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8/3/2019 Sbastien Balibar- Rotons, superfluidity, and He crystals
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Rotons, superfluidity,
and He crystals
Sbastien BalibarLaboratoire de physique statistique
Ecole Normale Suprieure, Paris (France)
LT 24, Orlando, aug. 2005
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Laszlo Tisza, june 17, 2005
From: tisza@MIT.EDU
Date: 17 juin 2005 17:55:40 GMT+02:00
o balibar@lps.ens.fr
Dear Sebastien,Dear Sebastien,
I am delighted to read in Physics Today that you are to receive the Fritz LondonI am delighted to read in Physics Today that you are to receive the Fritz London
Prize.Prize.This is wonderful! Please receive my warmest congratulations.This is wonderful! Please receive my warmest congratulations.
Yesterday I was leafing through old correspondence and I found a letter in whichYesterday I was leafing through old correspondence and I found a letter in which
I nominated Landau for the Prize. I am sure I was not alone.I nominated Landau for the Prize. I am sure I was not alone.
I was actually at LTI was actually at LT--7 in Toronto when the Prize was announced.7 in Toronto when the Prize was announced.
It is actually unconscionable of Landau not to have taken note of the remarkableIt is actually unconscionable of Landau not to have taken note of the remarkableSimonSimon -- London work on helium []London work on helium []
All he said that London was not a good physicist.All he said that London was not a good physicist.
I am looking forward to your book to straighten out matters.I am looking forward to your book to straighten out matters.
With warmest regards,With warmest regards,
LaszloLaszlo
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Outline
BEC and rotons: the London-Tisza-Landau controversy
Quantum evaporation
The surface of He crystals
The metastability limits of liquid helium
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Looking back to the history of superfluidity
1928-38 : discovery of superfluidity at Leiden, Toronto,Cambridge, Moscow
J.F. Allen and A.D. Misener (Cambridge, jan 1938):J.F. Allen and A.D. Misener (Cambridge, jan 1938):
flow rate Q in a capillary (radius R)flow rate Q in a capillary (radius R)
instead of Poiseuilles lawinstead of Poiseuilles law Q =Q = TTRR44 ((P / (8P / (8 LL l)l)
Q is nearly independent ofQ is nearly independent of((P and of R (10 to 500P and of R (10 to 500 QQm)m)
the observed type of flow cannot be treated asthe observed type of flow cannot be treated aslaminar nor turbulentlaminar nor turbulent
The hydrodynamics of helium II is non classicalThe hydrodynamics of helium II is non classical
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P. Kapitza rediscovers superleaks andP. Kapitza rediscovers superleaks and
introduces the wordintroduces the word superfluidsuperfluid ,,
in analogy within analogy with superconductorsuperconductor
P. Kapitza (Moscow, dec. 1937) :P. Kapitza (Moscow, dec. 1937) :
below Tbelow TPP, the viscosity of helium is very, the viscosity of helium is verysmallsmall**......
it is perhaps sufficient to suggest, byit is perhaps sufficient to suggest, by
analogy with superconductorsanalogy with superconductors, that the, that the
helium below thehelium below the PP--point enters a specialpoint enters a specialstate which might be calledstate which might be calleda a superfluidsuperfluid
* this had already been observed by Keesom* this had already been observed by Keesom
and van den Ende, Proc. Roy. Acad.and van den Ende, Proc. Roy. Acad.
