Excited-state dynamics of structurally characterized [ReI(CO)3(phen)(HisX)]+ (X = 83, 109) Pseudomonas aeruginosa azurins in aqueous solution

The triplet metal-to-ligand charge transfer ((3)MLCT) dynamics of two structurally characterized Re(I)(CO)(3)(phen)(HisX)-modified (phen = 1,10-phenanthroline; X = 83, 109) Pseudomonas aeruginosa azurins have been investigated by picosecond time-resolved infrared (TRIR) spectroscopy in aqueous (D(2)O) solution. The (3)MLCT relaxation dynamics exhibited by the two Re(I)-azurins are very different from those of the sensitizer [Re(I)(CO)(3)(phen)(im)](+) (im = imidazole). Whereas the Re(I)(CO)(3) intramolecular vibrational relaxation in Re(I)(CO)(3)(phen)(HisX)Az (4 ps) is similar to that of [Re(I)(CO)(3)(phen)(im)](+) (2 ps), the medium relaxation is much slower ( approximately 250 vs 9.5 ps); the 250-ps relaxation is attributable to reorientation of D(2)O molecules as well as structural reorganization of the rhenium chromophore and nearby polar amino acids in each of the modified proteins.     

Zn-OH2 and Zn-OH complexes with hydroborate-derived tripod ligands: a comprehensive study

The complete array of those hydrotris(pyrazolyl/thioimidazolyl)borate ligands that were developed and used in the author's laboratories, with N3, N2S, NS2, and S3 donor sets, was scanned for their ability to form Zn-OH2 and Zn-OH complexes. The coordination motifs found were Zn-OH2, Zn-OH, Zn-OH-Zn, and Zn-O2H3-Zn. Of these, the well-established Zn-OH motif was complemented with novel species bearing N3, NS2, and S3 tripods. The Zn-OH2 motif was observed only with pyrazolylborate ligands and only in unusual situations with coordination numbers higher than 4 for zinc. The new Zn-OH-Zn motif was realized for three different pyrazolylborates, for one NS2 tripod, and for two S3 tripods. Finally, it was verified that the Zn-O2H3-Zn motif again occurs only with pyrazolylborate ligands. The new complexes were identified by a total of 11 structure determinations.     

The $$SO(3,1) \times U(1)$$-gauge invariant approach to charged bosons in relativistic magnetars

Using a perturbative method, we investigate solutions of the Klein–Gordon equations for a charged massive field in the background of a magnetar, both in the interior solution and outside the star. A special attention is given to cases where the variables can be separated and the wave function is expressed in terms of the Heun’s general or confluent functions. By imposing various conditions on the parameters, one gets the energy quantization law and simple polynomial forms of the Heun’s functions, which can be used in computing first-order transition amplitudes.     

Compact fibre-based coherent anti-Stokes Raman scattering spectroscopy and interferometric coherent anti-Stokes Raman scattering from a single femtosecond fibre-laser oscillator

We demonstrate a new approach to CARS spectroscopy by efficiently synthesizing synchronized narrow-bandwidth (less than 10 cm⁻¹) pump and Stokes pulses (frequency difference continuously tunable upto ≈3000 cm⁻¹) based on spectral compression together with second harmonic generation (in periodically-poled nonlinear crystals) of femtosecond pulses emitted by a single compact Er-fibre oscillator. For a far better signal to non-resonant background contrast, interferometric CARS (I-CARS) is demonstrated and CARS signal enhancement upto three orders of magnitude is achieved by constructive interference with an auxiliary local oscillator at anti-Stokes field, also synthesized by spectral compression of pulses emitted from the same fibre oscillator.     

Transverse oriented electric field re-entrant resonator (TERR) with automatic tuning and coupling control for EPR spectroscopy and imaging of the beating heart

Sample motion, particularly that of a beating heart, induces baseline noise and spectral distortion on an EPR spectrum. In order to quench motional noise and restore the EPR signal amplitude and line-width, an L-band transverse oriented electric field re-entrant resonator (TERR) was designed and constructed with provisions for automatic tuning control (ATC) and automatic coupling control (ACC) suited for studies of isolated beating rat hearts. Two sets of electronic circuits providing DC biased voltage to two varactor diodes were implemented to electronically adjust coupling and tuning. The resonator has a rectangular cross-sectional sample arm of 25 mm diameter with a Q value of 1100 without sample. Once inserted with lossy aqueous samples of 0.45% NaCl, Q value drops to 400 with a volume of 0.5 ml and 150 with 5 ml. The ATC/ACC functions were tested with a moving phantom and isolated beating rat hearts with the improvement of signal to noise ratio (S/N, peak amplitude of signal over peak amplitude of baseline noise) of 6.7-, and 4 to 6-fold, respectively. With these improvements, EPR imaging could be performed on an isolated beating rat heart. Thus, this TERR resonator with ATC/ACC enables application of EPR spectroscopy and imaging for the measurement and imaging of radical metabolism, redox state, and oxygenation in the isolated beating rat heart.     

