Schedule for: 16w5069 - Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications

Few electron electrostatically gated quantum dots have been developed historically with two main purposes in mind. Firstly, they provide an excellent and controlled experimental laboratory for comparison with exact theoretical model calculations. Secondly, the versatility and tunability that results from having electrical control over the relevant quantum dot properties produced a potential platform for the development of spin based quantum computers and simulators. The materials in which the quantum dots are defined have important consequences for experiments via parameters such as those related to hyperfine, spin-orbit and electron-phonon coupling. The quantum dots described in this talk are defined in GaAs/AlGaAs heterostructure. In this talk I will review some recent experiments we have performed on triple few electron quantum dots. A brief introduction will be provided about this genre of quantum dot devices and the techniques which have been developed to make measurements, e.g. how information about the spin state is obtained directly from charge measurements and how it is possible to identify the electron occupation of each quantum dot in an array. The emphasis on the talk will be on the surprisingly important and coherent role that phonons play in some of the measurements either directly or in combination with spin-orbit effects. A variety of experimental probes such as Landau-Zener-Stuckelberg-Majorana spin interferometry will be used to illustrate the effects.

We model the dynamics of electrons in doped quantum wells driven by terahertz radiation and a superlattice biased by a dc voltage. We compute coherent, self-consistent electron states, density matrix equations of motion, and dipole absorption spectra. The model simultaneously accounts for intersubband transitions and many nonlinear phenomena that have been observed in these systems. We predict a bistable response for strong terahertz fields and bifurcations to coherent time-periodic quantum states. These bifurcation include, period-doubling bifurcations, producing a subharmonic response, Hopf bifurcations producing an incommensurate frequency response, and a cascade of period doubling bifurcations to a strange attractor. We also see a cascade of quasi-periodic orbits on the Hopf torus to a strange attractor. These bifurcation have been difficult to measure in single quantum wells. Therefore we design super-lattice heterostructures of quantum wells where these bifurcations occur and are easier to measure.

In their book on path integrals, Feyman and Hibbs formulated a "geometrical optics" of most probable paths in stochastic dynamical systems. The most probable path in state space between two given endpoints minimizes a stochastic action functional. Some significant features of this geometric optics: The speed along the most probable path equals the deterministic speed, and generally speaking, the "Snell’s law" that determines the geometry of the path is not invariant under orientation reversal. The paths from point \(a\) to point \(b\), and from \(b\) back to \(a\) may be different. We present a dramatic example demonstrating the breaking of orientation reversal. In the special cases with orientation reversal invariance, the stochastic dynamics is said to have detailed bal- ance. The local expression of detailed balance is the vanishing of a stochastic vorticity tensor which is determined from the velocity field and noise tensor of the dynamics. A more traditional notion of detailed balance is based upon the existence of equilibrium solutions to the Folker-Planck equation, in which the probability current vanishes identically. The condition for equilibrium solutions in this sense is vanishing vorticity. We can detect the breaking of detailed balance from direct measurements of stochastic trajectories: Project the dynamics down onto a two dimensional plane in state space, and look at the area swept out by the projected trajectory. If detailed balance is broken, there are planes of projection, so that the expected area grows linearly in time. We carry out this program for a simple RC network with "cold" and "hot" resistors. The breaking of detailed balance directly correlates with net heat transfer from the hot resistor to the cold resistor. One of the intriguing aspects of the area crtierion: We can implement it in practice, without knowledge of the velocity field and noise tensor of the stochastic dynamics.

How does confinement alter the transport properties of colloidal particles, the functionalities of molecular ma- chines and in general the mechanisms of energy-transfer and energy-conversion at small scales? This question, fundamental for the modelling of soft-matter systems and biological systems, is attracting the interest of many researchers in the field. In a basic model proposed, the confinement effects are considered through an entropic potential. It has been shown that transport through entropic barriers or entropic transport exhibits peculiar charac- teristics very different from those observed when activation takes place through energetic barriers. In this talk, I will briefly review recent progresses in the study of entropic transport and its applications to soft-matter and biolog- ical systems. I will show that the confinement plays a very important role in the mechanisms of energy-conversion at the nanoscale, in particular in the functionality of molecular machines.

We discuss and evaluate models for the dynamics of two novel measurement platforms: (i) a Pore Formation Measurement Platform (PFMP) for detecting the presence of pore forming proteins and peptides, (ii) the Ion Channel Switch (ICS) biosensor for detecting the presence of analyte molecules in a fluid chamber. Common to both measurement platforms is that they are comprised of an engineered tethered membrane. The electrical response is modelled using continuum theories for electrodiffusive flow coupled with boundary conditions for modelling chemical reactions and electrical double layers present at the bioelectronic interface. Experimental measurements are used to validate the predictive accuracy of the dynamic models.