Amsterdam 33, 243, 1930)Amsterdam 33, 243, 1930)
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5 march 1938,5 march 1938,
Institut Henri Poincar (Paris) :Institut Henri Poincar (Paris) :
Fritz London:Fritz London:superfluidity has to be connectedsuperfluidity has to be connected
with Bosewith Bose--Einstein condensationEinstein condensation
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Paris 1938: Laszlo Tisza introducesParis 1938: Laszlo Tisza introduces
thethe twotwo--fluid model fluid model
two parts:two parts: a superfluid with zero entropy and viscositya superfluid with zero entropy and viscosity
aa normal fluidnormal fluid with non zero entropy and non zero viscosity with non zero entropy and non zero viscosity
two independent velocity fields: vtwo independent velocity fields: vss and vand vnn
predicts thermomechanic effects:predicts thermomechanic effects:
the fountain effect observed by Allen and Jones, and the reverse effectthe fountain effect observed by Allen and Jones, and the reverse effect
thermal waves (second sound)thermal waves (second sound)
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Lev D. Landau Moscow 1941Lev D. Landau Moscow 1941 -- 4747
19381938: Landau comes out of prison thanks to: Landau comes out of prison thanks toKapitzaKapitza
19411941: in view of Kapitzas results on: in view of Kapitzas results on
thermal waves, Landau introduces a morethermal waves, Landau introduces a more
rigorous version of Tiszas two fluid model,rigorous version of Tiszas two fluid model,
but ignoresbut ignoresFritz London and BEC :Fritz London and BEC :
the explanation advanced by Tisza (!) not
only has no foundations in his suggestions
but is in direct contradiction with them
The normal fluid is made of quantumThe normal fluid is made of quantum
elementary excitations (elementary excitations (quasiparticlesquasiparticles):):
phonons etphonons etrotonsrotons ( elementary vortices ??)( elementary vortices ??)Calculates the thermodynamic propertiesCalculates the thermodynamic properties
prdicts the existence of a critical velocityprdicts the existence of a critical velocity
and thermal waves (and thermal waves ( second soundsecond sound inin
agreement with Kaptizas resultsagreement with Kaptizas results
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The London-Tisza-Landau controversy
LT0 at Cambridge (1946), opening talk:
Fritz London criticizes Landaus theory based on the shaky
grounds of imaginary rotons :
The quantization of hydrodynamics [by Landau]The quantization of hydrodynamics [by Landau]
is a very interesting attemptis a very interesting attempt
howeverhoweverquite unconvincingquite unconvincingas far as it is based on a representation of the statesas far as it is based on a representation of the states
of the liquid by phonons and what he callsof the liquid by phonons and what he calls rotonsrotons . There is unfortunately no. There is unfortunately no
indication that there exists anything like aindication that there exists anything like a rotonroton ; at least one searches in vain; at least one searches in vain
for a definition of this wordfor a definition of this wordnor any reason given why one of these two fluids should have a zero entropynor any reason given why one of these two fluids should have a zero entropy
(inevitably taken by Landau from Tisza)(inevitably taken by Landau from Tisza)
Despite their rather strong disagreement, Landau was awarded the
London prize in 1960, six years after London's death
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BEC in 4He
BEC takes place : the: thecondensate has been measuredcondensate has been measured
and calculated:and calculated:
at 0 bar: from 7 to 9%at 0 bar: from 7 to 9%
at 25 bar: from 2 to 4 %at 25 bar: from 2 to 4 %33He behaves differentlyHe behaves differently
and rotons exist
they are not elementary quantum vortices, but a consequence ofthey are not elementary quantum vortices, but a consequence of
local order in the liquidlocal order in the liquid
Moroni and Boninsegni(J. Low Temp. Phys. 136, 129, 2004)
London and Landau died tooLondon and Landau died too
early to realize that they bothearly to realize that they both
had found part of the truthhad found part of the truth
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neutron scattering: rotons exist
R+ and R- rotons have opposite group velocities
The roton gap decreases with pressure
0
2
4
6
8
10
12
14
0 5 10 15 20 25
Energy(K)
Wavenumber (nm-1
)
20 bar
svp
phonons
rotons
RR ++RR --
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rotons : a consequence of local order
F. London, LT0, Cambridge (1946) :F. London, LT0, Cambridge (1946) :there has to be some short range order in liquid helium.there has to be some short range order in liquid helium.
A liquidA liquid--solid instability (Schneider and Enz 1971):solid instability (Schneider and Enz 1971):
As the roton minimumAs the roton minimum ((decreases, order extends to larger and largerdecreases, order extends to larger and larger
distances and the liquid structure gets closer to that of a crystal.distances and the liquid structure gets closer to that of a crystal.
