Excitations, Bose-Einstein Condensation and Superfluidity of Quantum Liquids in Disorder

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Excitations, Bose-EinsteinCondensation and
Superfluidity of Quantum Liquids in Disorder

• Henry R. Glyde
• Department of Physics Astronomy
• University of Delaware

Turkish Physical Society 15 September2005
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Phase Diagram of Bulk Helium
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Goals

• Neutron scattering studies of excitations of
  quantum liquids in disorder.
• phonons and rotons in disorder
• new excitations in disorder
• Reveal the interdependence of Bose-Einstein
  Condensation (BEC), phonon-roton excitations, and
  superfluidity.
• Compare bulk liquid 4He and 4He in porous media
  (confinement and disorder).

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Bosons in Disorder
Liquid 4He in Aerogel, Vycor, Gelsil
(Geltech) Flux Lines in High Tc
Superconductors Josephson Junction
Arrays Granular Metal Films Cooper Pairs in
High Tc Superconductors Models of
Disorder excitation changes new excitations at
low energy
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Neutron Scattering Laboratories
Institute Laue Langevin Grenoble,
France ISIS Rutherford Appleton Laboratories
Oxfordshire, England NIST Center for Neutron
Research National Institute of Standards and
Technology Gaithersburg, Maryland
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Neutron Scattering ILL
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Excitations and Bose-Einstein Condensation in
Quantum Liquids in Disorder Henry R. Glyde,
University of Delaware, DMR-9972011
Figure 1. Top The Insitiut Laue Langevin (just
behind the ESRF synchrotron ring) in Grenoble.
Bottom Left to right, Jacques Bossy, Henry
Glyde, Francesco Albergamo and Olivier Plantevin
in front of the IN6 neutron spectrometer of ILL.
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Focused Research Group NSF
Neutron Scattering Studies of Surface and bulk
Disordered Quantum Systems Oscar
Vilches University of Washington John Larese
University of Tennessee Henry Glyde (PI)
University of Delaware
From left to right, J. Pearce, J. Larese, H.
Glyde and T. Arnold
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Excitations, BEC, and Superfluidity
Collaborators Jonathan Pearce Institut
Laue-Langevin Grenoble, France Francesco
Albergamo - ESRF, Grenoble, France Richard T.
Azuah - NIST Center for Neutron
Research, Gaithersburg, Maryland,
USA Jacques Bossy - Centre de
Recherche sur Les Très Basses
Temperature CNRS, Grenoble, France Bjorn Fåk
- Commissariat à lEnergie
Atomique Grenoble, France Helmut Schober
Institut Laue-Langevin Grenoble, France
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Excitations, BEC, and Superfluidity
Collaborators (Cont) Norbert Mulders
- University of Delaware Newark, Delaware
USA Oliver Plantevin - ESRF,
Grenoble Reinhard Scherm
- Physikalisch-Technische Bundesanstalt,
Braunschweig John Beamish
- University of Alberta Edmonton,
Canada Gerrit Coddens - Laboratoire des
solides irradiés Ecole Polytechnique Palais
eau, France
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Phase Diagram of Bulk Helium
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Superfluid Density ?s(T)
Bulk Liquid 4He
Superfluid Density
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London
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BEC, Excitations, and Superfluidity
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Bose-Einstein Condensation Atoms in Traps
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Bose-Einstein Condensation Atoms in Traps
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Bose-Einstein Condensation
Glyde, Azuah, and Stirling Phys. Rev. B62, 14337
(2000)
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Bose-Einstein Condensation

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Landau
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Phonon-Roton Dispersion Curve
? Donnelly et al., J. Low Temp. Phys. (1981) ?
Glyde et al., Euro Phys. Lett. (1998)
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BEC, Excitations, and Superfluidity
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Maxon in Bulk Liquid 4He
Talbot et al., PRB, 38, 11229 (1988)
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Roton in Bulk Liquid 4He
Talbot et al., PRB, 38, 11229 (1988)
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Beyond the Roton in Bulk Liquid 4He
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Phonons and Rotons Arise From Bose-Einstein
Condensation
Bogoliubov (1947) showed
Bose gas with BEC -- quasiparticles have
energy - phonon
(sound) form Quasiparticle mode coincides with
sound mode. Only one excitation when have BEC.
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Phonons and Rotons Arise From Bose-Einstein
Condensation
Gavoret and Nozières (1964) showed
Dense liquid with BEC only one excitation
density and quasiparticle modes have the same
energy, At low Q, as in Bose gas. No other
excitations at low energy (could have vortices).
Ma and Woo (1967), Griffin and Cheung (1973), and
others showed
Only a single mode at all Q with BEC -- the
phonon-roton mode.
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Excitations in a Bose Fluid
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Excitations, BEC, and Superfluidity
Bulk Liquid 4He BEC, well-defined excitations at
Q gt 0.8 Å-1 and superfluidity coincide e.g.,
all have some critical temperature,
T? 2.17 K SVP T? 1.92 K
20 bar
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BEC, Excitations, and Superfluidity
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Porous Media

