Towards understanding thermal jet quenching via lattice simulations

After reviewing how simulations employing classical lattice gauge theory permit to test a conjectured Euclideanization property of a light-cone Wilson loop in a thermal non-Abelian plasma, we show how Euclidean data can in turn be used to estimate the transverse collision kernel, C(k⊥), characterizing the broadening of a high-energy jet. First results, based on data produced recently by Panero et al, suggest that C(k⊥) is enhanced over the known NLO result in a soft regime k⊥ < a few T. The shape of k3⊥ C(k⊥) is consistent with a Gaussian at small k⊥.

Lattice NRQCD study of in-medium bottomonium states using Nf = 2+1, 48³ × 12 HotQCD configurations

The behavior of bottomonium state correlators at non-zero temperature, 140.4(β = 6.664) ≤ T ≤ 221(β = 7.280) (MeV), where the transition temperature is 154(9) (MeV), is studied, using lattice NRQCD on 48³ ×12 HotQCD HiSQ action configurations with light dynamical Nf = 2+1 (mu,s/ms = 0.05) staggered quarks. In order to understand finite temperature effects on quarkonium states, zero temperature behavior of bottomonium correlators is compared based on 32⁴ (β = 6.664,6.800 and 6.950) and 48³ ×64 (β = 7.280) lattices. We find that temperature effects on S-wave bottomoniumstates are small but P-wave bottomoniumstates show a noticeable temperature dependence above the transition temperature.

Quantum Simulation of Non-Abelian Lattice Gauge Theories

We use quantum link models to construct a quantum simulator for U(N) and SU(N) lattice gauge theories. These models replace Wilson’s classical link variables by quantum link operators, reducing the link Hilbert space to a finite number of dimensions. We show how to embody these quantum link models with fermionic matter with ultracold alkaline-earth atoms using optical lattices. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can thus address the corresponding dynamics in real time. Using exact diagonalization results we show that these systems share qualitative features with QCD, including chiral symmetry breaking and we study the expansion of a chirally restored region in space in real time.

O(N) Models with Topological Lattice Actions

A variety of lattice discretisations of continuum actions has been considered, usually requiring the correct classical continuum limit. Here we discuss “weird” lattice formulations without that property, namely lattice actions that are invariant under most continuous deformations of the field configuration, in one version even without any coupling constants. It turns out that universality is powerful enough to still provide the correct quantum continuum limit, despite the absence of a classical limit, or a perturbative expansion. We demonstrate this for a set of O(N) models (or non-linear σ-models). Amazingly, such “weird” lattice actions are not only in the right universality class, but some of them even have practical benefits, in particular an excellent scaling behaviour.

Interfaces, strings, and a soft mode in the square lattice quantum dimer model

The quantum dimer model on the square lattice is a U(1) gauge theory that addresses aspects of the physics of high-Tc superconductors. Using a quantum Monte Carlo method, we show that the theory exists in a confining columnar valence bond solid phase. The interfaces separating distinct columnar phases display plaquette order, which, however, is not realized as a bulk phase. Static “electric” charges are confined by flux tubes that consist of multiple strands, each carrying a fractionalized flux ¼. A soft pseudo-Goldstone mode (which becomes exactly massless at the Rokhsar-Kivelson point) extends deep into the columnar phase, with potential implications for high-Tc physics.

Holes localized on a Skyrmion in a doped antiferromagnet on the honeycomb lattice: Symmetry analysis

Using the low-energy effective field theory for hole-doped antiferromagnets on the honeycomb lattice, we study the localization of holes on Skyrmions, as a potential mechanism for the preformation of Cooper pairs. In contrast to the square lattice case, for the standard radial profile of the Skyrmion on the honeycomb lattice, only holes residing in one of the two hole pockets can get localized. This differs qualitatively from hole pairs bound by magnon exchange, which is most attractive between holes residing in different momentum space pockets. On the honeycomb lattice, magnon exchange unambiguously leads to f-wave pairing, which is also observed experimentally. Using the collective-mode quantization of the Skyrmion, we determine the quantum numbers of the localized hole pairs. Again, f-wave symmetry is possible, but other competing pairing symmetries cannot be ruled out.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

Supersymmetric quantum mechanics on the lattice: I. Loop formulation

Simulations of supersymmetric field theories on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in low dimensions by formulating the path integral on the lattice in terms of fermion loops. For N=2 supersymmetric quantum mechanics the loop formulation becomes particularly simple and in this paper – the first in a series of three – we discuss in detail the reformulation of this model in terms of fermionic and bosonic bonds for various lattice discretisations including one which is Q-exact.

