corsica,20062006
Congratulations Costas! Congratulations Costas!