An instability whenAn instability when (( =0 ; some information from acoustic crystallization ?=0 ; some information from acoustic crystallization ?
R. Feynman, Prog. in LT Phys. 1955 :R. Feynman, Prog. in LT Phys. 1955 :
A vortex ring ?A vortex ring ?
the dispersion relation of elementary excitations is:the dispersion relation of elementary excitations is:
hh[[qq = h= h22qq22/ 2mS(q)/ 2mS(q)P. Nozires J. Low Temp. Phys. 137, 45, 2004:P. Nozires J. Low Temp. Phys. 137, 45, 2004:
rotons are ghosts of a Bragg peakrotons are ghosts of a Bragg peak
The roton minimum is a consequence of a maximum in the struture factor S(q),The roton minimum is a consequence of a maximum in the struture factor S(q),
i.e. a large probability to find atoms at the average interatomic distance fromi.e. a large probability to find atoms at the average interatomic distance from
their neighbors.their neighbors.
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P.W. Anderson 1966:P.W. Anderson 1966:analogy with the photoelectric effectanalogy with the photoelectric effect
1 photon hv ejects 1 electron with a kinetic1 photon hv ejects 1 electron with a kinetic
energyenergy
EEkinkin = hv= hv -- EE00 (E(E00 : binding energy): binding energy)
11 rotonroton with a energy E >with a energy E > (( = 8.65 K evaporates= 8.65 K evaporates1 atom with a kinetic energy1 atom with a kinetic energy
EEkinkin "("( -- 7.15 = 1.5 K7.15 = 1.5 K v > 79 m/sv > 79 m/s
Quantum evaporation
RR -- RR ++
rotons (E > 8.65K)rotons (E > 8.65K)
evaporated atomsevaporated atoms
EEkinkin > 1.5K> 1.5K
gasgas
liquidliquid
S. Balibar et al. (PhD thesis 1976 and Phys. Rev. B18, 3096, 1978) :S. Balibar et al. (PhD thesis 1976 and Phys. Rev. B18, 3096, 1978) :heat pulses at T < 100 mKheat pulses at T < 100 mK ballistic rotons and phononsballistic rotons and phonons
atomsatoms evaporated by rotons travel with a minimum velocity 79 m/sevaporated by rotons travel with a minimum velocity 79 m/s
direct evidence for the existence of rotons and the quantization of heat at low Tdirect evidence for the existence of rotons and the quantization of heat at low T
For a quantitative study and the evidence for RFor a quantitative study and the evidence for R ++ and Rand R -- rotons, seerotons, see
M.A.H. Tucker, G.M. Wyborn et A.F.G. Wyatt , Exeter (1990M.A.H. Tucker, G.M. Wyborn et A.F.G. Wyatt , Exeter (1990--99)99)
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The surface of heliumThe surface of helium
crystalscrystalsFor a detailed review, seeFor a detailed review, see
S. Balibar, H. Alles, and A. Ya. Parshin,S. Balibar, H. Alles, and A. Ya. Parshin,
Rev. Mod. Phys. 77, 317 (2005)Rev. Mod. Phys. 77, 317 (2005)
The roughening transitions.The roughening transitions.
Helium crystals are model systems whoseHelium crystals are model systems whosestatic propertiesstatic properties
can be generalized to all classical crystalscan be generalized to all classical crystals
Crystallization waves and dynamic properties.Crystallization waves and dynamic properties.
Helium crystals are also exceptional systems whoseHelium crystals are also exceptional systems whose dynamicdynamic
propertiesproperties are quantum and surprising:are quantum and surprising:
at 100 mKat 100 mK44He crystals grow 10He crystals grow 101111 times faster thantimes faster than 33He crystalsHe crystals
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the roughening
transitionsAs T decreases, the surface is covered
with more and more facets.
