Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators

Utilising some recent ideas from our bilinear bi-parameter theory, we give an efficient proof of a two-weight Bloom type inequality for iterated commutators of linear bi-parameter singular integrals. We prove that if $T$ is a bi-parameter singular integral satisfying the assumptions of the bi-parameter representation theorem, then $$\| [b_k,\cdots[b_2, [b_1, T]]\cdots]\|_{L^p(\mu) \to L^p(\lambda)} \lesssim_{[\mu]_{A_p}, [\lambda]_{A_p}} \prod_{i=1}^k\|b_i\|_{{\rm{bmo}}(\nu^{\theta_i})} ,$$ where $p \in (1,\infty)$, $\theta_i \in [0,1]$, $\sum_{i=1}^k\theta_i=1$, $\mu, \lambda \in A_p$, $\nu := \mu^{1/p}\lambda^{-1/p}$. Here $A_p$ stands for the bi-parameter weights in $\mathbb R^n \times \mathbb R^m$ and ${\rm{bmo}}(\nu)$ is a suitable weighted little BMO space. We also simplify the proof of the known first order case.Juan de la Cierva - Formación 2015 FJCI-2015-24547, BCAM Severo Ochoa excellence accreditation SEV-2013-032

Spin dynamics in highly polarized silver at negative absolute temperatures

We have studied the spin dynamics of highly polarized silver nuclei at negative absolute temperatures up to inverted polarizations p≃-70%. The measured NMR spectra at B=0.4 and 0.8 mT display a clear inverted suppression-enhancement effect, arising from an interaction between the two spin species, 107Ag and 109Ag. The averaged interaction-field description accounts well for the intensity ratio of the isotopic NMR lines. The frequency difference of the absorption maxima has been used to study the merging and repulsion of the NMR modes at large negative polarizations. At B=0.2 mT, our spectra display only a single exchange-merged line, indicating that the two isotopes act as like spins. The transition from a single NMR line to two separate lines proceeds in a similar fashion as at positive temperatures. No effects attributable to the tendency of ferromagnetic alignment of spins at T<0 were observed.Peer reviewe

Perturbative QCD at non-zero chemical potential: Comparison with the large-Nf limit and apparent convergence

The perturbative three-loop result for the thermodynamic potential of QCD at finite temperature and chemical potential as obtained in the framework of dimensional reduction is compared with the exact result in the limit of large flavor number. The apparent convergence of the former as well as possibilities for optimization are investigated. Corresponding optimized results for full QCD are given for the case of two massless quark flavors.Comment: REVTEX4, 4 pages, 3 color figures. v2: fig. 3 now includes also lattice data for two-flavor QCD at nonzero chemical potentia

The pressure of deconfined QCD for all temperatures and quark chemical potentials

We present a new method for the evaluation of the perturbative expansion of the QCD pressure which is valid at all values of the temperature and quark chemical potentials in the deconfined phase and which we work out up to and including order g^4 accuracy. Our calculation is manifestly four-dimensional and purely diagrammatic -- and thus independent of any effective theory descriptions of high temperature or high density QCD. In various limits, we recover the known results of dimensional reduction and the HDL and HTL resummation schemes, as well as the equation of state of zero-temperature quark matter, thereby verifying their respective validity. To demonstrate the overlap of the various regimes, we furthermore show how the predictions of dimensional reduction and HDL resummed perturbation theory agree in the regime T~\sqrt{g}*mu. At parametrically smaller temperatures T~g*mu, we find that the dimensional reduction result agrees well with those of the nonstatic resummations down to the remarkably low value T~0.2 m_D, where m_D is the Debye mass at T=0. Beyond this, we see that only the latter methods connect smoothly to the T=0 result of Freedman and McLerran, to which the leading small-T corrections are given by the so-called non-Fermi-liquid terms, first obtained through HDL resummations. Finally, we outline the extension of our method to the next order, where it would include terms for the low-temperature entropy and specific heats that are unknown at present.Comment: 45 pages, 21 figures; v2: minor corrections and clarifications, references added; v3: Fig 16 added, version accepted for publication in PR

Bilinear representation theorem

We represent a general bilinear Calderón--Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so called sparse $T1$ theorem for bilinear singular integrals.Juan de la Cierva - Formaci\'on 2015 FJCI-2015-24547, Academy of Finland grants 294840 and 306901, National Science Foundation Grant No. DMS-1440140

Two-color QCD via dimensional reduction

We study the thermodynamics of two-color QCD at high temperature and/or density using a dimensionally reduced superrenormalizable effective theory, formulated in terms of a coarse grained Wilson line. In the absence of quarks, the theory is required to respect the Z(2) center symmetry, while the effects of quarks of arbitrary masses and chemical potentials are introduced via soft Z(2) breaking operators. Perturbative matching of the effective theory parameters to the full theory is carried out explicitly, and it is argued how the new theory can be used to explore the phase diagram of two-color QCD.Comment: 17 pages, 1 eps figure, jheppub style; v2: minor update, references added, published versio