Recent years have seen a growing interest in dynamical quantum processes; thus it was found that the electronic energy transfer through photosynthetic antennae displays quantum features, aspects known from the dynamics of charge carriers along polymer backbones and of excitations in quantum gases. Hence, in modelling energy transfer one has to extend the classical, master-equation-type formalism and incorporate quantum-mechanical aspects, while still taking into account the complex network of molecules over which the transport takes place.
Interestingly, the continuous time random walk (CTRW) scheme, widely employed in modelling transport in random environments, is mathematically very close to quantum- mechanical Hamiltonians of tight-binding type[1]; a simple way to see it is to focus on the time-evolution operators in statistical and in quantum mechanics: The transformation to the quantal domain leads then to continuous-time quantum walks (CTQWs).
Now, while the CTQW problem is then linear, and thus many results obtained in solving CTRWs (such as eigenvalues and eigenfunctions) can be readily reutilized for CTQWs, the physically relevant properties of the two models differ vastly: In the absence of traps CTQWs are time-inversion symmetric and no energy equipartition takes place at long times. Also, the quantum system keeps memory of the initial conditions, a fact exemplified by the occurrence of quasi-revivals [1]. In this talk we will discuss this and additional features, such as the topology dependence of CTQWs, ranging from very efficient transport on regular lattices [2] to localization and trapping effects on small-world networks [3] and on fractal and hyperbranched structures [4]. We will furthermore compare the CTQW results to the corresponding CTRW results on topologically equivalent networks. This allows us to systematically explore the similarities and differences between purely classical and purely quantum-mechanical processes [1, 4].

[1] O. Mülken and A. Blumen; Phys. Rev. E 71, 036128 (2005); Phys. Rev. E 73, 066117 (2006); Physics Reports 502, 37 (2011)
[2] O. Mülken, V. Bierbaum, and A. Blumen; J. Chem. Phys. 124, 124905 (2006).
[3] O. Mülken, V. Pernice, and A. Blumen; Phys. Rev. E 76, 051125 (2007)
[4] E. Agliari, A. Blumen, and O. Mülken; J. Phys. A 41, 445301 (2008); Phys. Rev. A 82, 012305 (2010); Intern. J. Bifurc. Chaos, 20, 271 (2010)

In female mammal embryo, X-Chromosome Inactivation is the vital process whereby each cell inactivates one, randomly selected X to equalize X products w.r.t. males. Such a chromosome wide stochastic regulation has attracted substantial interests because it is unknown how the X's undergo random, yet opposite fates. We proposed a possible physical explanation: a Symmetry Breaking mechanism, with a related set of new 'particles' involved and a corresponding phase diagram. Our model, confirmed by recent experiments in Harvard, describes how a 'blocking' complex, responsible for protecting the bound X from inactivation, is self-assembled and why only one is formed out of many diffusible molecules, resulting in a spontaneous symmetry breaking in the binding to two identical X's.

The idea that the distance among pairs of languages can be evaluated from lexical differences seems to have its roots in the work of the French explorer Dumont D'Urville. He collected comparative words lists of various languages during his voyages aboard the Astrolabe from 1826 to 1829 and, in his work about the geographical division of the Pacific, he proposed a method to measure the degree of relation between languages. The method used by the modern glottochronology, developed by Morris Swadesh in the 1950s, measures distances from the percentage of shared cognates, which are words with a common historical origin. The weak point of this method is that subjective judgment plays a relevant role. In fact, even if cognacy decisions are made by trained and experienced linguists, they typically vary for different authors. Recently, we have proposed a new automated method which is motivated by the analogy with genetics. The new approach has some advantages: the first is that it avoids subjectivity, the second is that results can be replicated by other scholars assuming that the database is the same, the third is that it is not requested a specific expertize in linguistic, and the last, but surely not the least, is that it allows for a rapid comparison of a very large number of languages. The distance between two languages is defined by considering a renormalized Levenshtein distance between pair of words with the same meaning and averaging on the words contained in a list. The renormalization, which takes into account the length of the words, plays a crucial role, and no sensible results can be found without it. In this paper we give a short review of our automated method and we illustrate it by the Indo-European family and the cluster of Malagasy dialects, showing in both cases that it is able find out new important aspects of the languages relationships.