965 research outputs found
A Lemma for a Strong Comparison Principle of Nonlinear Parabolic Equations
In this note, we prove a lemma for a strong comparison principle of nonlinear parabolic equations. We shall prove a function which is a viscosity subsolution minus a viscosity supersolution of the equation becomes a viscosity subsolution of a parabolic equation which may not coincide with the original equation. Thanks to a strong maximum principle of nonlinear parabolic equations we have a strong comparison principle
Reinterpretation of the Starobinsky model
The Starobinsky model of inflation, consistent with Planck 2015, has a
peculiar form of the action, which contains the leading Einstein term , the
term with a huge coefficient, and negligible higher-order terms. We
propose an explanation of this form based on compactification of extra
dimensions. Once tuning of order is accepted to suppress the linear
term , we no longer have to suppress higher-oder terms, which give
nontrivial corrections to the Starobinsky model. We show our predictions of the
spectral index, its runnings, and the tensor-to-scalar ratio. Finally, we
discuss a possibility that quantum gravity may appear at the scale GeV.Comment: 13 pages, 2 figures; published version, references and discussion on
the uncertainties of the predictions adde
Josephson effect in a multi-orbital model for SrRuO
We study Josephson current between s-wave/spin-triplet superconductor
junctions by taking into account details of band structures in
SrRuO such as three conduction bands, spin-orbit interaction in the
bulk and that at the interface. We assume five superconducting order parameters
in SrRuO: a chiral p-wave symmetry and four helical p-wave
symmetries. We calculate current-phase relationship in these
junctions, where is the macroscopic phase difference between two
superconductors. The results for a chiral p-wave pairing symmetry show that
term appears in the current-phase relation due to time-reversal
symmetry (TRS) breaking. On the other hand, term is absent in
the helical pairing states which preserve the TRS. We also study the dependence
of maximum Josephson current on an external magnetic flux in a
corner junction. The calculated results of show a relation
in a chiral state and
in a helical state. We calculate in a
corner and a symmetric SQUIDs geometry. In a symmetric SQUID geometry, the
relation is satisfied for all the pairing states and
it is impossible to distinguish chiral state from helical one. On the other
hand, results for a corner SQUID always show
and for a chiral and a helical states, respectively.
Experimental tests of these relations in a corner junctions and SQUIDs may
serve as a tool for unambiguous determination of the pairing symmetry in
SrRuO
Space-Time and Matter in IIB Matrix Model - gauge symmetry and diffeomorphism -
We pursue the study of the type IIB matrix model as a constructive definition
of superstring. In this paper, we justify the interpretation of space-time as
distribution of eigenvalues of the matrices by showing that some low energy
excitations indeed propagate in it. In particular, we show that if the
distribution consists of small clusters of size , low energy theory acquires
local SU(n) gauge symmetry and a plaquette action for the associated gauge
boson is induced, in addition to a gauge invariant kinetic term for a massless
fermion in the adjoint representation of the SU(n). We finally argue a possible
identification of the diffeomorphism symmetry with permutation group acting on
the set of eigenvalues, and show that the general covariance is realized in the
low energy effective theory even though we do not have a manifest general
covariance in the IIB matrix model action.Comment: 25 page
Atiyah-Patodi-Singer index on a lattice
We propose a non-perturbative formulation of the Atiyah-Patodi-Singer(APS)
index in lattice gauge theory, in which the index is given by the
invariant of the domain-wall Dirac operator. Our definition of the index is
always an integer with a finite lattice spacing. To verify this proposal, using
the eigenmode set of the free domain-wall fermion, we perturbatively show in
the continuum limit that the curvature term in the APS theorem appears as the
contribution from the massive bulk extended modes, while the boundary
invariant comes entirely from the massless edge-localized modes.Comment: 14 pages, appendices added, details of key equations added, typos
corrected, to appear in PTE
Scaling Behaviors of Branched Polymers
We study the thermodynamic behavior of branched polymers. We first study
random walks in order to clarify the thermodynamic relation between the
canonical ensemble and the grand canonical ensemble. We then show that
correlation functions for branched polymers are given by those for
theory with a single mass insertion, not those for the theory
themselves. In particular, the two-point function behaves as , not as
, in the scaling region. This behavior is consistent with the fact that
the Hausdorff dimension of the branched polymer is four.Comment: 17 pages, 3 figure
Sarcoidosis-associated hepatocellular carcinoma
Sarcoidosis is a systemic granulomatous inflammation of unknown etiology, and seems to involve the liver parenchyma in most cases. However, sarcoidosis-associated hepatocellular carcinoma is rare. We report here a case in which a hepatocellular carcinoma occurred within the liver, which was probably involved as a result of systemic sarcoidosis. A 57-year-old Japanese man had been followed up for 2 years because of diabetic nephropathy and sarcoidosis. On admission for pneumonia, imaging studies revealed an unexpected hepatic tumor. Histology revealed a hepatocellular carcinoma accompanied by T-lymphocytic infiltration and marked granulomatous inflammation, which was surrounding some tumor nodules. The background liver parenchyma exhibited a moderate degree of fibrosis with granulomatous inflammation. The patient had no other apparent liver disease such as viral hepatitis, steatohepatitis, or primary biliary cirrhosis. Therefore, in the present case, sarcoidosis may be considered the probable background etiology for hepatocarcinogenesis
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