Successive roughening transitions in high
symmetry directions:rough above TR psmooth below TRlarge scale fluctuations disappear
(no difference at the atomic scale)
detailed study of critical behaviorsstep energy, step width, growth rate, curvature
as a function of T and orientation
quantitative comparison with RG theory (P.
Nozires 1987-92)
a Kosterlitz-Thouless transition
1.4 K1.4 K
1 K1 K
0.4 K0.4 K
0.1 K0.1 K
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roughening transitions in He 4
QuickTime et undcompresseur miroMotion JPEG A
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the universal relationthe universal relation
D.S. Fisher and J.D. Weeks, PRL 1983D.S. Fisher and J.D. Weeks, PRL 1983
C. Jayaprakash, W.F. Saam and S. Teitel, PRL 1983 :C. Jayaprakash, W.F. Saam and S. Teitel, PRL 1983 :
kkBBTTRR = (2/= (2/TT)) KKRR dd22
TTRR : roughening transition temperature: roughening transition temperature
KK == EE + + 22EE// JJ22 : surface stiffness: surface stiffness
((EE : surface tension,: surface tension, JJ : angle): angle)
KKRR
== KK( T( TRR))
(0001) or(0001) or cc facets in facets in 44He: the universal relation isHe: the universal relation is
precisely satisfied withprecisely satisfied with KKRR = 0.315 cgs and T= 0.315 cgs and TRR= 1.30K= 1.30K
other facets inother facets in 44He are anisotropic : checking the universal relationHe are anisotropic : checking the universal relation
is more difficult since kis more difficult since kBBTTRR = (2/= (2/TT) () (KK11 KK22))1/21/2
dd22
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up to 11 different facets on helium 3 crystalsup to 11 different facets on helium 3 crystals
(110)(110)
(110)(110) (110)(110)
(100)(100)
(100)(100)
Wagner et al., Leiden 1996 :Wagner et al., Leiden 1996 :
(100) and (211) facets(100) and (211) facets
Alles et al. , Helsinki 2001 :Alles et al. , Helsinki 2001 :
up to 11 different facetsup to 11 different facets
0.55 mK0.55 mK2.2 mK2.2 mK
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quantum fluctuationsquantum fluctuations
and coupling strengthand coupling strength
inin 33HeHe
(110) facets can be seen only below(110) facets can be seen only below
~100 mK~100 mK
E. Rolley , S. Balibar, and F. Gallet,E. Rolley , S. Balibar, and F. Gallet,EuroPhys. Lett. 1986 and 1989 :EuroPhys. Lett. 1986 and 1989 :
due to a very weak coupling of thedue to a very weak coupling of the
crystal surface to the lattice, facetscrystal surface to the lattice, facets
are too small to be seen near Tare too small to be seen near TRR ==
260 mK (known from260 mK (known from KK = 0.06= 0.06erg/cmerg/cm22))
I. Todoshchenko et al. Phys. Rev. Lett. 93, 175301 (2004) and LT24 :I. Todoshchenko et al. Phys. Rev. Lett. 93, 175301 (2004) and LT24 :
quantum fluctuations are responsible for the weak coupling at high T butquantum fluctuations are responsible for the weak coupling at high T but
damped at low T where the coupling is strong and many facets visible.damped at low T where the coupling is strong and many facets visible.