Synthesis, structure and magnetic properties of cobalt(II) and copper(II) coordination polymers assembled by phthalate and 4-methylimidazole

New coordination polymers [M(Pht)(4-MeIm)2(H2O)]n (M=Co (1), Cu (2); Pht2−=dianion of o-phthalic acid; 4-MeIm=4-methylimidazole) have been synthesized and characterized by IR spectroscopy, X-ray crystallography, thermogravimetric analysis and magnetic measurements. The crystal structures of 1 and 2 are isostructural and consist of [M(4-MeIm)2(H2O)] building units linked in infinite 1D helical chains by 1,6-bridging phthalate ions which also act as chelating ligands through two O atoms from one carboxylate group in the case of 1. In complex 1, each Co(II) atom adopts a distorted octahedral N2O4 geometry being coordinated by two N atoms from two 4-MeIm, three O atoms of two phthalate residues and one O atom of a water molecule, whereas the square-pyramidal N2O3 coordination of the Cu(II) atom in 2 includes two N atoms of N-containing ligands, two O atoms of two carboxylate groups from different Pht, and a water molecule. An additional strong O–H⋯O hydrogen bond between a carboxylate group of the phthalate ligand and a coordinated water molecule join the 1D helical chains to form a 2D network in both compounds. The thermal dependences of the magnetic susceptibilities of the polymeric helical Co(II) chain compound 1 were simulated within the temperature range 20–300 K as a single ion case, whereas for the Cu(II) compound 2, the simulations between 25 and 300 K, were made for a linear chain using the Bonner–Fisher approximation. Modelling the experimental data of compound 1 with MAGPACK resulted in: g=2.6, |D|=62 cm−1. Calculations using the Bonner–Fisher approximation gave the following result for compound 2: g=2.18, J=–0.4 cm−1.

Polyfunctional Two- (2D) and Three- (3D) Dimensional Oxalate Bridged Bimetallic Magnets

We report major results concerning polyfunctional two- (2D) and three- (3D) dimensional oxalate bridged bimetallic magnets. As a consequence of their specific organisation they are composed of an anionic sub-lattice and a cationic counter-part. These bimetallic polymers can accommodate various counter-cations possessing specific physical properties in addition to the magnetic ones resulting from the interactions between the metallic ions in the anionic sub-lattice. Thus, molecular magnets possessing paramagnetic, conductive and optical properties are presented in this review.

DNA-Grafted Supramolecular Polymers: Helical Ribbon Structures Formed by Self-Assembly of Pyrene-DNA Chimeric Oligomers

The controlled arraying of DNA strands on adaptive polymeric platforms remains a challenge. Here, the noncovalent synthesis of DNA-grafted supramolecular polymers from short chimeric oligomers is presented. The oligomers are composed of an oligopyrenotide strand attached to the 5′-end of an oligodeoxynucleotide. The supramolecular polymerization of these oligomers in an aqueous medium leads to the formation of one-dimensional (1D) helical ribbon structures. Atomic force and transmission electron microscopy show rod-like polymers of several hundred nanometers in length. DNA-grafted polymers of the type described herein will serve as models for the development of structurally and functionally diverse supramolecular platforms with applications in materials science and diagnostics.

