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We propose a simple general framework to predict folding, native states, energy barriers, protein unfolding, as well as mutation induced diseases and other protein structural analyses. The model should not be considered as an alternative to classical approaches (Molecular Dynamics or Monte Carlo) because it neglects low scale details and rather focuses on global features of proteins and structural information. We aim at the description of phenomena that are out of the range of classical molecular modeling approaches due to the large computational cost: multimolecular interactions, cyclic behavior under variable external interactions, and similar. To demonstrate the effectiveness of the approach in a real case, we focus on the folding and unfolding behavior of tropoelastin and its mutations. Specifically, we derive a discrete mechanical model whose structure is deduced based on a coarse graining approach that allows us to group the amino acids sequence in a smaller number of `equivalent’ masses. Nearest neighbor energy terms are then introduced to reproduce the interaction of such amino acid groups. Nearest and non-nearest neighbor energy terms, inter and intra functional blocks are phenomenologically added in the form of Morse potentials. As we show, the resulting system reproduces important properties of the folding-unfolding mechanical response, including the monotonic and cyclic force-elongation behavior, representing a physiologically important information for elastin. The comparison with the experimental behavior of mutated tropoelastin confirms the predictivity of the model. Statement of significance Classical approaches to the study of phenomena at the molecular scale such as Molecular Dynamics (MD) represent an incredible tool to unveil mechanical and conformational properties of macromolecules, in particular for biological and medical applications. On the other hand, due to the computational cost, the time and spatial scales are limited. Focusing of the real case of tropoelastin, we propose a new approach based on a careful coarse graining of the system, able to describe the overall properties of the macromolecule and amenable of extension to larger scale effects (protein bundles, protein-protein interactions, cyclic loading). The comparison with tropoelastin behavior, also for mutations, is very promising.

International audience; Non-local and non-convex energies represent fundamental interacting effects regulating the complex behavior of many systems in biophysics and materials science. We study one-dimensional, prototypical schemes able to represent the behavior of several biomacromolecules and the phase transformation phenomena in solid mechanics. To elucidate the effects of thermal fluctuations on the non-convex non-local behavior of such systems, we consider three models of different complexity relying on thermodynamics and statistical mechanics: (i) an Ising-type scheme with an arbitrary temperature-dependent number of interfaces between different domains, (ii) a zipper model with a single interface between two evolving domains, and (iii) an approximation based on the stationary phase method. In all three cases, we study the system under both isometric condition (prescribed extension, matching with the Helmholtz ensemble of the statistical mechanics) and isotensional condition (applied force, matching with the Gibbs ensemble). Interestingly, in the Helmholtz ensemble the analysis shows the possibility of interpreting the experimentally observed thermal effects with the theoretical force–extension relation characterized by a temperature-dependent force plateau (Maxwell stress) and a force peak (nucleation stress). We obtain explicit relations for the configurational properties of the system as well (expected values of the phase fractions and number of interfaces). Moreover, we are able to prove the equivalence of the two thermodynamic ensembles in the thermodynamic limit. We finally discuss the comparison with data from the literature showing the efficiency of the proposed model in describing known experimental effects.

International audience; Phase nucleation and propagation phenomena can be characterized by a cooperative behavior regulated by non local interactions between the multistable domains and with the loading device. Cooperativity is often macroscopically witnessed by a stress-peak, distinguishing the nucleation from the propagation stress, and by a larger size of the first nucleated domain. When low dimensional scales are considered, both in nanostructures or single molecule behaviors, the interfacial energy can compete with entropic effects, leading to the experimental observation of a temperature dependent phase transition strategy. We propose a fully analytical model, in the framework of Statistical Mechanics, measuring such energetic competition and temperature dependent behavior, that well reproduces important experimental evidences. The effectiveness of the model is successfully tested in predicting the temperature dependent phase transition behavior of shape memory nanowires.

