Ground state and response properties of mercury clusters

The change of the cohesive energy and the optical absorption spectra of small singly sized Hg clusters is discussed. The cohesive energy allows one to determine the different regimes of chemical bonding. The optical spectra show an abrupt transition to a collective, plasmon-like absorption as a function of increasing cluster size. The position of the one plasmon peak is: 1) independent of the charge state, 2) nearly independent of cluster size, and 3) agrees with that of the classical Mie plasmon calculated from the experimental dielectric constants. The width of the plasmon peaks is discussed. A strong influence of electronic correlations on the cluster size dependence of the oscillator strength is observed.     

Mesoscopic resonating valence bond system on a triple dot

We theoretically introduce a mesoscopic pendulum from a triple dot. The pendulum is fastened through a singly occupied dot (spin qubit). Two other strongly capacitively coupled islands form a double-dot charge qubit with one electron in excess oscillating between the two low-energy charge states (1,0) and (0,1). The triple dot is placed between two superconducting leads. Under realistic conditions, the main proximity effect stems from the injection of resonating singlet (valence) bonds on the triple dot. This gives rise to a Josephson current that is charge- and spin-dependent and, as a consequence, exhibits a distinct resonance as a function of the superconducting phase difference.     

Limit Processes for TASEP with Shocks and Rarefaction Fans

We consider the totally asymmetric simple exclusion process (TASEP) with two-sided Bernoulli initial condition, i.e., with left density ρ ₋ and right density ρ ₊. We study the associated height function, whose discrete gradient is given by the particle occurrences. Macroscopically one has a deterministic limit shape with a shock or a rarefaction fan depending on the values of ρ _±. We characterize the large time scaling limit of the multipoint fluctuations as a function of the densities ρ _± and of the different macroscopic regions. Moreover, using a slow decorrelation phenomena, the results are extended from fixed time to the whole space-time, except along the some directions (the characteristic solutions of the related Burgers equation) where the problem is still open.     

Non-associative Ore extensions

We introduce non-associative Ore extensions, S = R[X; σ, δ], for any nonassociative unital ring R and any additive maps σ, δ: R → R satisfying σ(1) = 1 and δ(1) = 0. In the special case when δ is either left or right R _δ -linear, where R _δ = ker(δ), and R is δ-simple, i.e. {0} and R are the only δ-invariant ideals of R, we determine the ideal structure of the nonassociative differential polynomial ring D = R[X; id _R , δ]. Namely, in that case, we show that all non-zero ideals of D are generated by monic polynomials in the center Z(D) of D. We also show that Z( _D ) = R _δ [p] for a monic p ∈ R _δ [X], unique up to addition of elements from Z(R) _δ . Thereby, we generalize classical results by Amitsur on differential polynomial rings defined by derivations on associative and simple rings. Furthermore, we use the ideal structure of D to show that D is simple if and only if R is δ-simple and Z(D) equals the field R _δ ∩ Z(R). This provides us with a non-associative generalization of a result by Öinert, Richter and Silvestrov. This result is in turn used to show a non-associative version of a classical result by Jordan concerning simplicity of D in the cases when the characteristic of the field R _δ ∩ Z(R) is either zero or a prime. We use our findings to show simplicity results for both non-associative versions of Weyl algebras and non-associative differential polynomial rings defined by monoid/group actions on compact Hausdorff spaces.     

Raman spectroscopic studies of terthiophenes for molecular electronics

The effect of thiol and selenol functionalization on the vibrational spectra and photochemical stability of terthiophene based molecular wires was investigated using surface-enhanced Raman scattering (SERS). The molecules were found to exhibit markedly different properties at the silver surface of the SERS substrate, despite having almost identical Raman spectra in solution and in the solid state. In contrast to terthiophene (3T), the bisthiolterthiophene (T3) and biselenol-terthiophene (Se3) molecules were stable against photoinduced structural changes when adsorbed to the metal surface at low concentrations. This indicates that the strong bonds to the silver surface, via S or Se terminal atoms, leads to a rapid decay of photoexcited states. Comparison with ab initio calculations shows that both T3 and Se3 bind with only one of the functional groups to the Ag surface.     

Light‐Switchable Polymer from Cationic to Zwitterionic Form: Synthesis,Characterization, and Interactions with DNA and Bacterial Cells

A novel cationic polymer poly(N,N‐dimethyl‐N‐[3‐(methacroylamino) propyl]‐N‐[2‐[(2‐nitrophenyl)methoxy]‐2‐oxo‐ethyl]ammonium chloride) is synthesized by free‐radical polymerization of N‐[3‐(dimethylamino)propyl] methacrylamide and subsequent quaternization with o‐nitrobenzyl 2‐chloroacetate. The photolabile o‐nitrobenzyl carboxymethyl pendant moiety is transformed to the zwitterionic carboxybetaine form upon the irradiation at 365 nm. This feature is used to condense and, upon the light irradiation, to release double‐strand DNA tested by gel electrophoresis and surface plasmon resonance experiments as well as to switch the antibacterial activity to non‐toxic character demonstrated for Escherichia coli bacterial cells in solution and at the surface using the self‐assembled monolayers.

     

The Ideal Intersection Property for Groupoid Graded Rings

We show that, if a groupoid graded ring has a grading satisfying a certain nondegeneracy property, then the commutant of the center of the principal component of the ring has the ideal intersection property, that is it intersects nontrivially every nonzero ideal of the ring. Furthermore, we show that for skew groupoid algebras with commutative principal component, the principal component is maximal commutative if and only if it has the ideal intersection property.     

Optimal bond portfolios with fixed time to maturity

We study interest rate models where the term structure is given by an affine relation and in particular where the driving stochastic processes are so-called generalized Ornstein–Uhlenbeck processes.     

Separable Groupoid Rings

We show that groupoid rings are separable over their ring of coefficients if and only if the groupoid is finite and the orders of the associated principal groups are invertible in the ring of coefficients. We use this to show that if we are given a finite groupoid, then the associated groupoid ring is semisimple (or hereditary) if and only if the ring of coefficients is semisimple (or hereditary) and the orders of the principal groups are invertible in the ring of coefficients. To this end, we extend parts of the theory of graded rings and modules from the group graded case to the category graded, and, hence, groupoid graded situation. In particular, we show that strongly groupoid graded rings are separable over their principal components if and only if the image of the trace map contains the identity.