Seminars 2017

The dynamics of polymer melts and concentrated solutions depend strongly of the molecular weight of the polymer chains. The main effect of increasing molecular weight is the apparition of topological constraints between the chains called entanglements. These constraints dramatically change physical properties such as viscosity, dynamics, rheology and the mechanical behavior. Despite its importance, there are still open fundamental questions about the physics of entanglements. Due to many technical issues, building appropriates and practical approaches to simulate entanglements that help to tackle these open problems is a long-standing challenge. In this work, we show how a novel and promising coarse-graining for simulating entangled polymers can be successfully used to study topological constraints in heterogeneous systems like polymer melts under strong confinement (thin films) and nanostructured block copolymers, both important regarding basic research and technological applications.

Divergent series play an interesting and important role in Physics. The purpose of the talk is to review the main summation methods for these objects and explain their main features. Special attention will be devoted to abstract summation. Other issues related to the use of series in Physics (in particular the conditionally convergent ones) will be discussed.

I will give a gentle introduction to the effects of long-range temporal correlations in stochastic particle systems, focusing particularly on fluctuations about the typical behaviour. Specifically, in the first part of the talk, I will discuss how long-range memory dependence can modify the large deviation principle describing the probability of rare currents and lead, for example, to superdiffusive behaviour. In the second part, I will describe a more interdisciplinary project incorporating the psychological "peak-end" heuristic for human memory into a simple discrete choice model from economics. Along the way, I will attempt to indicate connections between different approaches, as well as mentioning recent work on the implementation of the "cloning" procedure for evaluation of large deviations in non-Markovian processes.

Controlling transport in quantum systems holds the key to many promising quantum technologies. Here we review the power of symmetry as a resource to manipulate quantum transport, and apply these ideas to engineer novel quantum devices. Using tools from open quantum systems and large deviation theory, we show that symmetry-mediated control of transport is enabled by a pair of twin dynamic phase transitions in current statistics, accompanied by a coexistence of different transport channels. By playing with the symmetry decomposition of the initial state, one can modulate the importance of the different transport channels and hence control the flowing current. Motivated by the problem of energy harvesting we illustrate these ideas in open quantum networks, an analysis which leads to the design of a symmetry-controlled quantum thermal switch. We review an experimental setup recently proposed for symmetry-mediated quantum control in the lab based on a linear array of atom-doped optical cavities, and the possibility of using transport as a probe to uncover hidden symmetries, as recently demonstrated in molecular junctions, is also discussed. Overall, these results demonstrate the importance of symmetry not only as a organizing principle in physics but also as a tool to control quantum systems.

[1] ‍ D. Manzano and P.I. Hurtado. ArXiv:1707.07895 (2017).

We investigate the existence of topological phases in a dense two-dimensional atomic lattice gas. The coupling of the atoms to the radiation field gives rise to dissipation and a non-trivial coherent long-range exchange interaction whose form goes beyond a simple power-law. The far-field terms of the potential - which are particularly relevant for atomic separations comparable to the atomic transition wavelength - can give rise to energy spectra with one-sided divergences in the Brillouin zone. The long-ranged character of the interactions has another important consequence: it can break the standard bulk-boundary relation in topological insulators. We show that topological properties such as the transport of an excitation along the edge of the lattice are robust with respect to the presence of lattice defects and dissipation. The latter is of particular relevance as dissipation and coherent interactions are inevitably connected in our setting.

Tight-binding model is a simple yet powerful method that can be used to study electronic band structures in solid-state physics. The method considers only the hopping, or the coupling, among the most adjacent atomic wavefunctions. In this talk, I will show that tight-binding model can be faithfully reproduced by using coupled acoustic resonators. Based on such a convenient platform, we are able to experimentally investigate novel physics that arises therein. Two examples will be discussed. As the first example, we consider a 4-by-4 non-Hermitian matrix, and study the complex behaviors of the eigenfrequencies, including formation and coalescence of multiple exceptional points upon the variation of system parameters [1]. Second, we construct a Su-Schrieffer-Heeger (SSH) dimerized chain using the similar acoustic cavities. Band inversion, together with a change in (quantized) Zak phase can be realized. An interface system can be constructed using two SSH chains with different Zak phases. By coupling two of such interface systems together; we obtain a new system with a five-site unit cell. For such a system, a specific separation of the 5-by-5 Hamiltonian into a topological subspace and a non-topological subspace can be found. By tuning the system parameters, the topological interface state, which exists in the topological subspace, can be embedded into a band continuum, which resides in the non-topological subspace. This gives rise to a new type of bound states in the continuum [2].

[1] ‍ Ding, K., Ma, G., Xiao, M., Zhang, Z.-Q. and Chan, C. T. Emergence, coalescence, and topological properties of multiple exceptional points and their experimental realization. Phys. Rev. X 6, 021007 (2016).
[2] ‍ Xiao, Y., Ma, G., Zhang, Z.-Q. and Chan, C. T. Topological subspace induced bound states in continuum. Phys. Rev. Lett., accepted.

The development of high-throughput techniques for gene expression profiling over the last two decades has rapidly led to the accumulation of vast amounts of datasets, which are available in public repositories. This has enabled large-scale meta-analyses of combined data to provide new biological insights, including the identification of new cancer genes. We compiled a human gene expression dataset from over 40000 microarrays. After strict quality control and data normalisation the data was quantified in an expression matrix of $\sim 20,000$ genes and $\sim 28,000$ samples, where we identified groups like normal tissues, neoplasmic tissues, cell lines and incompletely differentiated cells. Several unsupervised analyses of the data confirmed a global structure of the gene expression, which was consistent with earlier analyses, but with more details revealed due to the increased resolution. We suggested a suitable mixed-effects linear model for gene expression, which was used to further investigate it in solid tissue tumours, and to compare these with the respective healthy solid tissues. Our analysis identified 1285 genes with a systematic expression change in cancer. The list was significantly enriched with known cancer genes from large, peer-reviewed databases, whereas the remaining ones were proposed as new cancer gene candidates.

In marked difference from incompressible fluid flows, microscale gas flows commonly couple the dynamic and thermodynamic fluid descriptions, through the combination of bulk-flow evolution and external boundary conditions. Yet, while the thermal boundary conditions have a significant effect on the generated flows, traditional studies on rarefied gas systems have been limited to gas-surface interactions where the surfaces temperatures are prescribed. Such an assumption, however, seems of little practical value, as the surface temperature at any experimental setup can only be imposed indirectly through a direct prescription of the boundary heat-flux. To examine this observation, the present work demonstrates the impact of replacing an isothermal surface condition with a heat-flux condition in a variety of one-dimensional and unsteady micro-flow setups. These include gas-flow animation problems, acoustic wave propagation, and active flow control applications. Possible extensions to higher-dimension configurations, including shear-driven flows and hydrodynamic instability problems, are also reviewed.

Granular materials are considered as a complex media when elastic waves propagates in the bulk. This complexity comes from their micro-inhomogeneous character and from the highly nonlinear behavior of the contact between the particles. Compared to the classical elastic solids, one major difference is due to the importance of the rotational degrees of freedom of each particle for the description of the elastic behavior of the media. In this work, the effects of the rotational degrees of freedom are shown through theoretical predictions, numerical simulations and experimental results. Nonlinear wave propagation phenomena also happen in granular materials. Two examples are presented. The first one is the asymmetry of the nonlinear wave generation in a granular crystal submitted to gravity. The second one is the study of one single contact sphere-plane as a nonlinear resonator.