International audience; We study the rate-independent decohesion process for a chain linked to a substrate through a series of breakable elements with a softening mechanism. Such an assumption describes the realistic case when connecting links can undergo softening transitions before breaking. For instance, this is a diffuse mechanism observed both in fracture of soft materials and biological adhesion. The analysis of this model is developed in the framework of equilibrium statistical mechanics. In order to describe mechanically induced detachment of the chain from the substrate both in the cases of hard devices (prescribed extension) or soft devices (applied force), we consider both Helmholtz and Gibbs ensembles. In any case, the model can be exactly solved and is characterized by a phase transition at a given critical temperature, corresponding to the complete detachment of the chain even without mechanical actions. Interestingly, according to the 'size' of the softened region, we observe two different regimes. In one case (fragile regime) during the decohesion the measure of the softened region is negligible, whereas in the other case (ductile regime) we obtain a finite measure of the softened region that is constant, giving a temperature dependent analytic measure of the process zone.

The increasing rate of production and diffusion of photovoltaic (PV) technologies for industrial and domestic applications urges improvement of the sustainability of their demanufacuring processes in order to reduce the amount of electronic wastes. Sustainability of demanufacturing processes concerns the reduction of energy consumption, the reduction of polluting substances as well as the reduction of the effort spent in recovery of the components. No optimal process exists so far, provided a number of different approaches have been devised. A promising choice relies on the use of thermo-mechanical treatments for inducing a delamination process where interfacial bonding between layers are weakened and, finally, broken inducing delamination of the layers. In this view, the paper presents a preliminary theoretical industrialization study. We introduce a mathematical model based of the equations of thermo-elasticity to prove the feasibility of the technological process; the results of a Finite Element (FE) Analysis are then discussed to show the validity of the new sustainable demanufacturing process endeavouring the delamination process. The analysis is performed searching the optimal thermally induced cycles at cryogenic temperatures.

The class of quantum operations known as Local Operations and Classical Communication (LOCC) induces a partial ordering on quantum states. We present the results of systematic numerical computations related to the volume (with respect to the unitarily invariant measure) of the set of LOCC-convertible bipartite pure states, where the ordering is characterised by an algebraic relation known as majorization. The numerical results, which exploit a tridiagonal model of random matrices, provide quantitative evidence that the proportion of LOCC-convertible pairs vanishes in the limit of large dimension, and therefore support a previous conjecture by Nielsen. In particular, we show that the problem is equivalent to the persistence of a non-Markovian stochastic process and the proportion of LOCC-convertible pairs decays algebraically with a nontrivial persistence exponent. We extend this analysis by investigating the distribution of the maximal success probability of LOCC-conversions. We show a dichotomy in behaviour between balanced and unbalanced bipartitions. In the latter case the asymptotics is somehow surprising: in the limit of large dimensions, for the overwhelming majority of pairs of states a perfect LOCC-conversion is not possible; nevertheless, for most states there exist local strategies that succeed in achieving the conversion with a probability arbitrarily close to one. We present strong evidences of a universal scaling limit for the maximal probability of successful LOCC-conversions and we suggest a connection with the typical fluctuations of the smallest eigenvalue of Wishart random matrices., 29 pages, 8 figures

The class of incoherent operations induces a pre-order on the set of quantum pure states, defined by the possibility of converting one state into the other by transformations within the class. We prove that if two $n$-dimensional pure states are chosen independently according to the natural uniform distribution, then the probability that they are comparable vanishes as $n\rightarrow\infty$. We also study the maximal success probability of incoherent conversions and find an explicit formula for its large-$n$ asymptotic distribution. Our analysis is based on the observation that the extreme values (largest and smallest components) of a random point uniformly sampled from the unit simplex are distributed asymptotically as certain explicit homogeneous Markov chains., Comment: 12 pages, 4 figures

Single-molecule stretching experiments on DNA, RNA, and other biological macromolecules opened up the possibility of an impressive progress in many fields of Life and Medical sciences. The reliability of such experiments may be crucially limited by the possibility of determining the influence of the apparatus on the experimental outputs. Here we deduce an analytical model that we show to be coherent with previous numerical results and that quantitively reproduce AFM experimental tests on titin macromolecules and P-selectin AFM experiments with variable probe stiffnesses. We believe that the obtained analytical description can represent an important step forward in the interpretation of Single Molecule Force Spectroscopy experiments and intermolecular interactions phenomena.