growth shapes
below 100 mK
eq. shape at 320 mK
K = 0.06 erg/cm2
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up to 60 different facetsup to 60 different facets
in liquid crystalsin liquid crystals
shear modulus
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3He crystals at 320 mK: coalescence without viscosity
no facets
H.J. Maris: a
purely geometrical
problem
dR/dt k/R2
neck radius:R ~ t1/3
(as for superfluid
drops)
inertia: t1/2
viscosity: t ln(Et)
R. Ishiguro, F. Graner, E. Rolley and S. Balibar,
PRL 93, 235301 (2004)
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Crystallization waves
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melting and freezing
2 restoring forces2 restoring forces ::
--surface tensionsurface tension KK
(more precisely the "surface stiffness"(more precisely the "surface stiffness" KK))-- gravity ggravity g
inertia : mass flow in the liquidinertia : mass flow in the liquid((VVCC>> VVLL))
[ 2 !VL
VC VL 2
Kq3 VC VL gq? A
helium 4 crystals grow from a superfluid (no viscosity, large thermal conductivity)helium 4 crystals grow from a superfluid (no viscosity, large thermal conductivity)the latent heat is very small (see phase diagram)the latent heat is very small (see phase diagram)
the crystals are very pure wih a high thermal conductivitythe crystals are very pure wih a high thermal conductivity
no bulk resistance to the growth, the growth velocity is limited by surface effectsno bulk resistance to the growth, the growth velocity is limited by surface effects
smooth surfaces : step motionsmooth surfaces : step motion
rough surfaces : collisisions with phonons (no thermal rotons belowrough surfaces : collisisions with phonons (no thermal rotons below ~0.6K)~0.6K) (cf. electron(cf. electron
mobility in metals)mobility in metals)
v = kv = k(Q(Q with k ~ Twith k ~ T--44 : the growth rate diverges at low T: the growth rate diverges at low T
helium crystals can grow and melt so fast thathelium crystals can grow and melt so fast thatcrystallization wavescrystallization wavespropagate at theirpropagate at their
surfaces as if they were liquids.surfaces as if they were liquids.
crystalcrystal
superfluidsuperfluid
experimental measurement of the surface stiffnessexperimental measurement of the surface stiffness KK
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surface stiffness measurementssurface stiffness measurements
thethesurface tensionsurface tension EE is anisotropicis anisotropic
the anisotropy ofthe anisotropy ofthe surface stiffnessthe surface stiffnessKK!E!Exx EExxUU is even larger, especially foris even larger, especially for
stepped surfaces close to facets.stepped surfaces close to facets.
KKBB ww FF/d/dJJ
KK//// ww 66HJHJdd
step width, energystep width, energy FF, interactions, interactions HH
E. Rolley, S. Balibar and C. GuthmannE. Rolley, S. Balibar and C. GuthmannPRL 72, 872, 1994 and J. Low Temp. Phys. 99, 851, 1995PRL 72, 872, 1994 and J. Low Temp. Phys. 99, 851, 1995
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the metastability limits of
liquid He Liquid-gas and liquid-solid : 1st
order transitions
suppress impurities and wallsliquid helium can be observed in a
metastable state for a finite time
following J. Nissen (Oregon) and
H.J. Maris (Brown Univ.),
we use high amplitude, focused
acoustic waves
the tensile strength of liquid He:
how much can one stress liquid
He without bubble nucleation ?a similar question: how far can
one pressurize liquid He without
crystal nucleation ?
a 1.3 MHz transducera 1.3 MHz transducer
spherical geometryspherical geometry
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high amplitudehigh amplitude
acoustic wavesacoustic waves
At the focal point:P = Pstat+ HP cos (2T .t)
f ~1 MHz
large pressure oscillations
away from any wall(here : s 35 bar)
during ~ T/10 ~ 100 ns
in a volume (P/10)3 ~ 15 Qm3
-50
0
50
0 5 10 15 20 25 30 35
Excitation
(Volt)
Time (microseconds)
Signal(ar
b.units)
cavitation at Pm
= 25.3 bar
flight time (22Qs)
G.Beaume, S. Nascimbene, A. Hobeika, F. Werner,G.Beaume, S. Nascimbene, A. Hobeika, F. Werner,F. Caupin and S. Balibar (2002F. Caupin and S. Balibar (2002 -- 2003)2003)
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The tensile strength of liquid heliumThe tensile strength of liquid heliumF. Caupin , S. Balibar et al.F. Caupin , S. Balibar et al.
