Stimulated creation of quanta during inflation and the observable universe

Inflation provides a natural mechanism to account for the origin of cosmic structures. The generation of primordial inhomogeneities during inflation can be understood via the spontaneous creation of quanta from the vacuum. We show that when the corresponding stimulated creation of quanta is considered, the characteristics of the state of the universe at the onset of inflation are not diluted by the inflationary expansion and can be imprinted in the spectrum of primordial inhomogeneities. The non-gaussianities (particularly in the so-called squeezed configuration) in the cosmic microwave background and galaxy distribution can then tell us about the state of the universe that existed at the time when quantum field theory in curved spacetime first emerged as a plausible effective theory.     

On the origin of optics

The first optical devices in animals evolved in the Cambrian period. The first reflector known dates from around 508 million years ago (Ma); the first eyes with lenses evolved at around 521 Ma. Consideration of the introduction of vision leads to a hypothesis for the cause of evolution's Big Bang—the Cambrian explosion. Suddenly, and for no obvious reason, the range and variety of life-forms erupted somewhere between 520 and 515 Ma (as limited by of our dating techniques). At no other time in Earth's history there has been such a profusion, such an exuberance, and such an overwhelming diversity in so short time, within one million years. Prior to this Cambrian explosion event, all animals were soft-bodied and mainly worm-like, as they had been for millions of years before that. But during the Cambrian explosion many of the major animal groups on Earth today independently evolved their hard body parts for the first time. Following the appearance of the first trilobites, some animals evolved shells and spines, some with bright colours, to visually warn of their new armour. Others evolved streamlined appearances and swimming oars to advise trilobites that they could not be caught. The Light Switch Theory provides an explanation for what triggered this event—that it was the development of vision (in trilobites); the introduction of optics. Once visual capability arose, it allowed predators to identify prey, triggering an arms race. From here on, vision became a dominant force of evolution and resulted in the eyes and reflecting optics that we have in nature today. This paper provides a summary of the first optical devices to evolve in animals, along with the implications of these in their relevance to the Big Bang of evolution, written for the physical sciences.     

Determination of gap symmetry from angle-dependent H(c2) measurements on CeCu₂Si₂

The tetragonal heavy-fermion compound CeCu?Si? exhibits a superconducting ground state (S type, T(c) = 0.67 K) close to a magnetic instability. Here, we present angle-resolved resistivity measurements of the upper critical field H(c2). In-plane rotation of S-type CeCu?Si? single crystals reveals a fourfold oscillation of H(c2). An extended weak-coupling BCS model for a d-wave symmetry including strong Pauli-limiting effects confirms the aforementioned angular dependence and points towards d(xy) symmetry of the order parameter.     

Exploded manifolds

This paper provides an introduction to exploded manifolds. The category of exploded manifolds is an extension of the category of smooth manifolds with an excellent holomorphic curve theory. Each exploded manifold has a tropical part which is a union of convex polytopes glued along faces. Exploded manifolds are useful for defining and computing Gromov–Witten invariants relative to normal crossing divisors, and using tropical curve counts to compute Gromov–Witten invariants.     

There is no upper bound for the diameter of the commuting graph of a finite group

We construct a family of finite 2-groups which have commuting graph of increasing diameter.     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

The geometry of the Gauss–Picard modular group

We give a construction of a fundamental domain for PU(2,1,mathbbZ [i]){{rm PU}(2,1,mathbb{Z} [i])}, that is the group of holomorphic isometries of complex hyperbolic space with coefficients in the Gaussian ring of integers mathbbZ [i]{mathbb{Z} [i]}. We obtain from that construction a presentation of that lattice and relate it, in particular, to lattices constructed by Mostow.     

Designed Iron Catalysts for Allylic C−H Functionalization of Propylene and Simple Olefins

Propylene gas is produced worldwide by steam cracking on million-metric-ton scale per year. It serves as a valuable starting material for π-bond functionalization but is rarely applied in transition metal-catalyzed allylic C−H functionalization for fine chemical synthesis. Herein, we report that a newly-developed cationic cyclopentadienyliron dicarbonyl complex allows for the conversion of propylene to its allylic C−C bond coupling products under catalytic conditions. This approach was also found applicable to the allylic functionalization of simple α-olefins with distinctive branched selectivity. Experimental and computational mechanistic studies supported the allylic deprotonation of the metal-coordinated alkene as the turnover-limiting step and led to insights into the multifaceted roles of the newly designed ligand in promoting allylic C−H functionalization with enhanced reactivity and stereoselectivity.