A tephra lattice for Greenland and a reconstruction of volcanic events spanning 25–45 ka b2k

Tephra layers preserved within the Greenland ice-cores are crucial for the independent synchronisation of these high-resolution records to other palaeoclimatic archives. Here we present a new and detailed tephrochronological framework for the time period 25,000 e 45,000 a b2k that brings together results from 4 deep Greenland ice-cores. In total, 99 tephra deposits, the majority of which are preserved as cryptotephra, are described from the NGRIP, NEEM, GRIP and DYE-3 records. The major element signatures of single glass shards within these deposits indicate that 93 are basaltic in composition all originating from Iceland. Specifically, 43 originate from Grimsv € otn, 20 are thought to be sourced from the Katla volcanic system and 17 show affinity to the Kverkfj € oll system. Robust geochemical characterisations, independent ages derived from the GICC05 ice-core chronology, and the stratigraphic positions of these deposits relative to the Dansgaard-Oeschger climate events represent a key framework that provides new information on the frequency and nature of volcanic events in the North Atlantic region between GS-3 and GI-12. Of particular importance are 19 tephra deposits that lie on the rapid climatic transitions that punctuate the last glacial period. This framework of well-constrained, time-synchronous tie-lines represents an important step towards the independent synchronisation of marine, terrestrial and ice-core records from the North Atlantic region, in order to assess the phasing of rapid climatic changes during the last glacial period.

Hierarchical self-assembly of the DNA-grafted supramolecular polymers

Conjugation of functional entities with a specific set of optical, mechanical or biological properties to DNA strands allows engineering of sophisticated DNA-containing architectures. Among various hybrid systems, DNA-grafted polymers occupy an important place in modern materials science. In this contribution we present the non-covalent synthesis and properties of DNA-grafted linear supramolecular polymers (SPs), which are assembled in a controllable manner from short chimeric DNA-pyrene oligomers. The synthetic oligomers consist of two parts: a 10 nucleotides long DNA chain and a covalently attached segment of variable number of phosphodiester-linked pyrenes. The temperature-dependent formation of DNA-grafted SPs is described by a nucleation-elongation mechanism. The high tendency of pyrenes to aggregate in water, leads to the rapid formation of SPs. The core of the assemblies consists of stacked pyrenes. They form a 1D platform, to which the DNA chains are attached. Combined spectroscopic and microscopic studies reveal that the major driving forces of the polymerization are π-stacking of pyrenes and hydrophobic interactions, and DNA pairing contributes to a lesser extent. AFM and TEM experiments demonstrate that the 1D SPs appear as elongated ribbons with a length of several hundred nanometers. They exhibit an apparent helical structure with a pitch-to-pitch distance of 50±15 nm. Since DNA pairing is a highly selective process, the ongoing studies are aimed to utilize DNA-grafted SPs for the programmable arrangement of functional entities. For example, the addition of non-modified complementary DNA strands to the DNA-grafted SPs leads to the cooperative formation of higher-order assemblies. Also, our experiments suggest that the fluorescent pyrene core of 1D ribbons serves as an efficient donor platform for energy transfer applications.

Supersymmetric quantum mechanics on the lattice: II. Exact results

Simulations of supersymmetric field theories with spontaneously broken supersymmetry require in addition to the ultraviolet regularisation also an infrared one, due to the emergence of the massless Goldstino. The intricate interplay between ultraviolet and infrared effects towards the continuum and infinite volume limit demands careful investigations to avoid potential problems. In this paper – the second in a series of three – we present such an investigation for N=2 supersymmetric quantum mechanics formulated on the lattice in terms of bosonic and fermionic bonds. In one dimension, the bond formulation allows to solve the system exactly, even at finite lattice spacing, through the construction and analysis of transfer matrices. In the present paper we elaborate on this approach and discuss a range of exact results for observables such as the Witten index, the mass spectra and Ward identities.

Supersymmetric quantum mechanics on the lattice: III. Simulations and algorithms

In the fermion loop formulation the contributions to the partition function naturally separate into topological equivalence classes with a definite sign. This separation forms the basis for an efficient fermion simulation algorithm using a fluctuating open fermion string. It guarantees sufficient tunnelling between the topological sectors, and hence provides a solution to the fermion sign problem affecting systems with broken supersymmetry. Moreover, the algorithm shows no critical slowing down even in the massless limit and can hence handle the massless Goldstino mode emerging in the supersymmetry broken phase. In this paper – the third in a series of three – we present the details of the simulation algorithm and demonstrate its efficiency by means of a few examples.