Bose-Einstein Condensation and Superfluidity

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Bose-Einstein Condensation and Superfluidity
Gordon Baym University of Illinois,
Urbana January 2004
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Fermions (Fermi-Dirac, 1926) Particles that
obey the exclusion principle (Pauli, 1925).
Cant put two in same state at the same time.
Bosons (Bose-Einstein, 1924-5) Particles that
dont obey the exclusion principle. Can put many
in the same state at the same time
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S. Bose
A. Einstein
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S.N. Bose 1924 concept of light quanta as
particles with 2 polarization states. New
statistics gt Planck distribution
A. Einstein 1924 Extension to monoatomic ideal
gases
Condensation
Condensate
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I maintain that in this case a number of
molecules steadily growing with increasing
density goes over in the first quantum state ...
a separation is affected one part condenses,
the rest remains a saturated ideal gas.
A. Einstein, 1925
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Bose-Einstein Condensation
Hot atoms (bosons) in a box Cool below
Bose-Einstein transition temperature At
absolute zero temperature motion ceases
Bose-Einstein condensate
Gravity
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Free Bose gas
Potential well (trap)
Box
In condensed system have macroscopic occupation
of single (generally lowest) mode
ground state
flow state (vortex)
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MANY-PARTICLE WAVE FUNCTION
condensate wave function
FINITE TEMPERATURE
Thermal wavelength
No. condensed particles
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Which statistics apply to nature? i.e., is
ordinary matter made of fermions or bosons?
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The Fermi-Dirac solution ... is probably the
correct one for gas molecules, since it is known
to be the correct one for electrons in an atom,
and one would expect molecules to resemble
electrons more closely than light quanta.

P.A.M. Dirac, 1926
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With a heavy heart I have become converted to
the idea that Fermi , not Einstein-Bose, is the
correct statistics for electrons.
W. Pauli to E. Schrödinger, Nov. 1926
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Superfluid 4He The first Bose-Einstein
condensate
W.H. Keesom and Miss A.P. Keesom (1935)
specific heat of liquid helium F.London (1938)
Spectroscopic data gt 4He obeys Bose-Einstein
statistics The strange change of state of
liquid helium at 2.19 o abs., even though it
occurs in the liquid and not in the gaseous
state, is due to the condensation mechanism of
the Bose-Einstein gas.
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It seems difficult not to imagine a connexion
with the condensation phenomenon of the
Bose- Einstein statistics. (London, 1938)
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Superfluid Liquid Helium
1938
(Tony Leggett)
Temperatures below Lambda point 2.17o
above absolute zero
Flows through tiny capillaries without friction
Flows around a closed pipe forever

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Spin bucket of superfluid helium slowly.
Helium liquid remains at rest! Spin fast
enough. Form vortex in center of liquid!
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L. Landau (1941) rejects suggestion
that helium-II should be considered as a
degenerate ideal Bose gas. Importance of
interactions!
ROLE OF STATISTICS Sydoriak, Grilley, and
Hammel (1948) liquified 3He. Osborne, Winstock,
and Abraham (1948) no superflow down to 1.05
K. Bose character critical to superfluidity
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Order parameter of Bose-condensed system
-- 0 in normal system -- constant in BEC
complex order parameter
Free particle state, Ngt
If Ngt and N-1gt differ only by number of
particles in condensate then
In weakly interacting Bose gas
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Time dependent order parameter
condensate wave function
condensate density
superfluid velocity
chemical potential
superfluid acceleration eqn.
Equilibrium
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Flow and superfluidity
Complex order parameter
gt flow
Superfluid velocity Superfluid mass density
Normal mass density
Momentum density of superfluid flow rs vs
Condensate density differs from superfluid mass
density
At T0 in 4He, rs r, n0 0.09 n
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BOSE CONDENSED SYSTEMS
Low temperature systems of bosons liquid 4He
trapped bosonic atoms excitons in
semiconductors (?) Nuclear matter pion
condensation kaon condensation Vacuum as Bose
condensed state Chiral symmetry breaking
Gluon condensation Higgs condensation
Graviton condensation, gmn
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PION CONDENSED MATTER
Softening of collective spin-isospin oscillation
of nuclear matter
Above critical density have transition to new
state with nucleons rotated in isospin space
with formation of macroscopic pion field
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Important, if it exists, for enhanced cooling of
neutron stars by neutrino emission
Transition density very sensitive to effective
particle-hole interactions (Landau g) and D-hole
interactions
Analogous neutral pion condensate can coexist
with
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STRANGENESS (KAON) CONDENSATES
Analogous to p condensate Chiral SU(3) X SU(3)
symmetry of strong interactions gt effective
low energy interaction
Kaplan and Nelson (1986), Brown et al. (1994)
Effective mass term lowers K energies in matter
gt condensation
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Rotate u and s quark states
Form
condensate Admix in n
in p
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Results very sensitive to K- interactions in
matter (Pandharipande, Pethick and Vesteinn,
1995) -
Would soften equation of state and lower
maximum neutron star mass to 1.5 solar masses
Would enhance neutrino luminosity and cooling of
neutron stars Can also form
condensate gt macroscopic ? field
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Condensates in vacuum
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EXPERIMENTAL BOSE-EINSTEIN DECONDENSATION
Ultrarelativistic heavy ion collisions 2000
RHIC 100 GeV/A 100 GeV/A colliding
beams 2007? LHC 2600 GeV/A 2600 GeV/A
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Relativistic Heavy Ion Collider (RHIC)
(Brookhaven, NY)
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Break chiral symmetry in different state?
(Disordered chiral condensate?)
Np 104, V 103 fm3 p- BEC unlikely
entropy too high
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Applications in Biology
A strong proponent of the idea that Bose-Einstein
condensation may provide the unitary sense of
self that seems to be characteristic of
consciousness, in relation to Fröhlichs ideas
is Ian Marshall (1989)
R. Penrose, Shadows of the Mind (1994)
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Application to the Movies
Information, Adaptive Contracting, Distributional
Dynamics, Bayesian Choice, Bose-Einstein
Statistics and the Movies
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