see Phys. Rev. B 64, 064507 (2001) and J. Low Temp. Phys. 129, 363 (2002)see Phys. Rev. B 64, 064507 (2001) and J. Low Temp. Phys. 129, 363 (2002)
A singularityA singularity
at 2.2K andat 2.2K and
--7 bar in7 bar in
agreementagreement
withwith
predictions ofpredictions of
TTPP
at negativeat negative
pressurepressure
-15
-12
-9
-6
-3
0
3
0 1 2 3 4 5 6
Caupin 2001
Caupin 2001
Hall 1995
Pettersen 1994
Nissen 1989
Nissen 1989
Sinha 1982
Ca
vitation
Pressure
(bar)
Temperature (K)
liquid-gas equilibrium
nucleation line(Barcelona)
standard theory
(V X= 2.10-16
cm3s)
spinodal limit
(Barcelona)
critical
point
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acoustic cristallizationacoustic cristallization
on a glass wallon a glass wallX. Chavanne, S. Balibar and F. CaupinX. Chavanne, S. Balibar and F. CaupinPhys. Rev. Lett. 86, 5506 (2001)Phys. Rev. Lett. 86, 5506 (2001)
amplitude of the acoustic
wave at the nucleation
threshold :
s 4.3 bar
0.168
0.170
0.172
0.174
0.176
0.178
20 22 24 26 28 30 32
densit(g/cm
3)
temps (microsecondes)
transmission
reflexion
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the extended phase diagram of
liquid 4He
no homogeneous nucleation
solid4He up to 160 bar
superfluidity at high P ?
Nozieres JLTP 137, 45 (2004).
an instability where (= 0 ?L. Vranjes, J.Boronat et al.
(preprint 2005) : P > 200 bar ?
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R. Ishiguro, F.Caupin and S. Balibar, LT24
HeNe laser
lens
spherical
transducer
experimental cell
a spherical transducer:
larger amplitude
larger non-linear effects
calibration of the acoustic pressure : Brillouin scattering
inside the acoustic wave (in progress)
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-0.04
-0.03
-0.02
-0.01
0.00
0.01
0 20 40 60 80 100
sc
atteredlight(arb.units)
time (Qs)
25.2 bar
0 bar
Possible observation of homogeneous crystallization
cavitation
no nucleation
crystallization ?
We observe 2 nucleationregimes:
at high P: crystallization ?
at low P : cavitation
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Intensity and time delay
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0 5 10 15 20 25
Signalintensity(arb
.
units)
Pressure (bar)
1.00
1.50
2.00
2.50
3.00
3.50
0 5 10 15 20 25
Nucleatio
ntime(periods)
Pressure (bar)
The signal intensity increases when approaching Pm = 25.3 bar
nucleation at high P is delayed by 1/2 period compared to low P
crystallization at high P ?
calibration of the nucleation pressure :
Brillouin scattering inside the wave
R. Ishiguro, F. Caupin, and S. Balibar, this conference
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with many thanks to the co-authors of my papers:
students, postdocs, visitors, hosts and collaborators
(chronological order)
B. Perrin, A. Libchaber, D. Lhuillier, J. Buechner,
B. Castaing, C. Laroche, D.O. Edwards,P.E. Wolf, F. Gallet, E.
Rolley,P. Nozires, C. Guthmann,F. Graner,R.M.Bowley, W.F.
Saam,J.P. Bouchaud,M. Thiel, A. Willibald, P. Evers, A.
Levchenko,P. Leiderer,R.H. Torii,H.J.Maris,S.C.Hall,
M.S.Pettersen, C. Naud, E.Chevalier,J.C.Sutra Fourcade,
H. Lambar,P. Roche, O.A.Andreeva, K.O. Keshishev,
D. Lacoste,J. Dupont-Roc,F. Caupin, S. Marchand,
T. Mizusaki, Y. Sasaki, F. Pistolesi,X. Chavanne, T. Ueno,M. Fechner, C. Appert, C. Tenaud, D. d'Humires,
F. Werner, G. Beaume, A. Hobeika, S. Nascimbene,
C. Herrmann,R. Ishiguro,H. Alles and A.Ya. Parshin
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Dripping of helium 3 crystals
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