Download - Universal thermodynamics of Dirac fermions near the unitary limit regime and BEC-BCS crossover
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CCNU, Ji-sheng Chen Aug, 2006
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Aug, 2006,
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CCNU, Ji-sheng Chen Aug, 2006
Universal thermodynamics of Dirac fermions near the unitary limit regime and BEC-BCS crossover
Ji-sheng ChenPhys Dep., CCNU, Wuhan 430079
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Aug, 2006,
Contents1.Motivations
2. The universal dimensionless coefficient ξand energy gap Δ
3. Conclusions and prospects
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1. MotivationPhase transtion and phase structure
a 、 Changes of symmetry is the central topic of physics (nuclear physics, condensed physics, high energy physics etc.)
b 、 Through in-medium Lorentz violation! Many-body effects
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Aug, 2006,
Many-Body PhysicsA challenging topic:1, Strong coupled limit2, Long-range
force/correlating~thermodynamicsStatistical physics:microscopic
dynamics approach the macroscopic thermodynamics?
Clear dynamics~unclear thermodynamics
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Aug, 2006,
Why Study Ultra-Cold Gases?Answer: Coherent Quantum
Phenomena
High Temperature:Random thermal motion dominates
Low Temperature:Underlying quantum behavior revealed
Quantum wave-like
behaviorClassical particle-like
behavior
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Aug, 2006,
Quantum Coherence
Technology:Precision Measurement,
Navigation, Sensing
Direct Applications:Quantum Computing,
Quantum Information Processing
Intellectually Exciting:Counterintuitive,
Fundamental part of nature
Single particle “textbook” physics
Correlated Many-body physics-Connections to other fields
Condensed Matter, Nuclear
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Aug, 2006,
Full description of ( Condensed Matter) Phase diagram
a,Astrophysicsb,Heavy ion collisionsc,Strongly correlated electronsd,Cosmology。。。
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Aug, 2006,
Collective correlating;Ground state : Ladder diagram ressumation1 、 Binding energy:K,Kc, symmetry energy coefficient,isospin…2 、 Pairing Correlations:…
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Aug, 2006,
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Aug, 2006,
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Aug, 2006,
Ultra-Cold dilute degenerate atomic fermions gas(quantum effects) BEC vs BCS: Cross-Over Near the Feshbach resonance, the bare scattering lengths between two-body particles diverge!
| |a 6 9(10 ), (10 )T K T nK
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Aug, 2006,
Novel Physics
Key point:”physics”
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Aug, 2006,
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Aug, 2006,
Unitary limit, |a| diverges(main characteristic).
Short range force but long-range correlation, system details “erased”!
Dilute unitary gas: not “ideal free Fermi gas.”
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Universal property: dimensional analysis, the only dimensionful parameter is the Fermi momentum . The corresponding energy scale is the Fermi kinetic energy The system details do not contribute to the thermodynamics properties
fk
2
2fkm
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Aug, 2006,
Various approaches tried and results differ remarkably.
1,The “theoretical results” ξ ∼ 0.3 − 0.6. 2,Experimental results quite different, ξ ≈
0.74±0.07[5], ξ = 0.51±0.04[6], ξ ≈ 0.7[7], ξ = 0.27+0.12−0.09[8].
New result is about ξ=0.46 ±0.05, Science 311, 503 (2006)
3, The lattice result ξ = 0.25 ± 0.03 of Lee Dean et al.
This ξ attracts much attention in recent yearsToo many updating works
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Aug, 2006,
A challenging topic in contemporary physics: Related to many realistic problems
Bewitching in the fundamental Fermi-Dirac statisticsEven closely related with the SU(Nc) physics, e.g.,1. nucl-th/0606019, T Schaefer,From Trapped Atoms to Liberated Quarks1. nucl-th/0606046, E.V. Shuryak, Locating strongly coupled color superconductivity using universality and experiments with trapped ultracold atoms
MBX
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Aug, 2006,
Its exact value/how to approach? MFT? No, “go beyond” MFT For example, epsilon expansion (Incorporate T?) cond-mat/0604500, Y Nishida, D T Son
Phys. Rev. Lett. 97, 050403 (2006)(ξ=0.475,Δ/μ=1.31 or Δ/Ef=0.62 )
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Aug, 2006,
1, 20-40 particles extending to infinite particles system, eliable? Quantum Monte Carlo simulation, for example
Carlson et al., PRL, 91, 050401(0.44) (2003), “More accurate” 0.42, Δ/μ=1.2 PRL(2005)PRL 95, 030404 (2005) (0.42) PRL 96, 090404 (2006)(0.42)…Tc=0.23 Tf;Phys. Rev. Lett. 96, 160402 (2006): 0.493, Tc =0.15 Tf. New result “More exact” 0.44, Tc=0.25 Tf, cond-mat/0608154
2, Local density functional theory? At finite T?
