CCNU Jisheng Chen Aug 2006 Aug 2006 Universal

CCNU, Ji-sheng Chen Aug, 2006

Aug, 2006,

Universal thermodynamics of Dirac fermions near the unitary limit regime and BEC-BCS crossover Ji-sheng Chen Phys Dep. , CCNU, Wuhan 430079 chenjs@iopp. ccnu. edu. cn CCNU, Ji-sheng Chen Aug, 2006

Contents 1. Motivations 2. The universal dimensionless coefficient ξand energy gap Δ 3. Conclusions and prospects Aug, 2006,

1. Motivation Phase 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! Manybody effects Aug, 2006,

Many-Body Physics A challenging topic: 1, Strong coupled limit 2, Long-range force/correlating~thermodynamics Statistical 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 ke i l e l dominates c parti ical s s a l C r Aug, 2006, behavio Low Temperature: Underlying quantum behavior revealed tum n a u Q vior a h e b ike l e v wa

Quantum Coherence Intellectually Exciting: Counterintuitive, Fundamental part of nature Single particle “textbook” physics Correlated Many-body physics -Connections to other fields Condensed Matter, Nuclear Technology: Precision Measurement, Navigation, Sensing Aug, 2006, Direct Applications: Quantum Computing, Quantum Information Processing

Full description of （Condensed Matter) Phase diagram a, Astrophysics b, Heavy ion collisions c, Strongly correlated electrons d, Cosmology 。。。 Aug, 2006,

Collective correlating; Ground state：Ladder diagram ressumation 1、Binding energy: K, Kc, symmetry energy coefficient, isospin… 2、Pairing Correlations: … Aug, 2006,

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Ultra-Cold dilute degenerate atomic fermions gas(quantum effects) n n BEC vs BCS: Cross-Over Near the Feshbach resonance, the bare scattering lengths between two-body particles diverge! Aug, 2006,

Novel Physics Key point: ”physics” Aug, 2006,

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Unitary limit, |a| diverges(main characteristic). Short range force but long-range correlation, system details “erased”! n Dilute unitary gas: not “ideal free Fermi gas. ” n Aug, 2006,

n n 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 thermodynamics properties n Aug, 2006,

This ξ attracts much attention in recent years Too many updating works 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. Aug, 2006,

MBX n A challenging topic in contemporary physics: Related to many realistic problems Bewitching in the fundamental Fermi-Dirac statistics Even closely related with the SU(Nc) physics, e. g. , 1. nucl-th/0606019, T Schaefer, From Trapped Atoms to Liberated Quarks 1. nucl-th/0606046, E. V. Shuryak, Locating strongly coupled color superconductivity using universality and experiments with trapped ultracold atoms Aug, 2006,

Its exact value/how to approach? n n 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? Carlo for , 0. 44 ) (2003), simulation, “More accurate” 0. 42 Quantum Monte Carlsonnet al. , PRL, 91, 050401( Δ/μ=1. 2 example PRL(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. PRL 95, 030404 (2005) ( mat/0608154 2, Local density functional theory? At finite T? Aug, 2006,

More challenging topic: the superfluid phase transition temperature Tc/energy gap 0. 05 -1. 5 At the unitary cross-over point, the superfluid transition temperature is also of the order of the Fermi kinetic energy and thus the weakcoupling 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,

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n Aug, 2006, cond-mat/0608282 v 1 11 Aug 2006

Try to obtain the analytical results with a novel approach! n n n Analogism between the ultra-cold atoms and infrared singularity in gauge theory Consider it from another point of view Return to non-relativistic limit Make a detour Aug, 2006,

Motivation: Topology similar to Feshbach resonance Anti-screened “vector boson” propagator with a negative Debye mass squared m=1 Key point: ”physics” Aug, 2006, Landau Pole?

To address this topic from the fundamental “gauge” theory A, Construct a simple Model: “QED” ; B, Thomson Problem as a arm to attack this problem Aug, 2006,

Why and how? n n n 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,

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Gauge invariance ensured by the Lorentz transversality condition with HLS: Aug, 2006,

General expressions for energy density and pressure as well as entropy Aug, 2006,

Generalized Renormalizaion condition Aug, 2006,

At T=0 n Tailor Aug, 2006,

Reasonablely consistent with the BCS theory but with an effective scattering length n n n Non-relativistic limit With the relativistic expression through odd-even staggering Non-relativistic limit, Tc ≈ 0. 157 Tf Relativistic limit: Tc ≈ 0. 252 Tf Aug, 2006, Statistical weight factor 5/3 4/3

Main result for two-dimensions n n 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 Fractional Quantum Hall Effect gas Aug, 2006, Kondo Physics, Confinement

ong range correlation controls the global behaviors of the system d=2, ξ =0 Quantum Many-body Effect Aug, 2006, Similar to this diagram? Strong repulsion leads to “attraction”

Ising universal class controversial: 2 -D ξ =1? ? ? Relativistic limit, ξ =7/9 d<2, Unstable, no phase transition d=2, ξ =0 Non-relativistic limit, ξ=0. 44 Aug, 2006, or 4/9

A new type of fermions superfluity for d=3 n n Stability: sound speed squared still positive Rough work n n Aug, 2006, Specific heat capacity, bulk and shear viscosity of fermions, … Polarized fermion gas, …

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. n 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 n binding energy. Communications with many active experts. Aug, The 2006, sound speed detection can judge this dilemma.

Extending to finite a Unitary limit regime with finite scattering length at both T and density Mean field theory: the lowest order Aug, 2006,

Repulsive approaches to effective attraction Main results of nucl-th/0602065 n n 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 Aug, 2006, relativistic approaches to thermodynamics

D-dimensions: nucl-th/0608063 Aug, 2006,

3. Conclusions and Prospects a. Non trivial screening effects Anti-screened(off-shell) vector boson propagator Coupled Dyson-Schwinger equations “instead of” the involved integral equations of Fock-like exchange Effective interaction: Landau pole “contribution” Infinite Feynman Diagrams But not conventional resummation Aug, 2006,

B, Highlights: many-body physics a, In-medium vector condensation formalism Lorentz violation may be an important tool within the frame of continuum field theory b, 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! Aug, 2006,