The spin resonance and high frequency optical properties of the cuprates

We argue that recently observed superconductivity-induced blue shift of the plasma frequency $\delta \omega_{pl}$ in $Bi_2Sr_2CaCu_2O_{8+\delta}$ is related to the change in the integrated dynamical structure factor associated with the development of the spin resonance below $T_c$. We show that the magnitude of $\delta \omega_{pl}$ is consistent with the small integrated spectral weight of the resonance, and its temperature dependences closely follow that of the spin resonance peak.Comment: 5 pages, 3 figure

Complexity of Bradley-Manna-Sipma Lexicographic Ranking Functions

In this paper we turn the spotlight on a class of lexicographic ranking functions introduced by Bradley, Manna and Sipma in a seminal CAV 2005 paper, and establish for the first time the complexity of some problems involving the inference of such functions for linear-constraint loops (without precondition). We show that finding such a function, if one exists, can be done in polynomial time in a way which is sound and complete when the variables range over the rationals (or reals). We show that when variables range over the integers, the problem is harder -- deciding the existence of a ranking function is coNP-complete. Next, we study the problem of minimizing the number of components in the ranking function (a.k.a. the dimension). This number is interesting in contexts like computing iteration bounds and loop parallelization. Surprisingly, and unlike the situation for some other classes of lexicographic ranking functions, we find that even deciding whether a two-component ranking function exists is harder than the unrestricted problem: NP-complete over the rationals and $\Sigma^P_2$-complete over the integers.Comment: Technical report for a corresponding CAV'15 pape

Quantum-critical superconductivity in underdoped cuprates

We argue that the pseudogap phase may be an attribute of the non-BCS pairing of quantum-critical, diffusive fermions near the antiferromagnetic quantum critical point. We derive and solve a set of three coupled Eliashberg-type equations for spin-mediated pairing and show that in some $T$ range below the pairing instability, there is no feedback from superconductivity on fermionic excitations, and fermions remain diffusive despite of the pairing. We conject that in this regime, fluctuations of the pairing gap destroy the superconducting condensate but preserve the leading edge gap in the fermionic spectral function.Comment: 5 pages, 3 figure

The Waldmeier Effect in Sunspot Cycles

We discuss two aspects of the Waldmeier Effect, namely (1) the rise times of sunspot cycles are anti-correlated to their strengths (WE1) and (2) the rates of rise of the cycles are correlated to their strengths (WE2). From analysis of four different data sets we conclude that both WE1 and WE2 exist in all the data sets. We study these effects theoretically by introducing suitable stochastic fluctuations in our regular solar dynamo model.Comment: Magnetic Coupling between the Interior and Atmosphere of the Sun; Astrophysics and Space Science Proceeding

On Multiphase-Linear Ranking Functions

Multiphase ranking functions ($\mathit{M{\Phi}RFs}$) were proposed as a means to prove the termination of a loop in which the computation progresses through a number of "phases", and the progress of each phase is described by a different linear ranking function. Our work provides new insights regarding such functions for loops described by a conjunction of linear constraints (single-path loops). We provide a complete polynomial-time solution to the problem of existence and of synthesis of $\mathit{M{\Phi}RF}$ of bounded depth (number of phases), when variables range over rational or real numbers; a complete solution for the (harder) case that variables are integer, with a matching lower-bound proof, showing that the problem is coNP-complete; and a new theorem which bounds the number of iterations for loops with $\mathit{M{\Phi}RFs}$. Surprisingly, the bound is linear, even when the variables involved change in non-linear way. We also consider a type of lexicographic ranking functions, $\mathit{LLRFs}$, more expressive than types of lexicographic functions for which complete solutions have been given so far. We prove that for the above type of loops, lexicographic functions can be reduced to $\mathit{M{\Phi}RFs}$, and thus the questions of complexity of detection and synthesis, and of resulting iteration bounds, are also answered for this class.Comment: typos correcte

A New Approximate Min-Max Theorem with Applications in Cryptography

We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max theorem and convex approximation techniques, offering quantitative improvements over the standard way of using min-max theorems as well as more concise and elegant proofs

Coherent vs incoherent pairing in 2D systems near magnetic instability

We study the superconductivity in 2D fermionic systems near antiferromagnetic instability, assuming that the pairing is mediated by spin fluctuations. This pairing involves fully incoherent fermions and diffusive spin excitations. We show that the competition between fermionic incoherence and strong pairing interaction yields the pairing instability temperature $T_{ins}$ which increases and saturates as the magnetic correlation length $\xi \to \infty$. We argue that in this quantum-critical regime the pairing problem is qualitatively different from the BCS one.Comment: 7 pages, 2 figure

Hydrodynamics and the Detection of the QCD Axial Anomaly in Heavy Ion Collisions

We consider the experimental implications of the axial current triangle diagram anomaly in a hydrodynamic description of high density QCD. We propose a signal of an enhanced production of spin-excited hadrons in the direction of the rotation axis in off-central heavy ion collisions.Comment: 15 pages, 19 figures; v2: refs added, minor changes to the plots; v3, comments adde