sébastien balibar- rotons, superfluidity, and he crystals

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: [email protected]

Date: 17 juin 2005 17:55:40 GMT+02:00

o [email protected]

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

sont requis pour visionner cette image.


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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

QuickTime et undcompresseur Animation



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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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sébastien balibar- rotons, superfluidity, and he crystals

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