• AEROGEL 95 porous
• Open 87 porous A
• 87 porous B
• -- grown with deuterated materials or
  flushed with D2
• VYCOR 30 porous
• Å pore Dia. -- grown with B11 isotope
• GELSIL (GELTECH) 50 porous
• 25 Å pores
• 44 Å pores
• MCM-41 30 porous
• 47 Å pores

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Superfluid Properties in Confinement/Disorder
Confinement reduces Tc below
. Confinement modifies (T
dependence). Confinement reduces
(magnitude). Porous media is a laboratory to
investigate the relation between superfluidity,
excitations, and BEC. Measure corresponding
excitations and condensate fraction, no(T).
(new, 1995) Localization of Bose-Einstein
Condensation by Disorder
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Tc in Porous Media
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Superfluid Density in Porous Media
Chan et al. (1988)
Miyamoto and Takeno (1996)
Geltech (25 Å pores)
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-Yamamoto et al, cond-mat/0310375 (Oct 2003)
Phase Diagram of Gelsil (Geltech) - 25 A Diameter
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Schematic Phase Diagram of Helium Confined to
Nanoscales e.g. 2 - 3 nm
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Phonon-Roton Dispersion Curve
? Donnelly et al., J. Low Temp. Phys. (1981) ?
Glyde et al., Euro Phys. Lett. (1998)
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Phonons, Rotons, and Layer Modes in Vycor and
Aerogel
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Layer Mode in Vycor and Aerogel
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Temperature Dependenceof Roton Energy
Fåk et al., PRL, 85 (2000)
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Liquid 4He in Disorder and Boson Localization
Conclusions

• Liquid helium in porous media supports well
  defined phonon-roton excitations up to wave
  vectors Q 2.8 Å.
• Energies and widths (within precision) are the
  same as in bulk 4He at all T.
• Liquid also supports layer modes at roton wave
  vectors.
• MCM-41 at partial fillings, can also see
  ripplons on 4He liquid surfaces.

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Porous Media

• AEROGEL 95 porous
• Open 87 porous A
• 87 porous B
• -- grown with deuterated materials or
  flushed with D2
• VYCOR 30 porous
• A pore Dia. -- grown with B11 isotope
• GELSIL (GELTECH) 50 porous
• 25 A pores
• 44 A pores
• MCM-41 30 porous
• 47 A pores

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Intensity in Single Excitation vs. T
Glyde et al., PRL, 84 (2000)
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Phonon-Roton Mode in VycorT 1.95 K
(Tc 2.05 K)
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Phonon-Roton Mode in VycorT 2.05 K
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Phonon-Roton Mode in VycorT 2.15 K
(Tc 2.05 K)
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Phonon-Roton Mode in VycorT 2.25 K
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Fraction, fs(T), of Total Scattering Intensity in
Phonon-Roton Mode- Vycor 70 A pores
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Fraction, fs(T), of total scattering intensity in
Phonon-Roton Mode- gelsil 44 A pore diameter
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Roton in 25 A Pore Diameter Gelsil(Geltech)
Plantevin et al., PRB, 65 (2002) Liquid 4He
in 25 A Gelsil Tc 1 K Bulk Liquid 4He T?
2.17 K
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Roton in Geltech Silica Partial Filling
Plantevin et al., PRB, 65 (2002)
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Liquid 4He in Geltech Silica
Tc (Superfluidity) 0.725 K
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Bose-Einstein CondensationLiquid 4He in Vycor
Tc (Superfluidity) 1.95-2.05 K
Azuah et al., JLTP (2003)
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Bose-Einstein CondensationLiquid 4He in Vycor
Tc (Superfluidity) 1.95-2.05 K
Azuah et al., JLTP (2003)
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Schematic Phase Diagram of Helium Confined to
Nanoscales e.g. 2 - 3 nm
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Excitations, BEC, and Superfluidity
Liquid 4He in disorder BEC, well-defined
excitations are separated from superfluidity in
disorder e.g., Tc - superfluidity Have
phonon-roton excitations and BEC at temperatures
T gt Tc Disorder localizes the condensate, T
gt Tc New Here Measurements of phonon-roton
excitations and BEC in disorder
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Schematic Phase Diagram in Ideal Nanoscale
mediae.g. 2 - 3 nm
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Liquid 4He in Disorder and Boson Localization
Conclusions