In recent years, atomic force microscopy (AFM) has been used to look into the elasticity of modular proteins, which comprise a certain number of identical protein domains [3]. The molecule is typically pulled from one end while the other is kept fixed, and either the length of the biomolecule or the force applied on it is controlled. In the above experiments, the force-extension curve (FEC) is recorded, which gives the force needed to stretch the biomolecule as a function of its length. In modular proteins, the FEC shows a sawtooth behaviour under length- control: the unfolding of the different units that constitute the polyprotein is accompanied by a drop of the force. Moreover, the force at which the unfolding takes place, increases with the stretching rate [4–8]. On the other hand, there are also protein domains that are composed of several stable structural units or “un- foldons”. The unfolding pathway is defined as the order and the way in which these “unfoldons” unravel, and it depends on the pulling speed. Consistently with the physical intuition, the weakest unfoldon opens first at low pulling rates. At higher rates, no longer is the first unit that unfolds but the pulled one [9–12]. In this talk, we discuss how some key aspects of these pulling experiments can be understood by using “toy” models [13–15]. Basically, the extension of each unit follows an overdamped Langevin equation. First, for the analysis of the FEC, the units are independent except for the global constraint given by the length-control condi- tion. Second, we study the unfolding pathway by taking into account the spatial structure of the molecule, which introduces crucial additional couplings among the units. References [1] F.Ritort,J.Phys.:Condens.Matter18,R531-R583(2006) [2] S.KumarandM.S.Li,Phys.Rep.486,1(2010) [3] P.E.MarszalekandY.F.Dufrêne,Chem.Soc.Rev.41,3523(2012) [4] S.B.Smith,Y.CuiandC.Bustamante,Science271,795-799(1996) [5] M. Carrion-Vázquez, A. F. Oberhauser, S. B. Fowler, P. E. Marszalek, S. E. Broedel, J. Clarke and J. M. Fernandez, Proc. Natl. Acad. Sci. USA 96, 3694-3699 (1999) [6] H.LuandK.Schulten,ProteinsStruct.Funct.Genet.35,453-463(1999) [7] T.E.Fisher,P.E.MarszalekandJ.M.Fernandez,NatureStruct.Biol.7,719-724(2000) [8] Y.Cao,R.KuskeandH.Li,Biophys.J.95,782-788(2008) [9] C.Hyeon,R.I.Dima,andD.Thirumalai,Structure14,1633(2006) [10] M.S.LiandM.Kouza,J.Chem.Phys.130,145102(2009) [11] C.Guardiani,D.DiMarino,A.Tramontano,M.ChinappiandF.Cecconi,J.Chem.TheoryComput.10,3589(2014) [12] M.Kouza,C.K.Hu,M.S.LiandK.Kolinski,J.Chem.Phys.139,065103(2013) [13] L.L.Bonilla,A.Carpio,andA.Prados,EPL108,28002(2014)[HighlightedinRevistaEspañoladeFísica29(3),29(2015)] [14] L. L. Bonilla, A. Carpio, and A. Prados, Phys. Rev. E 91, 052712 (2015). [Highlighted in Revista Española de Física 29 (3), 29 (2015)] [15] C.A.Plata,F.Cecconi,M.Chinappi,andA.Prados,J.Stat.Mech.P08003(2015)

Please see http://www.birs.ca/workshops/2016/16w5069/Programme16w5069.pdf

Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

Please see http://www.birs.ca/workshops/2016/16w5069/Programme16w5069.pdf

Synthesis of vertically stacked two dimensional van der Waals heterostructures displaying a wide variety of applications is now possible with the advent of advanced experimental techniques. The properties of these het- erostructures (and their applicability) are tunable with the relative orientation, lattice mismatch and separation between the layers. Theoretical modeling and simulation form a crucial part of the discovery and design of these materials, and provide important clues to the origin of exotic phenomena that may emerge in these heterostructure. Analysis of these two dimensional van der Waals heterostructures with arbitrary angles of rotation between the layers involves unrealistically large and computationally expensive ab-initio calculations. To overcome this shortcoming, we have developed a model for weakly interacting heterostructures that treats the effect of one layer on the other as a perturbation, and restricts the calculations only to their primitive cells. Thus, circumventing the problem of computations over large supercells. We start by approximating the interaction potential between the twisted bilayers to that of a hypothetical configuration (viz. ideally stacked untwisted layers [1]); and then proceed to self-consistently calculating the charge density and hence, the interaction potential of the heterostructures. In this work, we test our model for bilayers of various combinations of graphene, hexagonal boron nitride and transition metal dichalcogenides, and discuss the advantages and shortcomings of the self-consistently calculated interaction potential of the heterostructure. [1] Georgios A Tritsaris et. al. “Perturbation theory for weakely coupled two-dimensional layers”, Journal of Materials Research 31, 959-966 (2016).