We study the problem of adhesion and debonding of an elastic body interacting with a rigid substrate through a layer made of soft breakable adhesive material. The general problem is formulated in the multidimensional vectorial case, while a detailed analysis is carried for the one dimensional case leading to the study of a 1D semilinear wave equation. The initial boundary value problem is affected by the presence of a source term characterizing the interaction of the string withe the adhesive layer. This discontinuous force jumps to zero when a critical value of the displacement is reached. We obtain conditions for the initial boundary value problem ensuring the regularity of the solutions and the attachment–detachment conditions. Finally, we focus on a numerical investigation of the problem by considering regularizations of the source term and different initial conditions.

We are interested in the properties of multipartite entanglement of a system composed by $n$ $d$-level parties (qudits). Focussing our attention on pure states we want to tackle the problem of the maximization of the entanglement for such systems. In particular we effort the problem trying to minimize the purity of the system. It has been shown that not for all systems this function can reach its lower bound, however it can be proved that for all values of $n$ a $d$ can always be found such that the lower bound can be reached. In this paper we examine the high-temperature expansion of the distribution function of the bipartite purity over all balanced bipartition considering its optimization problem as a problem of statistical mechanics. In particular we prove that the series characterizing the expansion converges and we analyze the behavior of each term of the series as $d\to \infty$., 29 pages, 11 figures

Published in Procedia Engineering 180:812-82, 2017; International audience; An exhibition system is typically a physical open space made of several buildings devoted to performing demonstrations or social activities. Several examples of exhibition systems can be found word wide. The management of these spaces, even in presence of a limited number of activities, requires significant efforts: safety, welcome, merchandising, public services, etc. Nowadays, the new trend is to offer multiple, contemporary use of exhibition spaces, allowing exhibition events and regular social activities (commercial, cultural, etc.) to be dynamically intertwined, either to endeavor the huge economic investments behind infrastructures or to increase the attractiveness of the exhibition activities.This is the case of “Fiera del Levante”, one of the oldest exhibitions located in a fascinating central area on the seaside of the city of Bari - Italy. Here, multiple social scopes, such as multi-exhibitions and contemporary social activities related to public offices, restaurants and entertainment, live together. This is an almost unique setting, which makes Fiera del Levante (FdL) a complex system and makes the management of the exhibition a challenging co-management task.The paper deals with the development and demonstration of a complex-system modeling framework for the decision support of the co-management of Fiera del Levante exhibition system, taking into account the interaction both physical aspects (building assets, infrastructure, equipment, fittings, …) and intangible aspects (permanent and temporary events, management and business activities, etc) and, of course, considering as a main input the needs of the different stakeholders involved.

We study a 1D semilinear wave equation modeling the dynamic of an elastic string interacting with a rigid substrate through an adhesive layer. The constitutive law of the adhesive material is assumed elastic up to a finite critical state, beyond such a value the stress discontinuously drops to zero. Therefore the semilinear equation is characterized by a source term presenting jump discontinuity. Well-posedness of the initial boundary value problem of Neumann type, as well as qualitative properties of the solutions are studied and the evolution of different initial conditions are numerically investigated.

We scrutinize the effects of non-ideal data acquisition on the homodyne tomograms of photon quantum states. The presence of a weight function, schematizing the effects of the finite thickness of the probing beam or equivalently noise, only affects the state reconstruction procedure by a normalization constant. The results are extended to a discrete mesh and show that quantum tomography is robust under incomplete and approximate knowledge of tomograms., Comment: 7 pages, 1 figure, published version

We reconsider the effect of indistinguishability on the reduced density operator of the internal degrees of freedom (tracing out the spatial degrees of freedom) for a quantum system composed of identical particles located in different spatial regions. We explicitly show that if the spin measurements are performed in disjoint spatial regions then there are no constraints on the structure of the reduced state of the system. This implies that the statistics of identical particles has no role from the point of view of separability and entanglement when the measurements are spatially separated. We extend the treatment to the case of n particles and show the connection with some recent criteria for separability based on subalgebras of observables., Comment: 10 pages

