Singlet excitations in pyrochlore: a study of quantum frustration

We apply the contractor renormalization (CORE) method to the spin half Heisenberg antiferromagnet on the frustrated checkerboard and pyrochlore lattices. Their ground states are spin-gapped singlets which break lattice symmetry. Their effective Hamiltonians describe fluctuations of orthogonal singlet pairs on tetrahedral blocks, at an emergent low energy scale. We discuss low temperature thermodynamics and new interpretations of finite size numerical data. We argue that our results are common to many models of quantum frustration.     

Separating atmospheric layers in adaptive optics

Several optical schemes have been proposed to measure the separate contributions of atmospheric layers for astronomical adaptive optics. I show here that simple conjugation of the wave-front sensors to the layers is sufficient. Although a larger camera is required for a larger field of view, only the pixels that sense stars are being read out. The nearly periodic Hartmann data are analyzed by Fourier filtering so that the signals from all stars are added up while most of the noise is excluded. Acoustic Hartmann wave-front sensors [Opt. Lett. 26, 1834 (2001)1 that switch between layers improve flexibility and sensitivity.     

Continuous scanning of atomic uranium levels

A simple, efficient method of uncovering and assigning high levels of atomic uranium is presented. 62 new levels have been discovered in the region 33 580–34 400 cm^?1. The experimental system is especially suitable for spectroscopic measurement of complex atoms.     

Excited-state intermolecular proton transfer of firefly luciferin V. Direct proton transfer to fluoride and other mild bases

We studied the direct proton transfer (PT) from electronically excited D-luciferin to several mild bases. The fluorescence up-conversion technique is used to measure the rise and decay of the fluorescence signals of the protonated and deprotonated species of D-luciferin. From a base concentration of 0.25 M or higher the proton transfer rates to the fluoride, dihdyrogen phosphate or acetate bases are fast and comparable. The fluorescence signals are nonexponential and complex. We suggest that the fastest decay component arises from a direct proton transfer process from the hydroxyl group of D-luciferin to the mild base. The proton donor and acceptor molecules form an ion pair prior to photoexcitation. Upon photoexcitation solvent rearrangement occurs on a 1 ps time-scale. The PT reaction time constant is ～2 ps for all three bases. A second decay component of about 10 ps is attributed to the proton transfer in a contact pair bridged by one water molecule. The longest decay component is due to both the excited-state proton transfer (ESPT) to the solvent and the diffusion-assisted PT process between a photoacid and a base pair positioned remotely from each other prior to photoexcitation.     

Excited-state intermolecular proton transfer of firefly luciferin IV. Temperature and pH dependence

Time-resolved emission as well as steady-state UV-vis techniques were employed to study the photoprotolytic processes that d-luciferin, the natural substrate of the firefly luciferase, undergoes in both acidic aqueous solutions and ice. The emission spectrum of D-luciferin in a 20 mM HCl aqueous solution or higher has an additional emission band at 590 nm red-shifted with respect to the strongest emission band positioned at 530 nm of the deprotonated NRO(-*) form in a pH-neutral aqueous solution. We attribute this emission band to the zwitterion form designated as (+)HNRO(-). The time-resolved emission signals show that the NRO(-*) emission band at 530 nm and the zwitterion emission band at 590 are strongly quenched by a recombination process with a proton in an acidic solution and in ice. In ice, the quenching rate is 10 times faster than in the liquid state. We attribute the fast quenching rate to the high value of the proton diffusion constant in ice.     

Semiclassics for Particles with Spin via a Wigner–Weyl-Type Calculus

We show how to relate the full quantum dynamics of a spin-½ particle on \({\mathbb{R}^d}\) to a classical Hamiltonian dynamics on the enlarged phase space \({\mathbb{R}^{2d} \times \mathbb{S}^{2}}\) up to errors of second order in the semiclassical parameter. This is done via an Egorov-type theorem for normal Wigner–Weyl calculus for \({\mathbb{R}^d}\) (Folland, Harmonic Analysis on Phase Space, 1989; Lein, Weyl Quantization and Semiclassics, 2010) combined with the Stratonovich–Weyl calculus for SU(2) (Varilly and Gracia-Bondia, Ann Phys 190:107–148, 1989). For a specific class of Hamiltonians, including the Rabi- and Jaynes–Cummings model, we prove an Egorov theorem for times much longer than the semiclassical time scale. We illustrate the approach for a simple model of the Stern–Gerlach experiment.     

Confinement and lattice quantum-electrodynamic electric flux tubes simulated with ultracold atoms

We propose a method for simulating (2+1)D compact lattice quantum-electrodynamics, using ultracold atoms in optical lattices. In our model local Bose-Einstein condensates' (BECs) phases correspond to the electromagnetic vector potential, and the local number operators represent the conjugate electric field. The well-known gauge-invariant Kogut-Susskind Hamiltonian is obtained as an effective low-energy theory. The field is then coupled to external static charges. We show that in the strong coupling limit this gives rise to "electric flux tubes" and to confinement. This can be observed by measuring the local density deviations of the BECs, and is expected to hold even, to some extent, outside the perturbative calculable regime.     

Relation spaces of hyperplane arrangements and modules defined by graphs of fiber zonotopes

We study the exactness of certain combinatorially defined complexes which generalize the Orlik-Solomon algebra of a geometric lattice. The main results pertain to complex reflection arrangements and their restrictions. In particular, we consider the corresponding relation complexes and give a simple proof of the n-formality of these hyperplane arrangements. As an application, we are able to bound the Castelnouvo-Mumford regularity of certain modules over polynomial rings associated to Coxeter arrangements (real reflection arrangements) and their restrictions. The modules in question are defined using the relation complex of the Coxeter arrangement and fiber polytopes of the dual Coxeter zonotope. They generalize the algebra of piecewise polynomial functions on the original arrangement.     

Electrochemical Behavior and Electroanalytical Determination of Indole‐3‐Acetic Acid Phytohormone on a Boron‐Doped Diamond Electrode

In this work, a boron‐doped diamond (BDD) electrode was used for the electroanalytical determination of indole‐3‐acetic acid (IAA) phytohormone by square‐wave voltammetry. IAA yielded a well‐defined voltammetric response at +0.93 V (vs. Ag/AgCl) in Britton–Robinson buffer, pH 2.0. The process could be used to determine IAA in the concentration range of 5.0 to 50.0 µM (n=8, r=0.997), with a detection limit of 1.22 µM. The relative standard deviation of ten measurements was 2.09 % for 20.0 µM IAA. As an example, the practical applicability of BDD electrode was tested with the measurement of IAA in some plant seeds.