Random Operator Approach for Word Enumeration in Braid Groups

We investigate analytically the problem of enumeration of nonequivalent primitive words in the braid group B_n for n >> 1 by analysing the random word statistics and the target space on the basis of the locally free group approximation. We develop a "symbolic dynamics" method for exact word enumeration in locally free groups and bring arguments in support of the conjecture that the number of very long primitive words in the braid group is not sensitive to the precise local commutation relations. We consider the connection of these problems with the conventional random operator theory, localization phenomena and statistics of systems with quenched disorder. Also we discuss the relation of the particular problems of random operator theory to the theory of modular functionsComment: 36 pages, LaTeX, 4 separated Postscript figures, submitted to Nucl. Phys. B [PM

Artificial tongues and leaves

The objective with synthetic multifunctional nanoarchitecture is to create large suprastructures with interesting functions. For this purpose, lipid bilayer membranes or conducting surfaces have been used as platforms and rigid-rod molecules as shape-persistent scaffolds. Examples for functions obtained by this approach include pores that can act as multicomponent sensors in complex matrices or rigid-rod π-stack architecture for artificial photosynthesis and photovoltaic

Disorder-assisted error correction in Majorana chains

It was recently realized that quenched disorder may enhance the reliability of topological qubits by reducing the mobility of anyons at zero temperature. Here we compute storage times with and without disorder for quantum chains with unpaired Majorana fermions - the simplest toy model of a quantum memory. Disorder takes the form of a random site-dependent chemical potential. The corresponding one-particle problem is a one-dimensional Anderson model with disorder in the hopping amplitudes. We focus on the zero-temperature storage of a qubit encoded in the ground state of the Majorana chain. Storage and retrieval are modeled by a unitary evolution under the memory Hamiltonian with an unknown weak perturbation followed by an error-correction step. Assuming dynamical localization of the one-particle problem, we show that the storage time grows exponentially with the system size. We give supporting evidence for the required localization property by estimating Lyapunov exponents of the one-particle eigenfunctions. We also simulate the storage process for chains with a few hundred sites. Our numerical results indicate that in the absence of disorder, the storage time grows only as a logarithm of the system size. We provide numerical evidence for the beneficial effect of disorder on storage times and show that suitably chosen pseudorandom potentials can outperform random ones.Comment: 50 pages, 7 figure

Some Aspects of Multifractal analysis

The aim of this survey is to present some aspects of multifractal analysis around the recently developed subject of multiple ergodic averages. Related topics include dimensions of measures, oriented walks, Riesz products etc

Random ballistic growth and diffusion in symmetric spaces

Sequential ballistic deposition (BD) with next-nearest-neighbor (NNN) interactions in a N-column box is viewed a time-ordered product of N\times N-matrices consisting of a single sl_2-block which has a random position along the diagonal. We relate the uniform BD growth with the diffusion in the symmetric space H_N=SL(N,R)/SO(N). In particular, the distribution of the maximal height of a growing heap is connected with the distribution of the maximal distance for the diffusion process in H_N. The coordinates of H_N are interpreted as the coordinates of particles of the one--dimensional Toda chain. The group-theoretic structure of the system and links to some random matrix models are also discussed.Comment: 29 pages, 7 figures. Revised and published version. To appear in Nuclear Physics

2023 Roadmap on ammonia as a carbon-free fuel

The 15 short chapters that form this 2023 ammonia-for-energy roadmap provide a comprehensive assessment of the current worldwide ammonia landscape and the future opportunities and associated challenges facing the use of ammonia, not only in the part that it can play in terms of the future displacement of fossil-fuel reserves towards massive, long-term, carbon-free energy storage and heat and power provision, but also in its broader holistic impacts that touch all three components of the future global food-water-energy nexus