Let a pure state \psi be chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix \rho of an N-dimensional subsystem. The bipartite entanglement properties of \psi are encoded in the spectrum of \rho. By means of a saddle point method and using a "Coulomb gas" model for the eigenvalues, we obtain the typical spectrum of reduced density matrices. We consider the cases of an unbiased ensemble of pure states and of a fixed value of the purity. We finally obtain the eigenvalue distribution by using a statistical mechanics approach based on the introduction of a partition function., Comment: 15 pages, 4 figures

A new family of polarized ensembles of random pure states is presented. These ensembles are obtained by linear superposition of two random pure states with suitable distributions, and are quite manageable. We will use the obtained results for two purposes: on the one hand we will be able to derive an efficient strategy for sampling states from isopurity manifolds. On the other, we will characterize the deviation of a pure quantum state from separability under the influence of noise., 14 pages, 1 figure

We study the behavior of bipartite entanglement at fixed von Neumann entropy. We look at the distribution of the entanglement spectrum, that is the eigenvalues of the reduced density matrix of a quantum system in a pure state. We report the presence of two continuous phase transitions, characterized by different entanglement spectra, which are deformations of classical eigenvalue distributions., 5 pages, 5 figures

We study the time evolution of ultra-cold atoms in an accelerated optical lattice. For a Bose- Einstein condensate with a narrow quasi-momentum distribution in a shallow optical lattice the decay of the survival probability in the ground band has a step-like structure. In this regime we establish a connection between the wave function renormalization parameter Z introduced in [Phys. Rev. Lett. 86, 2699 (2001)] to characterize non-exponential decay and the phenomenon of resonantly enhanced tunneling, where the decay rate is peaked for particular values of the lattice depth and the accelerating force., 12 pages

The ground state energy of a binary mixture of Bose-Einstein condensates can be estimated for large atomic samples by making use of suitably regularized Thomas-Fermi density profiles. By exploiting a variational method on the trial densities the energy can be computed by explicitly taking into account the normalization condition. This yields analytical results and provides the basis for further improvement of the approximation. As a case study, we consider a binary mixture of $^{87}$Rb atoms in two different hyperfine states in a double well potential and discuss the energy crossing between density profiles with different numbers of domain walls, as the number of particles and the inter-species interaction vary., Comment: 9 pages

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom -- the symplectic eigenvalues -- which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information., 17 pages, comments are welcome. v2: presentation improved and typos corrected. Close to the published version

Bipartite entanglement between two parties of a composite quantum system can be quantified in terms of the purity of one party and there always exists a pure state of the total system that maximizes it (and minimizes purity). When many different bipartitions are considered, the requirement that purity be minimal for all bipartitions gives rise to the phenomenon of entanglement frustration. This feature, observed in quantum systems with both discrete and continuous variables, can be studied by means of a suitable cost function whose minimizers are the maximally multipartite-entangled states (MMES). In this paper we extend the analysis of multipartite entanglement frustration of Gaussian states in multimode bosonic systems. We derive bounds on the frustration, under the constraint of finite mean energy, in the low and high energy limit., 4 pages, 2 figures. Contribution to "Folding and Unfolding: Interactions from Geometry. Workshop in honour of Giuseppe Marmo's 65th birthday", 8-12 June 2011, Ischia (NA) Italy

We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like anti-ferromagnetic interaction. We compute free energy, spin correlation functions and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Neverthless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class., To be published in Physical Review A

The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. In general, degeneracy cannot be avoided if the Hamiltonian contains m-body interaction terms with m, 4 pages

We study a binary mixture of Bose-Einstein condensates, confined in a generic potential, in the Thomas-Fermi approximation. We search for the zero-temperature ground state of the system, both in the case of fixed numbers of particles and fixed chemical potentials., Comment: 20 pages, 2 figures

We study the conditions for obtaining maximally multipartite entangled states (MMES) as non-degenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMES as eigenstates., 6 pages, 3 figures, published version

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration., 38 pages, 10 figures, published version

