Quiver varieties and a noncommutative P²

To any finite group Γ ⊂ SL₂(ℂ) and each element t in the center of the group algebra Of Γ we associate a category, Coh(ℙ²_(Γ, τ),ℙ¹). It is defined as a suitable quotient of the category of graded modules over (a graded version of) the deformed preprojective algebra introduced by Crawley-Boevey and Holland. The category Coh(ℙ²_(Γ, τ),ℙ¹) should be thought of as the category of coherent sheaves on a ‘noncommutative projective space’, ℙ²_(Γ, τ), equipped with a framing at ℙ¹, the line at infinity. Our first result establishes an isomorphism between the moduli space of torsion free objects of Coh(ℙ²_(Γ, τ),ℙ¹) and the Nakajima quiver variety arising from G via the McKay correspondence. We apply the above isomorphism to deduce a generalization of the Crawley-Boevey and Holland conjecture, saying that the moduli space of ‘rank 1’ projective modules over the deformed preprojective algebra is isomorphic to a particular quiver variety. This reduces, for Γ = {1}, to the recently obtained parametrisation of the isomorphism classes of right ideals in the first Weyl algebra, A₁, by points of the Calogero– Moser space, due to Cannings and Holland and Berest and Wilson. Our approach is algebraic and is based on a monadic description of torsion free sheaves on ℙ²_(Γ, τ). It is totally different from the one used by Berest and Wilson, involving τ-functions

Charge asymmetry of pions in the process e−e+→e−e+π+π−e^-e^+\to e^-e^+\pi^+\pi^-

The study of the charge asymmetry of produced particles allows to investigate the interference of different production mechanisms and to determine new features of the corresponding amplitudes. In the process $e^- e^+ \to e^- e^+ \pi^+ \pi^-$ the two-pion system is produced via two mechanisms: two-photon (C-even state) and bremsstrahlung (C-odd state) production. We study the charge asymmetry of pions in a differential in the pion momenta cross section originating from an interference between these two mechanisms. At low effective mass of dipions this asymmetry is directly related to the s- and p-phases of elastic $\pi\pi$ scattering. At higher energies it can give new information about the $f_0$ meson family, $f_2(1270)$ meson, etc. The asymmetry is expressed via the pion form factor $F_\pi$ and helicity amplitudes $M_{ab}$ for the subprocess $\gamma^*\gamma\to \pi^+\pi^-$ as $\sum G_{ab}{\rm Re}(F_\pi^*M_{ab})$ where we have calculated analytically the coefficients $G_{ab}$ for the region giving the main contribution to the effect. Several distributions of pions are presented performing a numerical analysis in a model with point-like pions. In the region near the dipion threshold the asymmetry is of the order of 1%. We show that with suitable cuts the signal to background ratio can be increased up to about 10%.Comment: 16 pages, 10 figures, LaTeX, style files for EPJC include

On details of the thermodynamical derivation of the Ginsburg--Landau equations

We examine the procedure of thermodynamical derivation of the Ginsburg--Landau equation for current, which is given unclear and contradictory interpretations in existing textbooks. We clarify all steps of this procedure and find as a consequence a limitation on the validity range of the thermodynamic Ginsburg--Landau theory, which does not seem to be explicitely stated up to now: we conclude that the thermodynamic theory is applicable only to a superconducting specimen that is not a part of an external current-carrying loop.Comment: 11 pages. Accepted for publication in 'Superconductor Science and Technology

Experimental study of magneto-superconductor RuSr2Eu1.5Ce0.5Cu2O10: Effect of Mo doping on magnetic behavior and Tc variation

Mo doped ruthenocuprates Ru1-xMoxSr2Eu1.5Ce0.5Cu2O10 are synthesized for x = 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0, and their magnetic and superconducting properties are studied. It has been found that the magnetic transition temperature TZFCpeak, which corresponds to the appearance of weak ferromagnetic effect, decreases from its value of 75 K for x = 0.0 to 22 K, 25 K and 18 K, respectively for the x = 0.2, 0.4 and 0.6 samples. Another finding is that the magnetic susceptibility reduces at TZFCpeak by a factor of about 6, 85 and 413 for x = 0.2, 0.4, and 0.6 respectively. The samples of x = 0.8 and 1.0 are found to have no magnetic or superconducting effects. The values of the superconducting transition temperature are obtained from the resistivity versus temperature data. An important result is that Tc increases by 4.5 K and 7.0 K for x = 0.2 and 0.4 respectively, and then decreases by 17 K for x = 0.6. The observed variation of Tc with x has been explained in terms of a theory which combines the effects of weakening magnetic behavior and reducing carrier concentration in a phenomenological manner. The resulting theory is found to provide a good agreement with the observed value of Tc.Comment: 14 pages with Text + Figs. To Appear in PHYS. REV. B, Ist Jan. 2006 issu

Is the term "type-1.5 superconductivity" warranted by Ginzburg-Landau theory?