• Observe phonon-roton modes up to
• T T? 2.17 K in porous media, i.e. above Tc
  for superfluidity
• Well defined phonon-roton modes exist because
  there is a condensate. Thus have BEC above Tc in
  porous media.
• Vycor Tc 2.05 K
• Geltech (44 Å) Tc 1.92 K
• Geltech (25 Å) Tc 1.0 K
• At temperatures Tc lt Tc lt T?
• - BEC is localized by disorder
• - No extended phase coherence across the
  sample
• - No superflow

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BEC, Excitations, and Superfluidity
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Excitations of superfluid 4He at pressures up to
40 bars
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Excitations of superfluid 4He at pressures up to
40 bars
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Phonon_roton Excitations-Pressure Dependence
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-Yamamoto et al, cond-mat/0310375 (Oct 2003)
Phase Diagram of Gelsil (Geltech) - 25 A Diameter
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Momentum distribution solid 4He
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Momentum distribution solid 4He
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Momentum distribution solid 4He
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Momentum distribution solid 4He
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Momentum distribution 4He
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Liquid 4He at Negative Pressure
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Bauer et al. 2000
Phase Diagram of Liquid 4He at
Negative pressures
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Bauer et al. 2000
Phonon-Roton energies at p 0 and p - 9 bar
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Liquid 4He at Negative Pressure in Porous Media
Liquid is attracted to pore walls MCM-41, d
47 Layers form on walls first Then pores
fill completely at a density less than bulk
density. Liquid is stretched between walls at
lower than normal density (pressure is
negative).
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Liquid 4He at Negative Pressure MCM-41
Adsorption isotherm Pores are full with 4He at
negative pressure at fillings C to H. C -5.5
bar.
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Liquid 4He at Negative Pressure
at Q 1.5 -1 as a function
of filling. H full filling, p 0. C
negative pressure, p -5.5 bar
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Liquid 4He at Negative Pressure
Dispersion curve at SVP and - 5 bar
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Liquid 4He at Negative Pressure
Maxon energy at Q 1.1 Å-1 as a function of
pressure.
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Excitations of superfluid 4He at pressures up to
40 bars
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Condensate fraction bulk 4HeMoroni and
Boninmsegni JLTP (2004)
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-Yamamoto et al, Phys. Rev Lett. (2004)
Phase Diagram of Gelsil (Geltech) - 25 A Diameter
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-Yamamoto et al, Phys. Rev. Lett. (2004)
Superfluid Density in Gelsil (Geltech) 25 A
diameter
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Pressure dependence of phonon (Q 0.7 ?-1)and
roton (Q2.1Å-1)
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Phonon-roton energies bulk 4He
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Superfluidity
Landau Theory Superfluidity follows from the
nature of the excitations
that there are phonon-roton
excitations only and no other low energy
excitations to which superfluid can decay have a
critical velocity and an energy gap (roton gap
?).
Via P-R excitations, superflow arises from
BEC. BEC and Phase Coherence, Ø
(r) Superfluidity follows directly from BEC,
phase conherence .
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Landau
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London
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Neutron Scattering ILL
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Glyde, Fak, et al. PRB (2000)
S(Q,w) of liquid 3He at SVP -spin density (low
E) -density (high E)
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Filling Dependence of Roton and Layer Modes
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Excitations and BEC in Liquid 4He A
R Sakhel and H R Glyde- reveal role of
condensate in determining S(Q,?), especially its
temperature dependence-consider wave vectors
Beyond the Roton (Q gt 2.5 Å-1)
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Beyond the Roton in Liquid 4He
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Beyond the Roton in Bulk Liquid 4He
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Beyond the Roton in Bulk Liquid 4He
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Beyond the Roton in Liquid 4He
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Beyond the Roton in Bulk Liquid 4He
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Beyond the Roton in Bulk Liquid 4He
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Excitations and Bose-Einstein Condensation in
Quantum Liquids in Disorder Henry R. Glyde,
University of Delaware, DMR-9972011
Figure 2. Discussing analsis of neutron
scattering data at Delaware are (left to right)
Zhicheng Yan, Richard Azuah, Assad Sakhel,
Jonathan DuBois, and Henry Glyde.
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Roton in Bulk Liquid 4He Multiexcitation
Response
Talbot et al., PRB, 38, 11229 (1988)
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Phonon-Roton Energy
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Liquid 4He at Negative Pressure
Dispersion curve as a function of filling. H
p 0. C -5.5 bar
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Beyond the Roton in Liquid 4He
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Beyond the Roton in Liquid 4He
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Phonon in Bulk Liquid 4He Q 0.4 Å-1
Stirling and Glyde, PRB, 41, 4224 (1990)
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Layer Mode in Vycor and Aerogel
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Beyond the Roton in Liquid 4He
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Beyond the Roton in Bulk Liquid 4He
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Beyond the Roton in Liquid 4He
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Bose-Einstein Condensation
Condensate Fraction
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Topic of Talk