Some features of the global entanglement of a composed quantum system can be quantified in terms of the purity of a balanced bipartition, made up of half of its subsystems. For the given bipartition, purity can always be minimized by taking a suitable (pure) state. When many bipartitions are considered, the requirement that purity be minimal for all bipartitions can engender conflicts and frustration arises. This unearths an interesting link between frustration and multipartite entanglement, defined as the average purity over all (balanced) bipartitions., 15 pages, 7 figures

We study maximally multipartite entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n=2 or 3 modes. We further numerically investigate the structure of these states and their frustration for n, 6 pages, 2 figures, comments are welcome

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions. We search for those (maximally multipartite entangled) states whose purity is minimum for all bipartitions and recast this optimization problem into a problem of statistical mechanics., final version

We diagonalize the XX model with a finite number of spins and periodic boundary conditions. We solve for the ground state, focus on the rapidity of the convergence to the thermodynamic limit and study the features of multipartite entanglement., Comment: 12 pages, 11 figures

We introduce the notion of maximally multipartite entangled states of n qubits as a generalization of the bipartite case. These pure states have a bipartite entanglement that does not depend on the bipartition and is maximal for all possible bipartitions. They are solutions of a minimization problem. Examples for small n are investigated, both analytically and numerically., 5 pages, 1 figure, final verson

We analytically and numerically study the effects of pulsed control on the decoherence of a qubit coupled to a quantum spin bath. When the environment is critical, decoherence is faster and we show that the control is relatively more effective. Two coupling models are investigated, namely a qubit coupled to a bath via a single link and a spin star model, yielding results that are similar and consistent., Comment: 10 pages, 4 figures, replaced with published version

We propose a method to characterize and quantify multipartite entanglement for pure states. The method hinges upon the study of the probability density function of bipartite entanglement and is tested on an ensemble of qubits in a variety of situations. This characterization is also compared to several measures of multipartite entanglement., Comment: 7 pages, 2 figures; published version; title changed; further explanations and comparison with several measures of multipartite entanglement added

Non Abelian geometric phases are attracting increasing interest because of possible experimental application in quantum computation. We study the effects of the environment (modelled as an ensemble of harmonic oscillators) on a holonomic transformation and write the corresponding master equation. The solution is analytically and numerically investigated and the behavior of the fidelity analyzed: fidelity revivals are observed and an optimal finite operation time is determined at which the gate is most robust against noise., Comment: 11 pages, 6 figures

Decoherence is one of the most serious drawback in quantum mechanical applications. We discuss the effects of noise in superconducting devices (Josephson junctions) and suggest a decoherence-control strategy based on the quantum Zeno effect.

Holonomic gates for quantum computation are commonly considered to be robust against certain kinds of parametric noise, the very motivation of this robustness being the geometric character of the transformation achieved in the adiabatic limit. On the other hand, the effects of decoherence are expected to become more and more relevant when the adiabatic limit is approached. Starting from the system described by Florio et al. [Phys. Rev. A 73, 022327 (2006)], here we discuss the behavior of non ideal holonomic gates at finite operational time, i.e., far before the adiabatic limit is reached. We have considered several models of parametric noise and studied the robustness of finite time gates. The obtained results suggest that the finite time gates present some effects of cancellation of the perturbations introduced by the noise which mimic the geometrical cancellation effect of standard holonomic gates. Nevertheless, a careful analysis of the results leads to the conclusion that these effects are related to a dynamical instead of geometrical feature., Comment: 8 pages, 8 figures, several changes made, accepted for publication on Phys. Rev. A

Geometric phases are an interesting resource for quantum computation, also in view of their robustness against decoherence effects. We study here the effects of the environment on a class of one-qubit holonomic gates that have been recently shown to be characterized by "optimal" working times. We numerically analyze the behavior of these optimal points and focus on their robustness against noise., Comment: 14 pages, 8 figures

A method is proposed to characterize and quantify multipartite entanglement in terms of the probability density function of bipartite entanglement over all possible balanced bipartitions of an ensemble of qubits. The method is tested on a class of random pure states., 7 pages, 5 figures. Submitted to "International Journal of Quantum Information"