Disorder-induced exciton localization and violation of optical selection rules in supramolecular nanotubes

Using numerical simulations, we study the effect of disorder on the optical properties of cylindrical aggregates of molecules with strong excitation transfer interactions. The exciton states and the energy transport properties of such molecular nanotubes attract considerable interest for application in artificial light-harvesting systems and energy transport wires. In the absence of disorder, such nanotubes exhibit two optical absorption peaks, resulting from three super-radiant exciton states, one polarized along the axis of the cylinder, the other two (degenerate) polarized perpendicular to this axis. These selection rules, imposed by the cylindrical symmetry, break down in the presence of disorder in the molecular transition energies, due to the fact that the exciton states localize and no longer wrap completely around the tube. We show that the important parameter is the ratio of the exciton localization length and the tube's circumference. When this ratio decreases, the distribution of polarization angles of the exciton states changes from a two-peak structure (at zero and ninety degrees) to a single peak determined by the orientation of individual molecules within the tube. This is also reflected in a qualitative change of the absorption spectrum. The latter agrees with recent experimental findings.     

Zero and finite temperature phase diagram of the spinless fermion model in infinite dimensions

The phase diagram of the model of spinless fermions with repulsive nearest neighbour interaction is calculated analytically on a hypercubic lattice in infinite dimensions (d → ∞). In spite of its simplicity the model displays a rich phase diagram depending on the doping δ, the interaction U and the temperature T. The system can be in the homogeneous phase (HOM), the nonsegregated AB charge density wave (AB-CDW), the AB phase separation region (PS-AB/HOM; coexistence of AB-CDW and HOM), the incommensurate phase (IP) or the IP phase separation region (PS-AB/IP; coexistence of AB-CDW and IP). We identify three important values of the interaction U_IPL = 0.572 < U_IPH = 1.914 < U_IP/PS = 4.212 which distinguish four intervals of U. These imply four different types of phase diagrams. In all the three phase diagrams with U below U_IP/PS the IP appears. We propose a new general ansatz for the order parameter of this phase. A competition between the IP, the PS-AB/IP and the PS-AB/HOM is found. The relevance of our findings for the phase scenario of the Hubbard model is shown.     

Nonmonotonic energy harvesting efficiency in biased exciton chains

We theoretically study the efficiency of energy harvesting in linear exciton chains with an energy bias, where the initial excitation is taking place at the high-energy end of the chain and the energy is harvested (trapped) at the other end. The efficiency is characterized by means of the average time for the exciton to be trapped after the initial excitation. The exciton transport is treated as the intraband energy relaxation over the states obtained by numerically diagonalizing the Frenkel Hamiltonian that corresponds to the biased chain. The relevant intraband scattering rates are obtained from a linear exciton-phonon interaction. Numerical solution of the Pauli master equation that describes the relaxation and trapping processes reveals a complicated interplay of factors that determine the overall harvesting efficiency. Specifically, if the trapping step is slower than or comparable to the intraband relaxation, this efficiency shows a nonmonotonic dependence on the bias: it first increases when introducing a bias, reaches a maximum at an optimal bias value, and then decreases again because of dynamic (Bloch) localization of the exciton states. Effects of on-site (diagonal) disorder, leading to Anderson localization, are addressed as well.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Quantum Zeno and anti-Zeno paradoxes

Continuous observation of a time independent projection operator is known to prevent change of state (the quantum Zeno paradox). We discuss the recent result that generic continuous measurement of time dependent projection operators will in fact ensure change of state: an anti-Zeno paradox.     

ac Conductivity of mixed spinel NiAl0.7Cr0.7Fe0.6O4

ac Conductivity measurements are carried out across the metal to insulator transition in NiAl_0.7Cr_0.7Fe_0.6O₄. The low frequency data is analyzed using Summerfield scaling theory for hopping conductivity. The exponent of the scaling behavior has significantly different values in the conducting and insulating regimes. The hopping frequency and the zero frequency conductivity are found to increase with temperature, slowly in the metallic regime and rapidly in the insulating regime.