Please see http://www.birs.ca/workshops/2016/16w5069/Programme16w5069.pdf

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Understanding deformations of macroscopic thin plates and shells has a long and rich history, culminating with the Foeppl-von Karman equations in 1904, characterized by a dimensionless coupling constant (the "Foeppl-von Karman number") that can easily reach vK = 10^7 in an ordinary sheet of writing paper. However, thermal fluctu- ations in thin elastic membranes fundamentally alter the long wavelength physics, as exemplified by experiments from the McEuen group at Cornell that twist and bend individual atomically-thin free-standing graphene sheets (with vK = 10^13!) We review here the remarkable properties of thermalized sheets, where enhancements of the bending rigidity by factors of ∼ 5000 have now been observed. We then move on to discuss thin amorphous spherical shells with a uniform nonzero curvature, accessible for example with soft matter experiments on diblock copolymers. This curvature couples the in-plane stretching modes with the out-of-plane undulation modes, giving rise to qualitative differences in the fluctuations of thermal spherical shells compared to flat membranes. Inter- esting effects arise because a shell can support a pressure difference between its interior and exterior. Thermal corrections to the predictions of classical shell theory for microscale shells diverge as the shell radius tends to infinity.

From multicellular tissues to bacterial colonies, three dimensional cellular structures arise through the inter- action of cellular activities and mechanical forces. Simple bacterial communities provide model systems for ana- lyzing such interaction. Biofilms are bacterial aggregates attached to wet surfaces and encased in a self-produced polymeric matrix. Biofilms in flows [1, 2] form filamentary structures that contrast with the wrinkled layers observed on air/solid interfaces [3, 4]. We are able to reproduce both types of shapes through elastic rod and plate models [2, 4] that incorporate information from the biomass production and differentiations process, such as growth rates, growth tensors or inner stresses, as well as constraints imposed by the interaction with environ- ment. A more precise study of biofilm dynamics requires tackling water absorption from its surroundings and fluid transport within the biological system. This process alters the material properties of the biofilm and the overall stresses. We analyze whether poroelastic approaches [5] can provide a suitable combined description of fluid-like and solid-like biofilm behavior. References [1] K.Drescher,Y.Shen,B.L.BasslerandH.A.Stone,Biofilmstreamerscausecatastrophicdisruptionofflowwithconsequencesfor environmental and medical systems, Proc. Nat. Acad. Sc. USA 110, 4345-4350 (2013). [2] D.R. Espeso, A. Carpio, E. Martinez-Garcia and V. de Lorenzo, Stenosis triggers spread of helical Pseudomonas biofilms in cylin- drical flow systems, Sci. Rep. 6, 27170 (2016). [3] A.Seminara,T.E.Angelini,J.N.Wilking,H.Vlamakis,S.Ebrahim,R.Kolter,D.A.WeitzandM.P.Brenner,Osmoticspreadingof Bacillus subtilis biofilms driven by an extracellular matrix, Proc. Natl. Acad. Sci. USA 109, 1116-1121 (2012). [4] D.R.Espeso,A.CarpioandB.Einarsson,Differentialgrowthofwrinkledbiofilms,Phys.Rev.E91,022710(2015). [5] M.A.Biot,Generaltheoryofthreedimensionalconsolidation,J.Appl.Phys.12,155-164(1941).

