Relativistic BCS-BEC crossover at zero temperature

He, Lianyi; Zhuang, Pengfei

doi:10.1103/physrevd.75.096003

Cited by 41 publications

(28 citation statements)

References 16 publications

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“…Going through the standard steps of converting the random matrix theory to a sigmamodel we find in the limit N → ∞ that g RMT ν (Ĵ) = g ν ( √ 2NĴ), which shows that the random-matrix partition function is equivalent to the finite-volume partition function, 45 provided that the dimensionless random-matrix diquark sources and singular values (i.e., the square roots of the eigenvalues of A T A) are related to the physical quantities bŷ…”

Section: Intermediate Densitymentioning

confidence: 93%

“…This phenomenon is called (relativistic) BEC-BCS crossover. It passes a number of nontrivial tests [21,22,26], and its possible realization in dense quark matter in QCD has been investigated in various model calculations [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] (see also [43][44][45][46][47][48] for related models). In view of the known relation between ∆ and the Dirac eigenvalues [12,15], a natural question arises: How is the diquark condensate ψψ reflected in the 3 To evade the sign problem, one has to assume an even number of flavors with degenerate quark masses in the β = 1 and β = 2 cases.…”

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confidence: 99%

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Singular values of the Dirac operator in dense QCD-like theories

Kanazawa

Wettig

Yamamoto

2011

J. High Energ. Phys.

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We study the singular values of the Dirac operator in dense QCD-like theories at zero temperature. The Dirac singular values are real and nonnegative at any nonzero quark density. The scale of their spectrum is set by the diquark condensate, in contrast to the complex Dirac eigenvalues whose scale is set by the chiral condensate at low density and by the BCS gap at high density. We identify three different low-energy effective theories with diquark sources applicable at low, intermediate, and high density, together with their overlapping domains of validity. We derive a number of exact formulas for the Dirac singular values, including Banks-Casher-type relations for the diquark condensate, Smilga-Stern-type relations for the slope of the singular value density, and Leutwyler-Smilga-type sum rules for the inverse singular values. We construct random matrix theories and determine the form of the microscopic spectral correlation functions of the singular values for all nonzero quark densities. We also derive a rigorous index theorem for non-Hermitian Dirac operators. Our results can in principle be tested in lattice simulations.Comment: 3 references added, version published in JHE

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Section: Intermediate Densitymentioning

confidence: 93%

mentioning

confidence: 99%

Singular values of the Dirac operator in dense QCD-like theories

Kanazawa

Wettig

Yamamoto

2011

J. High Energ. Phys.

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“…In flat space the relativistic BCS/BEC crossover has been studied in [36,37]. From the dual boundary field theory perspective this new ingredient corresponds to an explicit scalar operator of scaling dimension…”

Section: Fermionic Ordering In Holographymentioning

confidence: 99%

Pairing induced superconductivity in holography

Bagrov

Meszena

Schalm

2014

J. High Energ. Phys.

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We study pairing induced superconductivity in large N strongly coupled systems at finite density using holography. In the weakly coupled dual gravitational theory the mechanism is conventional BCS theory. An IR hard wall cut-off is included to ensure that we can controllably address the dynamics of a single confined Fermi surface. We address in detail the interplay between the scalar order parameter field and fermion pairing. Adding an explicitly dynamical scalar operator with the same quantum numbers as the fermion-pair, the theory experiences a BCS/BEC crossover controlled by the relative scaling dimensions. We find the novel result that this BCS/BEC crossover exposes resonances in the canonical expectation value of the scalar operator. This occurs not only when the scaling dimension is degenerate with the Cooper pair, but also with that of higher derivative paired operators. We speculate that a proper definition of the order parameter which takes mixing with these operators into account stays finite nevertheless.

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“…First, an ordinary BCS-BEC crossover may occur, though the critical temperature in the BEC region no longer tends towards an upper bound, due to relativistic effects. Second, the nonrelativistic BEC state undergoes a transition to a relativisitc BEC (RBEC) state, in which the critical temperature increases to the order of the Fermi energy [15] (see also [16][17][18][19][20] for additional work on the BCS-BEC crossover in relativistic matter).…”

Section: Introductionmentioning

confidence: 99%

Bose-Einstein condensate strings

Harkó

Lake

2015

Phys. Rev. D

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We consider the possible existence of gravitationally bound general relativistic strings consisting of Bose-Einstein condensate (BEC) matter which is described, in the Newtonian limit, by the zero temperature time-dependent nonlinear Schr\"odinger equation (the Gross-Pitaevskii equation), with repulsive interparticle interactions. In the Madelung representation of the wave function, the quantum dynamics of the condensate can be formulated in terms of the classical continuity equation and the hydrodynamic Euler equations. In the case of a condensate with quartic nonlinearity, the condensates can be described as a gas with two pressure terms, the interaction pressure, which is proportional to the square of the matter density, and the quantum pressure, which is without any classical analogue though, when the number of particles in the system is high enough, the latter may be neglected. Assuming cylindrical symmetry, we analyze the physical properties of the BEC strings in both the interaction pressure and quantum pressure dominated limits, by numerically integrating the gravitational field equations. In this way we obtain a large class of stable stringlike astrophysical objects, whose basic parameters (mass density and radius) depend sensitively on the mass and scattering length of the condensate particle, as well as on the quantum pressure of the Bose-Einstein gas.Comment: 22 pages, 24 figures. Published versio

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Relativistic BCS-BEC crossover at zero temperature

Cited by 41 publications

References 16 publications

Singular values of the Dirac operator in dense QCD-like theories

Singular values of the Dirac operator in dense QCD-like theories

Pairing induced superconductivity in holography

Bose-Einstein condensate strings

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