On the Derivatives of Quaternionic Functions Along Two-Dimensional Planes

In a previous paper we introduced the concept of a two-dimensional directional derivative of a quaternionic function along a two-dimensional plane. In this paper we provide a deeper analysis of its properties, as well as of its relations with hyperholomorphic functions, with holomorphic maps of two complex variables and with Cullen-regular functions. Received: October, 2007. Accepted: February, 2008.     

Solving the spectroscopic phase: imaging excited wave packets and extracting excited state potentials from fluorescence data

We develop an inversion scheme for obtaining the signs of transition-dipole amplitudes from fluorescence line intensities. Using the amplitudes thus obtained we show how to extract highly accurate excited state potential(s) and the transition-dipole(s) as a function of inter-nuclear displacements. The same dipole amplitudes can also be used to extract the phase and amplitude of unknown time-evolving wave packets, in essentially a quantum non-demolition manner. The procedure, which is demonstrated for the A((1)∑) and B((1)Π(u)) states of the Na(2) molecule, is shown to yield reliable results even when we are given incomplete or uncertain data. We also demonstrate the success of our approach in extracting double minimum potentials. The inversion scheme is in principle applicable to any polyatomic molecule.     

Phase coexistence in proton glass

Abstract

Proton glasses are crystals of composition M_1?x(NW₄)_xW₂A0₄, where M = K,Rb,Cs, W = H,D, A = P, As. For x = 0 there is a ferroelectric (FE) transition, while for x-1 there is an antiferroelectric (AFE) transition. In both cases, the transition is from a paraelectric (PE) state of tetragonal structure with dynamically disordered hydrogen bonds to an ordered state of orthorhombic structure. For an intermediate x range there is no transition, but the hydrogen rearrangements slow down, and eventually display nonergodic behavior characteristic of glasses. We and others have shown from spontaneous polarization, dielectric permittivity, nuclear magnetic resonance, and neutron diffraction experiments that for smaller x there is coexistence of ferroelectric and paraelectric phases, and for larger × there is coexistence of antiferroelectric and paraelectric phases. We present a method for analytically describing this coexistence, and the degree to which this coexistence is spatial and/or temporal. We discuss also the experimental determination of these coexistence parameters.     

Spectral manifestations of hybrid association of CdS colloidal quantum dots with methylene blue molecules

We have studied the spectral properties of mixtures formed by CdS colloidal quantum dots with an average diameter of 2.5 nm and methylene blue molecules and that are dispersed into gelatin. We have revealed that, in the presence of CdS quantum dots, the luminescence intensity of methylene blue increases. We suggest a model of this effect, which is based on electronic excitation energy transfer from luminescence centers of CdS quantum dots to methylene blue molecules.     

Activation energy of catalysis-related domain motion in E. coli adenylate kinase

Adenylate kinase from E. coli (AKeco), folded into domains CORE, AMPbd, and LID, catalyzes the reaction AMP + ATP <--> 2ADP. Previous X-ray crystallography and optical solution methods showed that the domains AMPbd and LID, and the conserved P-loop, execute large-amplitude catalysis-related motions. We used (15)N NMR spin relaxation methods to find that the simplified model-free (MF) analysis does not, whereas our general Slowly Relaxing Local Structure analysis does, detect catalytic domain motion. SRLS set for the first time the correlation time for domain motion at tau(L)perpendicular = 8.2 ns, to be compared with tau(m) = 15.1 ns for global tumbling. These results were obtained at 303 K. Herein we conduct a temperature-dependent investigation of tau(L)perpendicular and tau(m) in the range of 288-310 K. We found that the activation energy for global tumbling is Ea = 16.9 +/- 0.5 kJ/mol, the hydrodynamic volume of hydrated AKeco is 65.6 +/- 2.1 nm3, its radius is 2.50 +/- 0.03 nm, and the number of hydration layers is 1.77. The average tau(L)perpendicular value decreases from 11 ns at 288 K to 4 ns at 310 K, with activation energies of 29.7 +/- 3.3, 32.1 +/- 4.3, and 30.4 +/- 4.3 kJ/mol for the domains AMPbd and LID, and the catalytic P-loop, respectively. These values are two-to-three times smaller than typical activation energies of enzymatic reactions. Hence kinase catalysis appears not to be controlled by domain motion in the ligand-free enzyme. However, the latter process clearly facilitates important mechanical aspects such as steric recognition and capturing of the AMP and ATP substrates, their proper positioning for phosphorylation, and the release of the ADP product.     

Time-bin-modulated biphotons from cavity-enhanced down-conversion

We have generated a new type of biphoton state by cavity-enhanced down-conversion in a type-II phase-matched, periodically poled KTiOPO4 crystal. By introducing a weak intracavity birefringence, we obtained signal and idler photons whose quantum interference was modulated between singlet and triplet signatures according to their arrival-time difference. This cavity-enhanced biphoton source is spectrally bright, yielding a single-mode fiber-coupled coincidence rate of 0.7 pairs/s per mW of pump power per MHz of down-conversion bandwidth.