Angiogenesis is a multiscale process by which blood vessels grow from existing ones and carry oxygen to distant organs. Angiogenesis is essential for normal organ growth and wounded tissue repair but it may also be induced by tumors to amplify their own growth. Mathematical and computational models contribute to understand- ing angiogenesis and developing anti-angiogenic drugs, but most work only involves numerical simulations and analysis has lagged. A recent stochastic model of tumor induced angiogenesis including branching, elongation, and anastomosis (fusion) of blood vessels captures some of its intrinsic multiscale structures, yet allows one to extract a deterministic integropartial differential description of the vessel tip density [1]. Vessel tips proliferate due to branching, elongate following Langevin dynamics and, when they meet other vessels, join them by anastomosis and stop moving. Stalk endothelial cells follow the tip cells, so that the trajec- tories thereof constitute the advancing blood vessel. Anastomosis keeps the number of vessel tips relatively small, so that we cannot use the law of large numbers to derive equations for their density. Nevertheless, we show that ensemble averages over many replicas of the stochastic process correspond to the solution of the deterministic equations with appropriate boundary conditions [2]. Most of the time, the density of tips sprouting from a primary blood vessel advances chemotactically towards the tumor driven by a soliton similar to the famous Korteweg-de Vries soliton. There are two collective coordinates whose slow dynamics changes the shape and velocity of the soliton. Analyzing the equations for the collective coordinates paves the way for controlling angiogenesis through the soliton, the engine that drives this process [3]. References [1] L.L. Bonilla, V. Capasso, M. Alvaro, and M. Carretero, Hybrid modeling of tumor-induced angiogenesis, Phys. Rev. E 90, 062716 (2014). [2] F.Terragni,M.Carretero,V.CapassoandL.L.Bonilla,StochasticModelofTumor-inducedAngiogenesis:EnsembleAveragesand Deterministic Equations, Phys. Rev. E 93, 022413 (2016). [3] L.L.Bonilla,M.Carretero,F.Terragni,andB.Birnir,Solitondrivenangiogenesis,submittedforpublication,2016.

The most exciting effects associated with wetting and adsorption are caused by the fluid inhomogeneity at the nanoscale and the nonlocality of the intermolecular fluid–fluid and fluid–substrate interactions. Fluids adsorbed at walls, in capillary pores and slits and in sculpted geometries such as grooves and wedges can form different thermodynamic phases (e.g., figure 1) and exhibit many new phase transitions compared to their bulk counterparts. As well as being of fundamental interest to the modern statistical mechanical theory of inhomogeneous fluids, these are also relevant to nanofluidics, chemical- and bioengineering, design of surfaces with tunable wetting properties and lab-on-a-chip devices. In this talk we will discuss novel, first-order and continuous, interfacial transitions, including wetting, pre-wetting, capillary-condensation and filling, the formation of droplets and liquid bridges [1, 2], which can occur in sculpted pores with one or more dimensions on the order of several nanometers. These transitions are sensitive to both the range of the intermolecular forces and the interfacial fluctuation effects. Our methodology is based on the density functional theory (DFT) formulation of statistical mechanics of classical fluids. Within DFT, the grand free energy of a classical soft-matter system is expressed as a functional of the system’s one-body density field. In this way, DFT elegantly captures the small-scale inhomogeneity of the fluid structure in a theoretically consistent and computationally accessible manner, and can be viewed as a means to include the fluid structure into the thermodynamic equation of state. Dynamic DFT (DDFT) in its simplest form is a generalized diffusion equation corresponding to the Smoluchowsky picture of the dynamics of colloidal particles in a solvent. We will demonstrate how DDFT can be used effectively to study diffusion-driven spreading and coalescence of sessile nanodroplets. Our computations may provide insight into the dynamics of the three-phase contact line and static and dynamic contact angles of small nanodroplets, which remain in debate.

Novel paradigms of signal and information processing have received significant attention based on their promise of new functionalities, new interfacing capabilities, and in some cases speed-up for sensor, diagnostic, and computational applications. Such “unconventional computing” realizations are in some cases contemplated as competitive, but in most situations will be complementary to the modern electronics technology. An emerging research field of processing signals and information by using biomolecular processes will be surveyed in this talk, and specific examples and research results will be presented for enzyme-catalyzed biomolecular reactions. For additional information, see Ref. [1, 2, 3]. References [1] http://www.clarkson.edu/Privman. [2] V. Privman, S. Domanskyi, S. Mailloux, Y. Holade, and E. Katz, Kinetic Model for a Threshold Filter in an Enzymatic System for Bioanalytical and Biocomputing Applications, J. Phys. Chem. B 118, pp. 12435-12443 (2014); http://dx.doi.org/10.1021/jp508224y. [3] Invited Review: S. Domanskyi and V. Privman, Modeling and Modifying Response of Biochemical Processes for Biocomputing and Biosensing Signal Processing, Ch. 3 in Advances in Unconventional Computing, A. Adamatzky (ed.), Emergence, Complexity and Computation, Vol. 23 (Springer, in print, 2016); http://dx.doi.org/10.1007/978-3-319-33921-4_3.

