A toy model of polymer stretching

We present an extremely simplified model of multiple-domains polymer stretching in an atomic force microscopy experiment. We portray each module as a binary set of contacts and decompose the system energy into a harmonic term (the cantilever) and long-range interactions terms inside each domain. Exact equilibrium computations and Monte Carlo simulations qualitatively reproduce the experimental saw-tooth pattern of force-extension profiles, corresponding (in our model) to first-order phase transitions. We study the influence of the coupling induced by the cantilever and the pulling speed on the relative heights of the force peaks. The results suggest that the increasing height of the critical force for subsequent unfolding events is an out-of-equilibrium effect due to a finite pulling speed. The dependence of the average unfolding force on the pulling speed is shown to reproduce the experimental logarithmic law.Comment: New revised versio

Gauge Invariance and Symmetry Breaking by Topology and Energy Gap

For the description of observables and states of a quantum system, it may be convenient to use a canonical Weyl algebra of which only a subalgebra $\mathcal A$, with a non-trivial center $\mathcal Z$, describes observables, the other Weyl operators playing the role of intertwiners between inequivalent representations of $\mathcal A$. In particular, this gives rise to a gauge symmetry described by the action of $\mathcal Z$. A distinguished case is when the center of the observables arises from the fundamental group of the manifold of the positions of the quantum system. Symmetries which do not commute with the topological invariants represented by elements of $\mathcal Z$ are then spontaneously broken in each irreducible representation of the observable algebra, compatibly with an energy gap; such a breaking exhibits a mechanism radically different from Goldstone and Higgs mechanisms. This is clearly displayed by the quantum particle on a circle, the Bloch electron and the two body problem.Comment: 23 page

Two-walker discrete-time quantum walks on the line with percolation

One goal in the quantum-walk research is the exploitation of the intrinsic quantum nature of multiple walkers, in order to achieve the full computational power of the model. Here we study the behaviour of two non-interacting particles performing a quantum walk on the line when the possibility of lattice imperfections, in the form of missing links, is considered. We investigate two regimes, statical and dynamical percolation, that correspond to different time scales for the imperfections evolution with respect to the quantum-walk one. By studying the qualitative behaviour of three two-particle quantities for different probabilities of having missing bonds, we argue that the chosen symmetry under particle-exchange of the input state strongly affects the output of the walk, even in noisy and highly non-ideal regimes. We provide evidence against the possibility of gathering information about the walkers indistinguishability from the observation of bunching phenomena in the output distribution, in all those situations that require a comparison between averaged quantities. Although the spread of the walk is not substantially changed by the addition of a second particle, we show that the presence of multiple walkers can be beneficial for a procedure to estimate the probability of having a broken link.Comment: 16 pages, 9 figure

Localization-like effect in two-dimensional alternate quantum walks with periodic coin operations

Exploiting multi-dimensional quantum walks as feasible platforms for quantum computation and quantum simulation is attracting constantly growing attention from a broad experimental physics community. Here, we propose a two-dimensional quantum walk scheme with a single-qubit coin that presents, in the considered regimes, a strong localization-like effect on the walker. The result could provide new possible directions for the implementation of quantum algorithms or from the point of view of quantum simulation. We characterize the localization-like effect in terms of the parameters of a step-dependent qubit operation that acts on the coin space after any standard coin operation, showing that a proper choice can guarantee a non-negligible probability of finding the walker in the origin even for large times. We finally discuss the robustness to imperfections, a qualitative relation with coherences behavior, and possible experimental realizations of this model with the current state-of-the-art settings.Comment: 5 pages, 4 figures, RevTeX

Stochastic gravitational background from inflationary phase transitions

We consider true vacuum bubbles generated in a first order phase transition occurring during the slow rolling era of a two field inflation: it is known that gravitational waves are produced by the collision of such bubbles. We find that the epoch of the phase transition strongly affects the characteristic peak frequency of the gravitational waves, causing an observationally interesting redshift in addition to the post-inflationary expansion. In particular it is found that a phase transition occurring typically 10$\div$20 $e-$foldings before the reheating at $kT\simeq 10^{15}$ GeV may be detected by the next Ligo gravity waves interferometers. Moreover, for recently proposed models capable of generating the observed large scale voids as remnants of the primordial bubbles (for which the characteristic wave lengths are several tens of Mpc), it is found that the level of anisotropy of the cosmic microwave background provides a deep insight upon the physical parameters of the effective Lagrangian.Comment: 12 pages, 3 figures. Phys.Rev.D in pres

Synthesis And Characterization Of Polyynes End-Capped By Biphenyl Groups ({\Alpha},{\Omega}-Biphenylpolyynes)

Stable polyyne chains terminated with biphenyl end groups (a,u-biphenylpolyynes) were synthesized in a single step through a simple procedure by using the Cadiot-Chodkiewicz reaction conditions. The a,ubiphenylpolyynes were separated through HPLC analysis and identified by means of their electronic absorption spectra. The a,u-biphenylpolyynes were studied by FT-IR and Raman spectroscopy and the spectral interpretation was supported with DFT calculations. A peculiarly low reactivity of a,u-biphenylpolyynes with ozone was observed.Comment: The research leading to these results has received funding from the European Research Council Consolidator Grant EspLORE (ERC-2016-CoG Grant No.724610