Theory of small charge solitons in one-dimensional arrays of Josephson junctions

We identify and investigate the new parameter regime of small charge solitons in one-dimensional arrays of Josephson junctions. We obtain the dispersion relation of the soliton and show that it unexpectedly flattens in the outer region of the Brillouin zone. We demonstrate Lorentz contraction of the soliton in the middle of the Brillouin zone as well as broadening of the soliton in the flat band regime.Comment: 4 pages, 6 figures, final published versio

On the inducibility of small trees

The quantity that captures the asymptotic value of the maximum number of appearances of a given topological tree (a rooted tree with no vertices of outdegree $1$) $S$ with $k$ leaves in an arbitrary tree with sufficiently large number of leaves is called the inducibility of $S$. Its precise value is known only for some specific families of trees, most of them exhibiting a symmetrical configuration. In an attempt to answer a recent question posed by Czabarka, Sz\'ekely, and the second author of this article, we provide bounds for the inducibility $J(A_5)$ of the $5$-leaf binary tree $A_5$ whose branches are a single leaf and the complete binary tree of height $2$. It was indicated before that $J(A_5)$ appears to be `close' to $1/4$. We can make this precise by showing that $0.24707\ldots \leq J(A_5) \leq 0.24745\ldots$. Furthermore, we also consider the problem of determining the inducibility of the tree $Q_4$, which is the only tree among $4$-leaf topological trees for which the inducibility is unknown

Cooling and aggregation in wet granulates

Wet granular materials are characterized by a defined bond energy in their particle interaction such that breaking a bond implies an irreversible loss of a fixed amount of energy. Associated with the bond energy is a nonequilibrium transition, setting in as the granular temperature falls below the bond energy. The subsequent aggregation of particles into clusters is shown to be a self-similar growth process with a cluster size distribution that obeys scaling. In the early phase of aggregation the clusters are fractals with D_f=2, for later times we observe gelation. We use simple scaling arguments to derive the temperature decay in the early and late stages of cooling and verify our results with event-driven simulations.Comment: 4 pages, 6 figures, suggestions of the referees implemented, EPAPS supplementary material added: http://netserver.aip.org/cgi-bin/epaps?ID=E-PRLTAO-102-00391

Bose-Glass Phases in Disordered Quantum Magnets

In disordered spin systems with antiferromagnetic Heisenberg exchange, transitions into and out of a magnetic-field-induced ordered phase pass through a unique regime. Using quantum Monte Carlo simulations to study the zero-temperature behavior, these intermediate regions are determined to be a Bose-Glass phase. The localization of field-induced triplons causes a finite compressibility and hence glassiness in the disordered phase.Comment: 4 pages, 4 figure