Electronic charge and heat flows can be separated in three-terminal conductors. Two terminals support the charge current with the third one serving as the heat source. The properties of the mesoscopic junction determine how the injected heat current affects the charge and energy transport in the conductor. This way, the system can be designed to work as a non-local heat engine (if heat is converted into useful power). This effect has been recently observed in coupled quantum dot configurations (cf. Fig. 1) where the heat transfer is mediated by electron- electron interactions [1, 2, 3, 4]. The magnitude and sign of the generated current can be controled by external gate voltages. They also allow one to manipulate the heat flows in all-thermal operations such as a thermal transistor or a thermal diode [5]. The non-local coupling to the heat sources of a non-thermalized state in the quantum dot also leads to the unprecedented occurrence of a thermoelectric response with no net absorbed heat [6]. References [1] R.Sánchez, M.Büttiker, Optimal energy quanta to current conversion, Phys.Rev.B87,8,pp.075312(2011). [2] H.Thierschmannetal., Three-terminal energy harvester with coupled quantum dots, Nature Nanotech.10,pp.854-858(2015). [3] B.Rocheetal., Harvesting dissipated energy with a mesoscopic ratchet, Nature Comm.6,pp.6738(2015). [4] F. Hartmann et al., Voltage Fluctuation to Current Converter with Coulomb-Coupled Quantum Dots, Phys. Rev. Lett. 10, 14, pp. 146805 (2015). [5] H.Thierschmannetal., Thermoelectrics with Coulomb coupled quantum dots,arXiv:1603.08900(2016). [6] R.S.Whitney, R.Sánchez, F.Haupt, and J.Splettstoesser, Thermoelectricity without absorbing energy from the heat sources,Physia E 75, pp. 257-265 (2016).

Determing excited states in quantum physics or calculating the number of valence electrons in the Density Functional Theory (DFT) involve solving eigenvalue problems of very large dimensions. Moreover, very often the interesting features of these complex systems go beyond information contained in the extreme eigenpairs. For this reason, it is important to consider iterative solvers developed to compute a large amount of eigenpairs in the middle of the spectrum of large Hermitian and non-Hermitian matrices. In this talk, we present a newly developed Krylov-type methods and compare them with the well-established techniques in electronic structure calculations. We demonstrate their efficiency and robustness through various numerical examples.

We discuss a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by pre- scribing a probabilistic coarse-to-fine map. This corresponds to a directed probabilistic model where the coarse variables play the role of latent generators of the fine scale (all-atom) data. From an information-theoretic per- spective, the framework proposed provides an improvement upon the relative entropy method that quantifies the uncertainty due to the information loss that unavoidably takes place during the CG process. Furthermore, it can be readily extended to a fully Bayesian model where various sources of uncertainties are reflected in the parameters’ posterior. The latter can be used to produce not only point estimates of fine-scale reconstructions or macroscopic observables, but more importantly, predictive posterior distributions on these quantities. These quantify the confi- dence of the model as a function of the amount of data and the level of coarse-graining. The issues of model complexity and model selection are seamlessly addressed by employing a hierarchical prior that favors the discovery of sparse solutions, revealing the most prominent features in the coarse-grained model. A flexible and parallelizable, Monte Carlo - Expectation-Maximization (MC-EM) scheme is proposed for carrying out inference and learning tasks. A comparative assessment of the proposed methodology is presented for a lattice spin system and the SPC/E water model. This is a joint work with Markus Schöberl and Phaedon-Stelios Koutsourelakis, Technical University of Mu- nich.

Over the past few decades nanoscience and molecular biology has shown a strong growth worldwide in many areas of research and proved their significance in todays ́ competitive environment. However, there still remains an enormous potential for further development which could revolutionize every area of human life. Unfortunately, in some cases, that potential is screened out by complexity and multilevel character of systems and processes at a nanometer scale. The success of future applications in a high-tech industry requires deep understanding of fundamental mechanisms on different levels of description and their communication. That could be provided only by appropriate combination of experimental study with predictive theoretical modeling. Nowadays, more and more scientists in different fields of chemistry and biology are using computational modeling methods in their research, either as a technique per se, or as a complement to experimental work. However, despite the in- creasing attention to computational nanoscience and biology the specificity of application of standard theoretical and computational modeling in nanotechnology and bioscience is complicated due to complexity of the systems of interest and needs to be discussed separately, especially in the view of multilevel representation of systems and pro- cesses on nanoscale. One of most important and demanding applications in computational chemistry is multiscale modeling of properties and interaction of macro/bio molecules in solvents and mixtures. The presentation will address different aspects of theoretical and computational approaches and their combination at the different time and length scales to model impact of solvents on physicochemical properties of molecules as geometry, conforma- tional equilibria, reaction rates, as well as their UV-vis, IR, or NMR spectra. It will focus on the combination of statistical-mechanical molecular theory of liquids (3D reference interaction site model, known as 3D-RISM) with density functional theory (DFT) which provides the accurate and efficient way to predict the electronic properties of molecular system in different solvents and mixtures with high level of accuracy comparable with simulations but with less computational cost [1]. Similar to explicit solvent simulations, 3D-RISM properly accounts for chemical and physical activity of both solute and solvent molecules, such as hydrogen bonding and hydrophobic forces, by yielding the 3D site density distributions of the solvent. Moreover, it readily provides, via analytical expressions, the solvation thermodynamics, including the solvation free energy, its energetic and entropic decomposition, and partial molar volume and compressibility. Recently the number of new approaches and approximations was de- veloped in order to increase efficiency of 3D-RISM and DFT combination. They could be subdivided into two main groups focused on the optimization of 3D-RISM algorithm (memory optimization, parallelization, etc.) and methodology improvements [2]. I will present a review and analysis of latest achievements focused on improves of accuracy and applicability the combination. Some examples will be also discussed. References [1] GusarovS., ZieglerT., KovalenkoA., Self-Consistent Combination of the Three-Dimensional RISM Theory of Molecular Solvation with Analytical Gradients and the Amsterdam Density Functional Package, JPCA 110, 1, pp. 6083-6090 (2006). [2] Gusarov S., Bhalchandra P., Kovalenko A., Efficient treatment of solvation shells in 3D molecular theory of solvation, , J. Comp. Chem, 33, 1, pp. 1478-1494 (2012).

