Random-matrix theory of thermal conduction in superconducting quantum dots.

Theoretical Physic

Random-matrix theory and stroboscopic models of topological insulators and superconductors

Topological phases of matter are exceptional because they do not arise due to a symmetry breaking mechanism. Instead they are characterized by topological invariants -- integer numbers that are insensitive to small perturbations of the Hamiltonian. As a consequence they support conducting surface states that are protected against disorder and other imperfections. Furthermore, a variety of unusual transport properties arise due to the presence of topology. In this work the interplay between topology and sample imperfections is investigated with a focus on transport phenomena.</p

Extending Partial Representations of Circle Graphs

The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We study the partial representation extension problem for circle graphs, where the input consists of a graph G and a partial representation R′ giving some pre-drawn chords that represent an induced subgraph of G. The question is whether one can extend R′ to a representation R of the entire G, i.e., whether one can draw the remaining chords into a partially pre-drawn representation. Our main result is a polynomial-time algorithm for partial representation extension of circle graphs. To show this, we describe the structure of all representation a circle graph based on split decomposition. This can be of an independent interest

Introducing music students to harmony – an alternative method

If teaching and learning harmony could rely less on prescriptive rules and more on the music that students themselves play, an alternative teaching method for harmony beginners may become possible. This approach yields a specific kind of knowledge, namely non-propositional knowledge or knowledge acquired by direct experience. After considering the function of thinking and doing in experiential learning, the article shows how the teaching of harmony in the twentieth century steadily moved away from the legacy of Rameau, the founder of harmony as a discipline in the eighteenth century. By using as point of departure melodic motifs in the piano music that students play, this article demonstrates the integration of horizontal and vertical musical features when introducing music students to the study of harmony. Furthermore, it shows how a linear approach could eventually lead through two-part counterpoint to the writing of four-part harmony, demonstrated at the end of the article. This proposed method provides a foundation for acquiring basic music-writing skills that are less concerned with music theory as a regulatory discipline and more with music as a creative art.http://www.tandfonline.com/loi/redc202016-06-30hb201

Tau-function theory of chaotic quantum transport with β = 1, 2, 4

We study the cumulants and their generating functions of the probability distributions of the conductance, shot noise and Wigner delay time in ballistic quantum dots. Our approach is based on the integrable theory of certain matrix integrals and applies to all the symmetry classes β∈{1,2,4} of Random Matrix Theory. We compute the weak localization corrections to the mixed cumulants of the conductance and shot noise for β = 1, 4, thus proving a number of conjectures of Khoruzhenko et al. (in Phys Rev B 80:(12)125301, 2009). We derive differential equations that characterize the cumulant generating functions for all β∈{1,2,4}. Furthermore, when β = 2 we show that the cumulant generating function of the Wigner delay time can be expressed in terms of the Painlevé III′ transcendant. This allows us to study properties of the cumulants of the Wigner delay time in the asymptotic limit n→∞. Finally, for all the symmetry classes and for any number of open channels, we derive a set of recurrence relations that are very efficient for computing cumulants at all orders