universal thermodynamics of dirac fermions near the unitary limit regime and bec-bcs crossover
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CCNU, Ji-sheng Chen Aug, 2006
Aug, 2006,
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
chenjs@iopp.ccnu.edu.cn
Aug, 2006,
Contents1.Motivations
2. The universal dimensionless coefficient ξand energy gap Δ
3. Conclusions and prospects
Aug, 2006,
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
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
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
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
Aug, 2006,
Full description of ( Condensed Matter) Phase diagram
a,Astrophysicsb,Heavy ion collisionsc,Strongly correlated electronsd,Cosmology。。。
Aug, 2006,
Collective correlating;Ground state : Ladder diagram ressumation1 、 Binding energy:K,Kc, symmetry energy coefficient,isospin…2 、 Pairing Correlations:…
Aug, 2006,
Aug, 2006,
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
Aug, 2006,
Novel Physics
Key point:”physics”
Aug, 2006,
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.”
Aug, 2006,
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
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
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
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 )
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?
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
Aug, 2006,
Aug, 2006,
cond-mat/0608282 v1 11 Aug 2006
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
Aug, 2006,
Motivation:Topology similar to Feshbach resonance
Key point:”physics”Landau Pole?
Anti-screened “vector boson” propagator with a negative Debye mass squared m=1
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
Aug, 2006,
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)
Aug, 2006,
Aug, 2006,
Aug, 2006,
Gauge invariance ensured by the Lorentz transversalitycondition with HLS: 0A
Aug, 2006,
General expressions for energy density and pressure as well as entropy
0 ,|BA m n
Aug, 2006,
Generalized Renormalizaion condition
Aug, 2006,
At T=0 Tailor
Aug, 2006,
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
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
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
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
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,…
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.
Aug, 2006,
Extending to finite aUnitary limit regime with finite scattering length at both T and density
Mean field theory:
the lowest order
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
Aug, 2006,
D-dimensions:nucl-th/0608063
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
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...
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
Aug, 2006,
Thank You!
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