Self-Duality of Markov Processes and Intertwining Functions

We present a theorem which elucidates the connection between self-duality of Markov processes and representation theory of Lie algebras. In particular, we identify sufficient conditions such that the intertwining function between two representations of a certain Lie algebra is the self-duality function of a (Markov) operator. In concrete terms, the two representations are associated to two operators in interwining relation. The self-dual operator, which arise from an appropriate symmetric linear combination of them, is the generator of a Markov process. The theorem is applied to a series of examples, including Markov processes with a discrete state space (e.g. interacting particle systems) and Markov processes with continuous state space (e.g. diffusion processes). In the examples we use explicit representations of Lie algebras that are unitarily equivalent. As a consequence, in the discrete setting self-duality functions are given by orthogonal polynomials whereas in the continuous context they are Bessel functions.     

From Heisenberg to Gödel via Chaitin

In 1927 Heisenberg discovered that the “more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa.” Four years later Gödel showed that a finitely specified, consistent formal system which is large enough to include arithmetic is incomplete. As both results express some kind of impossibility it is natural to ask whether there is any relation between them, and, indeed, this question has been repeatedly asked for a long time. The main interest seems to have been in possible implications of incompleteness to physics. In this note we will take interest in the converse implication and will offer a positive answer to the question: Does uncertainty imply incompleteness? We will show that algorithmic randomness is equivalent to a “formal uncertainty principle” which implies Chaitin’s information-theoretic incompleteness. We also show that the derived uncertainty relation, for many computers, is physical. In fact, the formal uncertainty principle applies to all systems governed by the wave equation, not just quantum waves. This fact supports the conjecture that uncertainty implies algorithmic randomness not only in mathematics, but also in physics.     

Variational Bounds for the Generalized Random Energy Model

We compute the pressure of the random energy model (REM) and generalized random energy model (GREM) by establishing variational upper and lower bounds. For the upper bound, we generalize Guerra’s “broken replica symmetry bounds,” and identify the random probability cascade as the appropriate random overlap structure for the model. For the REM the lower bound is obtained, in the high temperature regime using Talagrand’s concentration of measure inequality, and in the low temperature regime using convexity and the high temperature formula. The lower bound for the GREM follows from the lower bound for the REM by induction. While the argument for the lower bound is fairly standard, our proof of the upper bound is new.     

Electric Chern–Simons term, enlarged exotic Galilei symmetry and noncommutative plane

The extended exotic planar model for a charged particle is constructed. It includes a Chern–Simons-like term for a dynamical electric field, but produces usual equations of motion for the particle in background constant uniform electric and magnetic fields. The electric Chern–Simons term is responsible for the noncommutativity of the boost generators in the 10-dimensional enlarged exotic Galilei symmetry algebra of the extended system. The model admits two reduction schemes by the integrals of motion, one of which reproduces the usual formulation for the charged particle in external constant electric and magnetic fields with associated field-deformed Galilei symmetry, whose commuting boost generators are identified with the nonlocal in time Noether charges reduced on-shell. Another reduction scheme, in which electric field transmutes into the commuting space translation generators, extracts from the model a free particle on the noncommutative plane described by the twofold centrally extended Galilei group of the nonrelativistic anyons.     

Duality for Stochastic Models of Transport

We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process which is obtained by placing the system in contact with proper reservoirs, working at different particle densities or different temperatures. We show that all the models are exactly solvable by duality, using a dual process with absorbing boundaries. The solution does also apply to the so-called thermalization limit in which particles or energy is instantaneously redistributed among sites. The results shows that duality is a versatile tool for analyzing stochastic models of transport, while the analysis in the literature has been so far limited to particular instances. Long-range correlations naturally emerge as a result of the interaction of dual particles at the microscopic level and the explicit computations of covariances match, in the scaling limit, the predictions of the macroscopic fluctuation theory.