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Aug, 2006,
More challenging topic: the superfluid phase transition temperature Tc/energy gap0.05-1.5At the unitary cross-over point, the
superfluid transition temperature is also of the order of the Fermi kinetic energy
and thus the weak-coupling theories such as the BCS- or the
Bogoliubov-type are not applicable.The differences for energy gap Δ can be as large as several times even with Monte Carlo
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Aug, 2006,
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Aug, 2006,
cond-mat/0608282 v1 11 Aug 2006
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Aug, 2006,
Try to obtain the analytical results with a novel approach! Analogism between the ultra-cold
atoms and infrared singularity in gauge theory
Consider it from another point of view
Return to non-relativistic limitMake a detour
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Motivation:Topology similar to Feshbach resonance
Key point:”physics”Landau Pole?
Anti-screened “vector boson” propagator with a negative Debye mass squared m=1
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Aug, 2006,
To address this topic from the fundamental “gauge” theoryA,Construct a simple Model: “QED” ; B, Thomson Problem as a arm to attack this problem
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Why and how? Let the fermion have an “electric” charge g Should be stabilized by a fictive opposite charged Thomson background in the meantime Simultaneously with other internal global U(1)(“hypercharge”) symmetry quantum numbers(Similar to the lepton number of electric charged electrons)
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Gauge invariance ensured by the Lorentz transversalitycondition with HLS: 0A
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General expressions for energy density and pressure as well as entropy
0 ,|BA m n
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Generalized Renormalizaion condition
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At T=0 Tailor
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Non-relativistic limit relativistic limit With the relativistic expression
through odd-even staggering
4 / 9
255 /1818 2
ff
km
Non-relativistic limit, Tc ≈ 0.157 Tf4 / 9 fk Relativistic limit: Tc ≈ 0.252 T
f
7 / 9
Statistical
weight factor
5/34/3
Reasonablely consistent with the BCS theory but with an effective scattering length
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Aug, 2006,
Main result for two-dimensions Can even approach the extreme occasion
S/V=P=E/V=0 for fermions at unitary, Surprisingly similar to Bose-Einstein Condensation of 3-dimensional for ideal Bose gas
0
Fractional Quantum Hall EffectKondo Physics, Confinement
*m
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Aug, 2006,
d=2, ξ =0Similar to this
diagram?Strong repulsion leads
to “attraction”
Long range correlation controls the global behaviors of the system
Quantum Many-body Effect
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Aug, 2006,
Ising universal classcontroversial: 2-D ξ =1???
d
Relativistic limit, ξ =7/9
Non-relativistic limit, ξ=0.44 or 4/9
d<2, Unstable, no phase transitiond=2, ξ =0
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Aug, 2006,
A new type of fermions superfluity for d=3
Stability: sound speed squared still positive
Rough work Specific heat capacity, bulk and shear
viscosity of fermions, … Polarized fermion gas,…
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Aug, 2006,
A Dilemma Thermodynamics university hypothesis Problem, d=3, T=0 P=2/3 E/V for ideal fermion/bose gas P<2/3 E/V for non-ideal gas Can be found in any statistical physics text books. At unitary, P=2/3 E/V??? Many arguments in the literature: due to the scaling property, similar to ideal gas?We find P=1/4 E/V, different from that for ideal fermion gas due to the implicit pairing correlation contribution to binding
energy. Communications with many active experts.The sound speed detection can judge this dilemma.
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Aug, 2006,
Extending to finite aUnitary limit regime with finite scattering length at both T and density
Mean field theory:
the lowest order
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Aug, 2006,
Exactly approach some of the experimental and quantum Monte Carlo simulation results
Same analytical result with power counting, James V. Steele, nucl-th/0010066
non-relativistic framework and T=0
Facilitates the comparison of non-relativistic and relativistic approaches to thermodynamics
4 / 9
54 / 9, , 0.157 , 1/ 4 / ,1847 / 9, , 0.252 , 1/ 7 / , lim9
f c f
f c f
E T T P E V non relativistic
E T T P E V Ultra relativistic it
Main results of nucl-th/0602065
Repulsive approaches to effective attraction
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Aug, 2006,
D-dimensions:nucl-th/0608063
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Aug, 2006,
3.Conclusions and Prospectsa.Non trivial screening effectsAnti-screened(off-shell) vector boson propagatorCoupled Dyson-Schwinger equations “instead of” the involved integral equations of Fock-like exchange
Effective interaction: Landau pole
“contribution”
Infinite Feynman DiagramsBut not conventional resummation
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Aug, 2006,
B,Highlights:many-body physicsa, In-medium vector condensation formalism Lorentz violation may be an important tool within the frame of continuum field theoryb,Classical Thomson Problem(Newton third law) may be a potential non-perturbative tool to address the long range universal fluctuations and correlations. Critical phenomena:MFT?Rich phase structure for hot and dense system~quantum Hall effects, Landau levels...
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Aug, 2006,
1,To boldly approach the unitary topic with the exact “QED”
2,Classical Thomson Problem/Newton third law as a tool to approach the quantum phase transition physics(classical universal thermodynamics)
3,With the unknown side to solve the other unknown side
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Aug, 2006,
Thank You!