1,721,045 research outputs found
Sull'equazione della corda vibrante
No full textAbstract: In the Cauchy-Dirichlet problem related to the non-linear equation of a vibrating string partial derivative/partial derivative x([1 + (partial derivative u/partial derivative x)2]partial derivative u/partial derivative x) - partial derivative2 u/partial derivative t2 = f(x, t) in OMEGA x [0, T] (OMEGA being a bounded interval of the real line) local existence and uniqueness of a solution is established. To this aim we use a generalized version of Gronwall's inequality: if u(t) is a solution in [0, T] of the inequality u(t) less-than-or-equal-to u0 + integral-t/0 {f(s) + g(s)u(beta)(s)} ds (beta > 1), then there exists T less-than-or-equal-to T such that in [0, T]: \u(t)\ less-than-or-equal-to c(T,beta,f,g,u0)
Role of the edges in a quasicrystalline Haldane model
No full textWe study the role of the edges in determining the features of the topological phase in a quasicrystalline higher-order topological insulator. We consider a specific model consisting of two stacked Haldane models with opposite Chern number and a 30 degrees twist, whose structure is crystallographically equivalent to that of the graphene quasicrystal. We find that the gap-opening in the low-energy spectrum of the higher-order topological insulator occurs at different energies when different kinds of edges are considered. Crucially, bearded bonds appear to be necessary for the gap to appear close to the charge neutrality point. In the more realistic case of zigzag edges, the gap opens symmetrically in the electron and hole sectors, away from zero energy. We explain our findings by inspecting the edge bands of the decoupled bilayer, in the approximation of quasiperiodicity
Levitons in helical liquids with Rashba spin-orbit coupling probed by a superconducting contact
No full textWe consider transport properties of a single edge of a two-dimensional topological insulator, in presence of Rashba spin-orbit coupling, driven by two external time-dependent voltages and connected to a thin superconductor. We focus on the case of a train of Lorentzian-shaped pulses, which are known to generate coherent single-electron excitations in two-dimensional electron gas, and prove that they are minimal excitations for charge transport also in helical edge states, even in the presence of spin-orbit interaction. Importantly, these properties of Lorentzian-shaped pulses can be tested computing charge noise generated by the scattering of particles at the thin superconductor. This represents a novel setup where electron quantum optics experiments with helical states can be implemented, with the superconducting contact as an effective beamsplitter. By elaborating on this configuration, we also evaluate charge noise in a collisional Hong-Ou-Mandel configuration, showing that due to the peculiar effects induced by Rashba interaction, a nonvanishing dip at zero delay appears
Suppression of the radiation squeezing in interacting quantum Hall edge channels
No full textWe study the quantum fluctuations of the two quadratures of the emitted electromagnetic radiation generated by a quantum Hall device in a quantum point contact geometry. In particular, we focus our attention on the role played by the unavoidable electron-electron interactions between the two edge channels at filling factor two. We investigate quantum features of the emitted microwave radiation, such as squeezing, by studying the current fluctuations at finite frequency, accessible through a two-filters set-up placed just after the quantum point contact. We compare two different drives, respectively a cosine and a train of Lorentzian pulses, used for the injection of the excitations into the system. In both cases quantum features are reduced due to the interactions, however the Lorentzian drive is still characterized by a robust squeezing effect which can have important application on quantum information
Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator
No full textThe experimental realization of twisted bilayer graphene strongly pushed the inspection of bilayer systems. In this context, it was recently shown that a two layer Haldane model with a thirty degree rotation angle between the layers represents a higher order topological insulator, with zero-dimensional states isolated in energy and localized at the physical vertices of the nanostructure. We show, within a numerical tight binding approach, that the energy of the zero dimensional states strongly depends on the geometrical structure of the vertices. In the most extreme cases, once a specific band gap is considered, these bound states can even disappear just by changing the vertex structure
Anomalous suppression of the shot noise in a nanoelectromechanical system
No full textIn this paper we report a relaxation-induced suppression of the noise for a single level quantum dot coupled to an oscillator with incoherent dynamics in the sequential tunneling regime. It is shown that relaxation induces qualitative changes in the transport properties of the dot, depending on the strength of the electron-phonon coupling and on the applied voltage. In particular, critical thresholds in voltage and relaxation are found such that a suppression below 1/2 of the Fano factor is possible. Additionally, the current is either enhanced or suppressed by increasing relaxation, depending on bias being greater or smaller than the above threshold. These results exist for any strength of the electron-phonon coupling and are confirmed by a four states toy model
A short review of one-dimensional wigner crystallization
No full textThe simplest possible structural transition that an electronic system can undergo is Wigner crystallization. The aim of this short review is to discuss the main aspects of three recent experimets on the one-dimensional Wigner molecule, starting from scratch. To achieve this task, the Luttinger liquid theory of weakly and strongly interacting fermions is briefly addressed, together with the basic properties of carbon nanotubes that are required. Then, the most relevant properties of Wigner molecules are addressed, and finally the experiments are described. The main physical points that are addressed are the suppression of the energy scales related to the spin and isospin sectors of the Hamiltonian, and the peculiar structure that the electron density acquires in the Wigner molecule regime
Transport properties of quantum dots in the Wigner molecule regime
Full text linkThe transport properties of quantum dots with up to N = 7 electrons ranging from a weak to a strong interacting regime are investigated via the projected Hartree-Fock technique. As interactions increase radial order develops in the dot, with the formation of ring and centred-ring structures. Subsequently, angular correlations appear, signalling the formation of a Wigner molecule state. We show striking signatures of the emergence of Wigner molecules, detected in transport. In the linear regime, conductance is exponentially suppressed as the interaction strength grows. A further suppression is observed when centred-ring structures develop, or peculiar spin textures appear. In the nonlinear regime, the formation of molecular states may even lead to a conductance enhancemen
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