A weakly coupled semiconductor superlattice (SSL) represents an almost ideal one-dimensional nonlinear dynamical system with a large number of degrees of freedom, the nonlinearity of which is due to sequential resonant tunneling between adjacent quantum wells. Fluctuations of the layer thicknesses, electron density, energy levels, and inter-well coupling transform a weakly coupled SSL into a complex nonlinear system, in which the electron transport is strongly dissipative. A great richness of nonlinear transport behavior has been observed in weakly coupled SSLs, including the formation of stationary electric-field domains, periodic as well as quasi-period current self-oscillations, and even driven as well as undriven chaos [1]. The oscillatory behavior is attributed to the localized, oscillatory motion of the domain boundary, which separates the high from the low electric-field domain. Only very recently, spontaneous chaotic [2] and quasi-periodic [3] current self-oscillations were observed at room temperature in GaAs/(Al,Ga)As SLs using an Al content of 45%, which results in the largest direct barrier for this materials system. Based on these weakly coupled GaAs/Ga0.55Al0.45As SLs operating at room temperature, an all-electronic true random number generator (TRNG) has been demonstrated [4]. The spontaneous chaotic current self-oscillations with large amplitudes characterized by a bandwidth of several hundred MHz do not require external feedback or conversion to an electronic signal prior to digitization. The fully electronic implementation suggests scalability and minimal post processing in comparison to existing optical implementations. The achievable bit rates of up to 80 Gbit/s are very competitive, being about two orders of magnitude larger than typical bit rates for currently available all-electronic TRNGs. Even more recently, the synchronization of chaos based on room temperature spontaneous chaotic current self-oscillations in a weakly coupled GaAs/Ga0.55Al0.45As SL has been demonstrated as a useful building block for various tasks in secure communications, including a source of all-electronic ultrafast TRNG [5]. Several types of chaos synchronization have been experimentally demonstrated, in particular leader- laggard, face-to-face, and zero-lag synchronization in networks of coupled SSLs. The realization of chaotic SSLs without external feedback and the synchronization among different structured SSLs open up the possibility for advanced secure multi-user communication methods based on large networks of coupled SSLs. References [1] L.L.BonillaandH.T.Grahn,Non-lineardynamicsofsemiconductorsuperlattices,Rep.Prog.Phys.68,pp.577–683(2005). [2] Y. Y. Huang, W. Li, W. Q. Ma, H. Qin, and Y. H. Zhang, Experimental observation of spontaneous chaotic current oscillations in GaAs/Al0.45Ga0.55As superlattices at room temperature, Chin. Sci. Bull. 57, pp. 2070–2072 (2012). [3] Y. Y. Huang, W. Li, W. Q. Ma, H. Qin, H. T. Grahn, and Y. H. Zhang, Spontaneous quasi-periodic current self-oscillations in a weakly coupled GaAs/(Al,Ga)As superlattice at room temperature, Appl. Phys. Lett. 102, 242107, 3 pages (2013). [4] W. Li, I. Reidler, Y. Aviad, Y. Y. Huang, H. L. Song, Y. H. Zhang, M. Rosenbluh, and I. Kanter, Fast physical random-number generation based on room-temperature chaotic oscillations in weakly coupled superlattices, Phys. Rev. Lett. 111, 044102, 5 pages (2013). [5] W. Li, Y. Aviad, I. Reidler, H. L. Song, Y. Y. Huang, K. Biermann, M. Rosenbluh, Y. H. Zhang, H. T. Grahn, and I. Kanter, Chaos synchronization in networks of semiconductor superlattices, Europhys. Lett. 112, 30007, 5 pages (2015).

