2,512 research outputs found
Credible Group Stability in Many-to-Many Matching Problems
It is known that in two-sided many-to-many matching problems, pairwise stable matchings may not be immune to group deviations, unlike in many- to-one matching problems (Blair 1988). In this paper, we show that pairwise stability is equivalent to credible group stability when one side has responsive preferences and the other side has categorywise- responsive preferences. A credibly group-stable matching is immune to any âexecutableâ group deviations with an appropriate definition of executability. Under the same preference restriction, we also show the equivalence between the set of pairwise-stable matchings and the set of matchings generated by coalition-proof Nash equilibria of an appropriately defined strategic-form game.
Relation between Confinement and Chiral Symmetry Breaking in Temporally Odd-number Lattice QCD
In the lattice QCD formalism, we investigate the relation between confinement
and chiral symmetry breaking. A gauge-invariant analytical relation connecting
the Polyakov loop and the Dirac modes is derived on a temporally odd-number
lattice, where the temporal lattice size is odd, with the normal (nontwisted)
periodic boundary condition for link-variables. This analytical relation
indicates that low-lying Dirac modes have little contribution to the Polyakov
loop, and it is numerically confirmed at the quenched level in both confinement
and deconfinement phases. This fact indicates no direct one-to-one
correspondence between confinement and chiral symmetry breaking in QCD. Using
the relation, we also investigate the contribution from each Dirac mode to the
Polyakov loop. In the confinement phase, we find a new "positive/negative
symmetry" of the Dirac-mode matrix element of the link-variable operator, and
this symmetry leads to the zero value of the Polyakov loop. In the
deconfinement phase, there is no such symmetry and the Polyakov loop is
nonzero. Also, we develop a new method for spin-diagonalizing the Dirac
operator on the temporally odd-number lattice modifying the Kogut-Susskind
formalism.Comment: 15pages, 9 figure
Credible Group Stability in Multi-Partner Matching Problems
It is known that in two-sided many-to-many matching markets, pair-wise stability is not logically related with the (weak) core, unlike in many-to-one matching markets (Blair, 1988). In this paper, we seek a theoretical foundation for pairwise stability when group deviations are allowed. Group deviations are defined in graphs on the set of agents. We introduce executable group deviations in order to discuss the credibility of group deviations and to defined credibly group stable matchings. We show, under responsive preferences, that credible group stability is equivalent to pairwise stability in the multi-partner matching problem that includes two-sided matching problems as special cases. Under the same preference restriction, we also show the equivalence between the set of pairwise stable matchings and the set of matchings generated by coalition-proof Nash equilibria of an appropriately defined strategic form game. However, under a weaker preference restriction, substitutability, these equivalences no longer hold, since pairwise stable matchings may be strictly Pareto-ordered, unlike under responsiveness.Multi-partner matching problem, Pairwise stable matching network, Credible group deviation
Quark tensor charge and electric dipole moment within the Schwinger-Dyson formalism
We calculate the tensor charge of the quark in the QCD-like theory in the
Landau gauge using the Schwinger-Dyson formalism. It is found that the dressed
tensor charge of the quark is significantly suppressed against the bare quark
contribution, and the result agrees qualitatively with the analyses in the
collinear factorization approach and lattice QCD. We also analyze the quark
confinement effect with the phenomenological strong coupling given by
Richardson, and find that this contribution is small. We show that the
suppression of the quark tensor charge is due to the superposition of the spin
flip of the quark arising from the successive emission of gluons which dress
the tensor vertex. We also consider the relation between the quark and the
nucleon electric dipole moments by combining with the simple constituent quark
model.Comment: 16 pages, 11 figures. arXiv admin note: text overlap with
arXiv:1401.285
Lattice analysis for the energy scale of QCD phenomena
We formulate a new framework in lattice QCD to study the relevant energy
scale of QCD phenomena. By considering the Fourier transformation of link
variable, we can investigate the intrinsic energy scale of a physical quantity
nonperturbatively. This framework is broadly available for all lattice QCD
calculations. We apply this framework for the quark-antiquark potential and
meson masses in quenched lattice QCD. The gluonic energy scale relevant for the
confinement is found to be less than 1 GeV in the Landau or Coulomb gauge.Comment: 4 pages, 4 figure
Some Relations for Quark Confinement and Chiral Symmetry Breaking in QCD
We analytically study the relation between quark confinement and spontaneous
chiral-symmetry breaking in QCD. In terms of the Dirac eigenmodes, we derive
some formulae for the Polyakov loop, its fluctuations, and the string tension
from the Wilson loop. We also investigate the Polyakov loop in terms of the
eigenmodes of the Wilson, the clover and the domain wall fermion kernels,
respectively. For the confinement quantities, the low-lying Dirac/fermion
eigenmodes are found to give negligible contribution, while they are essential
for chiral symmetry breaking. These relations indicate no direct one-to-one
correspondence between confinement and chiral symmetry breaking in QCD, which
seems to be natural because confinement is realized independently of the quark
mass
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