Finite-Temperature and -Density QED: Schwinger-Dyson Equation in the Real-Time Formalism

Based on the real-time formalism, especially, on Thermo Field Dynamics, we derive the Schwinger-Dyson gap equation for the fermion propagator in QED and Four-Fermion model at finite-temperature and -density. We discuss some advantage of the real-time formalism in solving the self-consistent gap equation, in comparison with the ordinary imaginary-time formalism. Once we specify the vertex function, we can write down the SD equation with only continuous variables without performing the discrete sum over Matsubara frequencies which cannot be performed in advance without further approximation in the imaginary-time formalism. By solving the SD equation obtained in this way, we find the chiral-symmetry restoring transition at finite-temperature and present the associated phase diagram of strong coupling QED. In solving the SD equation, we consider two approximations: instantaneous-exchange and $p_0$-independent ones. The former has a direct correspondence in the imaginary time formalism, while the latter is a new approximation beyond the former, since the latter is able to incorporate new thermal effects which has been overlooked in the ordinary imaginary-time solution. However both approximations are shown to give qualitatively the same results on the finite-temperature phase transition.Comment: 28 pages+15 figures (figures: not included, available upon request

Spin triplet superconductivity with line nodes in Sr2RuO4

Several possible odd-parity states are listed up group-theoretically and examined in light of recent experiments on Sr$_2$RuO$_4$. Those include some of the $f$-wave pairing states, {\mib d}({\mib k})\propto{\hat{\mib z}} k_xk_y(k_x + {\rm i}k_y) and {\hat{\mib z}} (k_x^2-k_y^2)(k_x + {\rm i}k_y) and other {\hat{\mib z}} (k_x + {\rm i}k_y)\cos ck_z ($c$ is the $c$-axis lattice constant) as most plausible candidates. These are time-reversal symmetry broken states and have line nodes running either vertically (the former two) or horizontally (the latter), consistent with experiments. Characterizations of these states and other possibilities are given.Comment: 4 pages, no figure

Lower bounds on Hilbert-Kunz multiplicities and maximal F-signature

ABSTRACT. Hilbert–Kunz multiplicity and F-signature are numerical invariants of commutative rings in positive characteristic that measure severity of singularities: for a regular ring both invariants are equal to one and the converse holds under mild assumptions. A natural question is for what singular rings these invariants are closest to one. For Hilbert–Kunz multiplicity this question was first considered by the last two authors and attracted significant attention. In this paper, we study this question, i.e., an upper bound, for F-signature and revisit lower bounds on Hilbert–Kunz multiplicity.La Caixa Junior Leader Postdoctoral Fellowship: LCF/BQ/PI21/1183003

Brownian dynamics around the core of self-gravitating systems

We derive the non-Maxwellian distribution of self-gravitating $N$-body systems around the core by a model based on the random process with the additive and the multiplicative noise. The number density can be obtained through the steady state solution of the Fokker-Planck equation corresponding to the random process. We exhibit that the number density becomes equal to that of the King model around the core by adjusting the friction coefficient and the intensity of the multiplicative noise. We also show that our model can be applied in the system which has a heavier particle. Moreover, we confirm the validity of our model by comparing with our numerical simulation.Comment: 11 pages, 4 figure

Scanning tunneling spectroscopic studies of the pairing state of cuprate superconductors

Quasiparticle tunneling spectra of both hole-doped (p-type) and electron-doped (n-type) cuprates are studied using a low-temperature scanning tunneling microscope. The results reveal that neither the pairing symmetry nor the pseudogap phenomenon is universal among all cuprates, and that the response of n-type cuprates to quantum impurities is drastically different from that of the p-type cuprates. The only ubiquitous features among all cuprates appear to be the strong electronic correlation and the nearest-neighbor antiferromagnetic Cu2+-Cu2+ coupling in the CuO2 planes

Orbital selectivity of the kink in the dispersion of Sr2RuO4

We present detailed energy dispersions near the Fermi level on the monolayer perovskite ruthenate Sr2RuO4, determined by high-resolution angle-resolved photoemission spectroscopy. An orbital selectivity of the kink in the dispersion of Sr2RuO4 has been found: A kink for the Ru 4d_xy orbital is clearly observed, but not for the Ru 4d_yz and 4d_zx ones. The result provides insight into the origin of the kink.Comment: 5 pages, 4 figures. Accepted for publication in Phys. Rev.

Real Space Imaging of Spin Polarons in Zn Doped SrCu2(BO3)2

We report on the real space profile of spin polarons in the quasi two-dimensional frustrated dimer spin system SrCu2(BO3)2 doped with 0.16% of Zn. The 11B nuclear magnetic resonance spectrum exhibits 15 additional boron sites near non-magnetic Zn impurities. With the help of exact diagonalizations of finite clusters, we have deduced from the boron spectrum the distribution of local magnetizations at the Cu sites with fine spatial resolution, providing direct evidence for an extended spin polaron. The results are confronted with those of other experiments performed on doped and undoped samples of SrCu2(BO3)2.Comment: 9 pages, 11 figures, including supplemental materials. accepted for publication in PR