Please see http://www.birs.ca/workshops/2016/16w5069/Programme16w5069.pdf

The modeling and simulation of nano-systems gives rise to a formidable list of exciting mathematical and numerical problems of various difficulties. In this talk, I will focus on two problematics: 1. the modeling and simulation of (infinite or very large) aperiodic systems; 2. the computation of error estimators. The general theory of one-particle linear models for homogeneous aperiodic materials was developed by Bel- lissard and collaborators in the 1990s, and was very successful in, notably, explaining with mathematical rigor the quantum Hall effect and some of the electronic properties of quasicrystals (see [1] and references therein). Homo- geneous multilayer 2D materials, in which aperiodicity originates from incommensurability and/or the presence of defects, can be described within this framework. On the other hand, the theory of self-consistent models (Hartree- Fock, Kohn-Sham, ...) for homogeneous aperiodic solids is not yet completely understood from a mathematical point of view [2]. The main difficulty is due to the long-range nature of the Coulomb interaction, which is only partially screened in insulators and semiconductors. Another important class of aperiodic systems encountered in chemistry and biology consists of solvated molecules. It is not possible to simulate both the solute and each and every solvent molecule surrounding it with brute force first-principle models. I will briefly present a multiscale QM/MM/PCM model [3], developed in the framework of an interdisciplinary collaboration between chemists and mathematicians, which allows one to run molecular dynamics simulations of very large solvated molecules. The second part of the talk will be concerned with the design of certified and optimized molecular simulation methods. Indeed, simulation packages should return not only the estimated value of the computed property, but also guaranteed error bars allowing one to estimate the accuracy of the simulation. Besides, since molecular simulation consumes about 20% of the CPU time available in scientific computing centers, it is important to try and optimize the use of the computational means, that is to minimize the computational cost to reach the desired accuracy. All this requires effective a posteriori error bars. Some preliminary results on the construction of discretization and algorithmic error bars for Kohn-Sham models will be presented [4]. The difficult question of model error will also be briefly addressed. References [1] J.Bellissard,Noncommutativegeometryofaperiodicsolids,GeometricandTopologicalMethodsforQuantumFieldTheory,(Villa de Leyva, 2001), pp. 86-156, World Sci. Publishing, River Edge, NJ, (2003). [2] E.Cancès,S.LahbabiandM.Lewin,Mean–fieldmodelsfordisorderedcrystals,J.Math.PuresApp.100241-274(2013). [3] F. Lipparini, G. Scalmani, L. Lagardère, B. Stamm, E. Cancès, Y. Maday, J.–P. Piquemal, M. Frisch, and B. Mennucci, Quantum, classical and hybrid QM/MM calculations in solution: General implementation of the ddCOSMO linear scaling strategy, J. Chem. Phys. 141 184108 (2014). [4] E. Cancès, G. Dusson, Y. Maday, B. Stamm and M. Vohralík, A perturbation–method–based post–processing for the plane wave discretization of Kohn–Sham models, J. Comput. Phys. 307, pp. 446-459 (2016).

Superpositions of indirectly coupled states are possible in quantum mechanics even when the intermediate states are far apart in energy. This is achieved via higher-order transitions in which the energetically forbidden intermediate states are only virtually occupied. Interest in such long-range transitions has increased recently within the context of quantum information processing with the possibility of low dissipation transfer of quantum states or coherent manipulation of two distant qubits .The recently achieved control and tunability of triple quantum dots allow to investigate phenomena relying on quantum superpositions of distant states mediated by tunneling. Recent experiments in these devices show clear evidence of charge and spin electron exchange between the outermost dots [1, 2, 3]. In the present talk I will discuss configurations of triple dots in series where long range transfer and quantum interferences determine the transport properties. I will show that the destructive interference between two virtual paths can lead to current cancelation, what we termed superexchange blockade[4]. Finally I will address long-range transport and quantum interferences in ac driven triple dots where transitions between distant and detuned dots are mediated by the exchange of photons[5]. We propose the phase difference between the two ac voltages as an external parameter, which can be easily tuned to manipulate the current characteristics. For gate voltages in phase opposition we find quantum destructive interferences among long-range and direct photon- assisted transitions, analogous to the interferences in closed-loop undriven triple dots. As the voltages oscillate in phase, interferences between multiple virtual paths give rise to dark states. Those totally cancel the current, and could be experimentally resolved. References [1] M.Busletal.,Bipolarspinblockadeandcoherentstatesuperpositionsinatriplequantumdot,NatureNanotech.8,261(2013). [2] F.Braakmanetal.,Long-distancecoherentcouplinginaquantumdotarray,NatureNanotech,8,432(2013). [3] R.Sanchezetal.,Long-RangeSpinTransferinTripleQuantumDots,Phys.Rev.Lett.,112,176803(2014). [4] R.Sanchez,F.Gallego-MarcosandG.Platero,Superexchangeblockadeintriplequantumdots,Phys.Rev.B,89,16140(R)(2014). [5] F. Gallego-Marcos,R. Sanchez and G. Platero, Coupled Landau-Zener-Stuckelberg quantum dot interferometers, Phys. Rev. B, 93, 075424 (2016).