It is shown that within the Ginzburg-Landau (GL) approximation the order parameters Delta1(r, T) and Delta2(r, T) in two-band superconductors vary on the same length scale, the difference in the zero-T coherence lengths xi0_i ~vF_i/Delta_i(0), i = 1, 2 notwithstanding. This amounts to a single physical GL parameter kappa and the classic GL dichotomy: kappa < 1/sqrt(2) for type-I and kappa > 1/sqrt(2) for type-II.Comment: 5 pages, revised and extended version; previous title "Two-band superconductors near Tc" change

Hydromagnetic instabilities in protoneutron stars

The stability properties of newly born neutron stars, or proto--neutron stars, are considered. We take into account dissipative processes, such as neutrino transport and viscosity, in the presence of a magnetic field. In order to find the regions of the star subject to different sorts of instability, we derive the general instability criteria and apply it to evolutionary models of PNSs. The influence of the magnetic field on instabilities is analyzed and the critical magnetic field stabilizing the star is obtained. In the light of our results, we estimate of the maximum poloidal magnetic field that might be present in young pulsars or magnetars.Comment: 18 pages, 4 figures, to appear in Astrophysical Journa

Softer than normal, but not as soft as one might think: Spontaneous flux lattices in ferromagnetic spin-triplet superconductors

A theory is developed for the spontaneous vortex lattice that is expected to occur in the ferromagnetic superconductors ZrZn_2, UGe_2, and URhGe, where the superconductivity is likely of spin-triplet nature. The long-wavelength fluctuations of this spontaneous flux lattice are predicted to be huge compared to those of a conventional flux lattice, and to be the same as those for spin-singlet ferromagnetic superconductors. It is shown that these fluctuations lead to unambiguous experimental signatures which may provide the easiest way to observe the spontaneous flux lattice.Comment: 4pp, 1 eps fi

Origin of Orthorhombic Transition, Magnetic Transition, and Shear Modulus Softening in Iron Pnictide Superconductors: Analysis based on the Orbital Fluctuation Theory

The main features in iron-pnictide superconductors are summarized as (i) the orthorhombic transition accompanied by remarkable softening of shear modulus, (ii) high-Tc superconductivity close to the orthorhombic phase, and (iii) stripe-type magnetic order induced by orthorhombicity. To present a unified explanation for them, we analyze the multiorbital Hubbard-Holstein model with Fe-ion optical phonons based on the orbital fluctuation theory. In the random-phase-approximation (RPA), a small electron-phonon coupling constant ($\lambda ~ 0.2$) is enough to produce large orbital (=charge quadrupole) fluctuations. The most divergent susceptibility is the $O_{xz}$-antiferro-quadrupole (AFQ) susceptibility, which causes the s-wave superconductivity without sign reversal (s_{++}-wave state). At the same time, divergent development of $O_{x2-y2}$-ferro-quadrupole (FQ) susceptibility is brought by the "two-orbiton process" with respect to the AFQ fluctuations, which is absent in the RPA. The derived FQ fluctuations cause the softening of $C_{66}$ shear modulus, and its long-range-order not only triggers the orthorhombic structure transition, but also induces the instability of stripe-type antiferro-magnetic state. In other words, the condensation of composite bosons made of two orbitons gives rise to the FQ order and structure transition. The theoretically predicted multi-orbital-criticality presents a unified explanation for abovementioned features of iron pnictide superconductors.Comment: 19 pages, 15 figure

Full one-loop QCD and electroweak corrections to sfermion pair production in γγ\gamma \gamma collisions

We have calculated the full one-loop electroweak (EW) and QCD corrections to the third generation scalar-fermion pair production processes $e^+e^- \to \gamma \gamma \to \tilde{f_i}\bar{\tilde{f_i}} (f=t,b,\tau)$ at an electron-positron linear collider(LC) in the minimal supersymmetric standard model (MSSM). We analyze the dependence of the radiative corrections on the parameters such as the colliding energy $\sqrt{\hat s}$ and the SUSY fundamental parameters $A_f$, $\tan \beta$, $\mu$, $M_{SUSY}$ and so forth. The numerical results show that the EW corrections to the squark-, stau-pair production processes and QCD corrections to the squark-pair production processes give substantial contributions in some parameter space. The EW relative corrections to squark-pair production processes can be comparable with QCD corrections at high energies. Therefore, these EW and QCD corrections cannot be neglected in precise measurement of sfermion pair productions via $\gamma\gamma$ collision at future linear colliders.Comment: to be appeared in Phys. Rev.