• Well defined p-r excitations (Q gt 0.8 Å) exist
  because there is Bose-Einstein condensation
  (BEC).
• Measure superfluid density ?s (T) and determine
  the normal to superfluid transition temperature
  Tc in Vycor (same sample). Find
• Tc 2.05 K lt T? 2.17 K
• (Vycor) (Bulk)
• - disorder suppresses Tc below T?
• Find well defined phononroton excitations in
  Vycor at temperatures T gt Tc, up to T T? 2.17
  K
• Thus BEC in Vycor above Tc , at temperatures
• Tc lt T lt T? . - localized BEC.

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Quantum Liquids in Confinement
Huang and Meng (1992) Dilute Bose gas in
disorder (T OK). Disorder potential
arises from hard sphere impurities placed at
random. Condensate fraction Superfluid
density where Astrakharchik et al (2002)
-- Monte Carlo extension to Bose fluid.

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Quantum Liquids in Confinement
Giorgini et al. (1994) Same model as Huang
Meng -- disorder arising from random
impurities Sound velocity Half width of
phonons
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Quantum Liquids in Confinement
Lopatin and Vinokur (2002) Same model as Huang
Meng -- disorder arising from random
impurities Reduction of critical temperature for
BEC by disorder Reduction of critical
temperature for superfluidity by disorder.
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-Yamamoto et al, cond-mat/0310375 (Oct 2003)
Superfluid Density in Gelsil (Geltech) 25 A
diameter
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Liquid 4He in Disorder and Boson Localization -
Vycor

• Well defined p-r excitations (Q gt 0.8 Å) exist
  because there is Bose-Einstein condensation
  (BEC).
• Measure superfluid density ?s (T) and determine
  the normal to superfluid transition temperature
  Tc in Vycor (same sample). Find
• Tc 2.05 K lt T? 2.17 K
• (Vycor) (Bulk)
• - disorder suppresses Tc below T?
• Find well defined phononroton excitations in
  Vycor at temperatures T gt Tc, up to T T? 2.17
  K
• Thus BEC in Vycor above Tc , at temperatures
• Tc lt T lt T? . - localized BEC.

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Phonons in bcc solid 4He
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Graduate Students
Jonathan DuBois Bose-Einstein Condensation of
Bosons in Traps, Variational Monte Carlo,
Diffusion MC Asaad Sakhel Models of
excitations in liquid 4He BEC in
traps Souleymane Omar Diallo Neutron
scattering measurements at ISIS, n(p) of solid
4He, condensate and n(p) in liquid 3He/4He
mixtures Ali Shams Models of localization of
BEC in porous media
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Liquid 4He in Disorder and Boson Localization
Francesco Albergamo - Institute Laue-Langevin,
Grenoble, France Henry R. Glyde -
University of Delaware David R. Daughton -
University of Delaware Norbert Mulders -
University of Delaware Jaques Bossy - Centre
de Recherche sur Les Tres Basses
Températures, Grenoble, France Helmut
Schober - Institute Laue-Langevin,
Grenoble, France
Albergamo et al., Phys. Rev. B69, 014514 (2004)