Please see http://www.birs.ca/workshops/2016/16w5069/Programme16w5069.pdf

Please see http://www.birs.ca/workshops/2016/16w5069/Programme16w5069.pdf

Please see http://www.birs.ca/workshops/2016/16w5069/Programme16w5069.pdf

Please see http://www.birs.ca/workshops/2016/16w5069/Programme16w5069.pdf

Please see http://www.birs.ca/workshops/2016/16w5069/Programme16w5069.pdf

Two-dimensional materials have generated a lot of interest in the past decade as a new toolbox for electron- ics [1]. This family includes insulators (boron nitride), semiconductors (transition metal dichalcogenides), and conductors (graphene). Vertical stacks of a few layers of such materials, interacting through van der Waals forces, create a venue to explore and tune desired mechanical and electronic properties. Numerical computations will be essential to explore the possibilites of such assemblies, such as tuning properties through the relative twist angle between layers, chemical doping, elastic stresses, etc. However, the generically incommensurate character of these systems represents a significant hurdle. Due to the lack of periodicity, many problems remain open in this field [2]. In this talk, we present some progress towards multi-scale calculations aimed at predicting macroscopic prop- erties of heterostructures. First, we recall the electronic properties of monolayer 2D materials and the geometry of mono- as well as few-layers assemblies. Tight-binding models can be parameterized from ab-initio, micro-scale DFT calculations [3]. These models can then be used as reduced models for meso-scale numerical calculations. We present a perturbation approach which allows the computation of observables such as the density matrix in an incommensurate bilayer stacking. We also present some prospects for the calculation of transport properties in incommensurate stockings. These results have been obtained in the framework of a collaboration with the groups of M. Luskin (Math, UofM), Efthimios Kaxiras (Physics, Harvard) and Eric Cancès (Ecole des Ponts). References [1] A.K.GEIMANDI.V.GRIGORIEVA,VanderWaalsheterostructures.Nature,Vol.499,419–425,2013 [2] G.A. TRITSARIS, S.N. SHIRODKAR, E. KAXIRAS, P. CAZEAUX, M. LUSKIN, P. PLECHÁCˇ AND E. CANCÈS, Perturbation theory for weakly coupled two-dimensional layers. Journal of Materials Research, Vol. 31(7), 959–966, 2016 [3] S.FANGANDE.KAXIRASElectronicStructureTheoryofWeaklyInteractingBilayers.arXivpreprint,arXiv:1604.05371,2016

Please see http://www.birs.ca/workshops/2016/16w5069/Programme16w5069.pdf

Please see http://www.birs.ca/workshops/2016/16w5069/Programme16w5069.pdf

Please see http://www.birs.ca/workshops/2016/16w5069/Programme16w5069.pdf

Please see http://www.birs.ca/workshops/2016/16w5069/Programme16w5069.pdf

Please see http://www.birs.ca/workshops/2016/16w5069/Programme16w5069.pdf

Please see http://www.birs.ca/workshops/2016/16w5069/Programme16w5069.pdf

Self-organization of living organisms is of an astonishing complexity and efficiency. More specifically, biological systems are the site of a huge number of specific chemical reactions that require the right biomolecule to be at the right place, in the right order and in a reasonably short time to sustain cellular function and ultimately cellular life. From a dynamic point of view, this raises the fundamental question of how biomolecules effectively find their target(s); in other words, what kinds of forces bring all these specific cognate partners together in an environment as dense and ionized as cellular micro-environments. Here, we explore the possibility that biomolecules interact through long-range interactions as they are predicted from first principles of electrodynamics; “long-range“ meaning that the mentioned interactions are effective over distances much larger than the typical dimensions of the molecules involved (i.e., larger than around 5 nm in biological systems). After discussing the theoretical background of long-range electromagnetic interactions, we investigate their possible detection in a biological context from experimental devices which are nowadays available.

5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon.