Correlation of optical conductivity and ARPES spectra of strong-coupling large polarons and its display in cuprates

Common approach is used to calculate band due to strong-coupling large polaron (SCLP) photodissociation in ARPES and in optical conductivity (OC) spectra. It is based on using the coherent-states representation for the phonon field in SCLP. The calculated positions of both band maximums are universal functions of one parameter - the SCLP binding energy Ep: ARPES band maximum lies at binding energy about 3.2Ep; the OC band maximum is at the photon energy about 4.2Ep. The half-widths of the bands are mainly determined by Ep and slightly depend on Frohlich electron-phonon coupling constant: for its value 6-8 the ARPES band half-width is 1.7-1.3Ep and the OC band half-width is 2.8-2.2Ep. Using these results one can predict approximate position of ARPES band maximum and half-width from the maximum of mid-IR OC band and vice versa. Comparison of the results with experiments leads to a conclusion that underdoped cuprates contain SCLPs with Ep=0.1-0.2 eV that is in good conformity with the medium parameters in cuprates. The values of the polaron binding energy determined from experimental ARPES and OC spectra of the same material are in good conformity too: the difference between them is within 10 percent.Comment: 17 pages, 6 figure

Conjugacy in Baumslag's group, generic case complexity, and division in power circuits

The conjugacy problem belongs to algorithmic group theory. It is the following question: given two words x, y over generators of a fixed group G, decide whether x and y are conjugated, i.e., whether there exists some z such that zxz^{-1} = y in G. The conjugacy problem is more difficult than the word problem, in general. We investigate the complexity of the conjugacy problem for two prominent groups: the Baumslag-Solitar group BS(1,2) and the Baumslag(-Gersten) group G(1,2). The conjugacy problem in BS(1,2) is TC^0-complete. To the best of our knowledge BS(1,2) is the first natural infinite non-commutative group where such a precise and low complexity is shown. The Baumslag group G(1,2) is an HNN-extension of BS(1,2). We show that the conjugacy problem is decidable (which has been known before); but our results go far beyond decidability. In particular, we are able to show that conjugacy in G(1,2) can be solved in polynomial time in a strongly generic setting. This means that essentially for all inputs conjugacy in G(1,2) can be decided efficiently. In contrast, we show that under a plausible assumption the average case complexity of the same problem is non-elementary. Moreover, we provide a lower bound for the conjugacy problem in G(1,2) by reducing the division problem in power circuits to the conjugacy problem in G(1,2). The complexity of the division problem in power circuits is an open and interesting problem in integer arithmetic.Comment: Section 5 added: We show that an HNN extension G = < H, b | bab^-1 = {\phi}(a), a \in A > has a non-amenable Schreier graph with respect to the base group H if and only if A \neq H \neq

Algebraic Geometry over Free Metabelian Lie Algebra I: U-Algebras and Universal Classes

This paper is the first in a series of three, the aim of which is to lay the foundations of algebraic geometry over the free metabelian Lie algebra $F$. In the current paper we introduce the notion of a metabelian Lie $U$-algebra and establish connections between metabelian Lie $U$-algebras and special matrix Lie algebras. We define the $\Delta$-localisation of a metabelian Lie $U$-algebra $A$ and the direct module extension of the Fitting's radical of $A$ and show that these algebras lie in the universal closure of $A$.Comment: 34 page

A Practical Cryptanalysis of the Algebraic Eraser

Anshel, Anshel, Goldfeld and Lemieaux introduced the Colored Burau Key Agreement Protocol (CBKAP) as the concrete instantiation of their Algebraic Eraser scheme. This scheme, based on techniques from permutation groups, matrix groups and braid groups, is designed for lightweight environments such as RFID tags and other IoT applications. It is proposed as an underlying technology for ISO/IEC 29167-20. SecureRF, the company owning the trademark Algebraic Eraser, has presented the scheme to the IRTF with a view towards standardisation. We present a novel cryptanalysis of this scheme. For parameter sizes corresponding to claimed 128-bit security, our implementation recovers the shared key using less than 8 CPU hours, and less than 64MB of memory.Comment: 15 pages. Updated references, with brief comments added. Minor typos corrected. Final version, accepted for CRYPTO 201

Quadratic equations over free groups are NP-complete

We prove that the problems of deciding whether a quadratic equation over a free group has a solution is NP-complete

Discriminating Groups

A group G is termed discriminating if every group separated by G is discriminated by G. In this paper we answer several questions concerning discrimination which arose from [2]. We prove that a finitely generated equationally Noetherian group G is discriminating if and only if the quasivariety generated by G is the minimal universal class containing G. Among other results, we show that the non-abelian free nilpotent groups are non-discriminating. Finally we list some open problems concerning discriminating groups

Clinical and epidemiological characteristics of outbreaks of acute intestinal diarrheal infections

Group carried out epidemiological investigation of the incidence of acute intestinal infections of unknown etiology. Analysis of long-term dynamics of the incidence of acute enteric infections, the population of the city of Rybinsk in 2002 – 2006 he was shown on the epidemiological significance of these infections on the analyzed area. Specific factors of transmission of enteric pathogens on the basis of analysis of existing materials have not been established, but the analysis of risk factors can be said about the dominance of food factor in the transmission of the epidemic process of acute intestinal infections. In order to identify the etiology of acute intestinal infections should be more widely applied in practice techniques for the detection of viral agents in epidemiological investigations