Excited-state proton transfer in N-methyl-6-hydroxyquinolinium salts: solvent and temperature effects

The excited-state proton transfer (ESPT) reaction of the "super"photoacid N-methyl-6-hydroxyquinolinium (MHQ) was studied using both fluorescence upconversion and time-correlated single photon counting (TCSPC) techniques. The ultrafast ESPT kinetics were investigated in various alcohols and water and determined to be solvent-controlled. The ESPT temperature dependence of MHQ was also studied in various alcohols and compared to that observed for another "super"photoacid, 5,8-dicyano-2-naphthol (DCN2). A full set of kinetic and thermodynamic parameters describing the ESPT was obtained. The protolytic photodissociation rate constant for MHQ was higher than that for DCN2, while the ESPT activation energies of MHQ were smaller. These findings are attributed to the approximately 3 orders of magnitude differences in excited-state acidities of MHQ and DCN2.     

Dielectric spectra broadening as the signature of dipole-matrix interaction. I. Water in nonionic solutions

Whenever water interacts with another dipolar entity, a broadening of its dielectric relaxation occurs. Often this broadening can be described by the Cole-Cole (CC) spectral function. A new phenomenological approach has been recently presented [A. Puzenko, P. Ben Ishai, and Y. Feldman, Phys. Rev. Lett. 105, 037601 (2010)] that illustrates a physical mechanism of the dipole-matrix interaction underlying the CC behavior in complex systems. By considering the relaxation amplitude Δε, the relaxation time τ, and the broadening parameter α, one can construct a set of 3D trajectories, representing the dynamic behavior of different systems under diverse conditions. Our hypothesis is that these trajectories will contribute to a deeper understanding of the dielectric properties of complex systems. The paper demonstrates how the model describes the state of water in aqueous solutions of non-ionic solutes. For this purpose complex dielectric spectra for aqueous solutions of D-glucose and D-fructose are analyzed.     

Mixing of the upper triangular matrix walk

We study a natural random walk over the upper triangular matrices, with entries in the field ${\mathbb{Z}_2}$ , generated by steps which add row i + 1 to row i. We show that the mixing time of the lazy random walk is O(n ²) which is optimal up to constants. Our proof makes key use of the linear structure of the group and extends to walks on the upper triangular matrices over the fields ${\mathbb{Z}_q}$ for q prime.     

Markov type and threshold embeddings

For two metric spaces X and Y, say that X threshold-embeds into Y if there exist a number K > 0 and a family of Lipschitz maps ${\{\varphi_{\tau} : X \to Y : \tau > 0\}}$ such that for every ${x,y \in X}$ , $$d_X(x, y) \geq \tau \implies d_Y(\varphi_\tau (x),\varphi_\tau (y)) \geq \|{\varphi}_\tau\|_{\rm Lip}\tau/K,$$ where ${\|{\varphi}_{\tau}\|_{\rm Lip}}$ denotes the Lipschitz constant of ${\varphi_{\tau}}$ . We show that if a metric space X threshold-embeds into a Hilbert space, then X has Markov type 2. As a consequence, planar graph metrics and doubling metrics have Markov type 2, answering questions of Naor, Peres, Schramm, and Sheffield. More generally, if a metric space X threshold-embeds into a p-uniformly smooth Banach space, then X has Markov type p. Our results suggest some non-linear analogs of Kwapien’s theorem. For instance, a subset ${X \subseteq L_1}$ threshold-embeds into Hilbert space if and only if X has Markov type 2.     

Self-similar amplification in fiber Bragg gratings written in fiber amplifiers

We show, by using numerical simulations, that self-similar pulses with a duration on the order of few nanoseconds and an energy on the order of 10?μJ can be obtained at the output of a fiber Bragg grating (FBG) written in a fiber amplifier. The evolution of the amplified pulses is determined by the combined effect of Kerr nonlinearity, normal-dispersion, gain, and gain saturation, which limit the pulse energy. The output pulse mainly depends on the initial pulse energy rather than on the initial pulse profile. The reduced group velocity in FBGs can significantly increase the total gain for a given amplifier length. Hence we find that the proposed amplification scheme can be highly advantageous for amplification of nanosecond-scale pulses in fiber amplifiers.     

On d-Multiplicative Secret Sharing

A multiplicative secret sharing scheme allows players to multiply two secret-shared field elements by locally converting their shares of the two secrets into an additive sharing of their product. Multiplicative secret sharing serves as a central building block in protocols for secure multiparty computation (MPC). Motivated by open problems in the area of MPC, we introduce the more general notion of d-multiplicative secret sharing, allowing to locally multiply d shared secrets, and study the type of access structures for which such secret sharing schemes exist.     

Full counting statistics of a Luttinger liquid conductor

Nonequilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the time resolved full counting statistics of the transmitted charge is derived. It is given by the Fredholm determinant of the counting operator with a time-dependent scattering phase. The result has a form of counting statistics of noninteracting particles with fractional charges, induced by scattering off the boundaries between the LL wire and the noninteracting leads.     

Nonequilibrium Luttinger liquid: zero-bias anomaly and dephasing

A one-dimensional system of interacting electrons out of equilibrium is studied in the framework of the Luttinger liquid model. We analyze several setups and develop a theory of tunneling into such systems. A remarkable property of the problem is the absence of relaxation in energy distribution functions of left and right movers yet the presence of the finite dephasing rate due to electron-electron scattering, which smears zero-bias-anomaly singularities in the tunneling density of states.     

Towards a dephasing diode: asymmetric and geometric dephasing

We study the effect of a noisy environment on spin and charge transport in ballistic quantum wires with spin-orbit coupling (Rashba coupling). We find that the wire then acts as a dephasing diode, inducing very different dephasing of the spins of right and left movers. We also show how Berry phase (geometric phase) in a curved wire can induce such asymmetric dephasing, in addition to purely geometric dephasing. We propose ways to measure these effects through spin detectors, spin-echo techniques, and Aharanov-Bohm interferometry.