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We address the issue of dissipative vs. non-dissipative behavior in a mesoscopic set of coupled elements such as oscillators, with one half having gain and the other half having losses. We introduce a graph with coupling as the graph edges in given fixed number and gain/loss elements as its nodes. This relates to parity-time symmetry, notably in optics, e.g. set of coupled fibers, and more generally to the issue of taming divergence related to imaginary parts of eigenvectors in various network descriptions, for instance biochemical, neuronal, ecological. We thus look for the minimization of the imaginary part of all eigenvalues altogether, with a collective figure of merit. As more edges than gain/loss pairs are introduced, the unbroken cases , i.e., stable cases with real eigenvalues in spite of gain and loss, become statistically very scarce. A minimization from a random starting point by moving one edge at a time is studied, amounting to investigate how the hugely growing configuration number impedes the attainment of the desired minimally-dissipative target. The minimization path and its apparent stalling point are analyzed in terms of network connectivity metrics. We expand in the end on the relevance in biochemical signaling networks and the so-called "stability-optimized circuits" relevant to neural organization. [ABSTRACT FROM AUTHOR]

Intriguing issues in one-dimensional non-reciprocal topological systems include the breakdown of usual bulk-edge correspondence and the occurrence of half-integer topological invariants. In order to understand these unusual topological properties, we investigate the topological phase diagrams and the zero-mode edge states of a generalized non-reciprocal Su-Schrieffer-Heeger model with a general form fulfilling the chiral symmetry, based on some analytical results. Meanwhile, we provide a concise geometrical interpretation of the bulk topological invariants in terms of two independent winding numbers and also give an alternative interpretation related to the linking properties of curves in three-dimensional space. For the system under the open boundary condition, we construct analytically the wavefunctions of zero-mode edge states by properly considering a hidden symmetry of the system and the normalization condition with the use of biorthogonal eigenvectors. Our analytical results directly give the phase boundary for the existence of zero-mode edge states and unveil clearly the evolution behavior of edge states. In comparison with results via exact diagonalization of finite-size systems, we find our analytical results agree with the numerical results very well. [ABSTRACT FROM AUTHOR]

We revisit the classical problem of electromagnetic wave refraction from a lossless dielectric to a lossy conductor, where both media are considered to be non-magnetic, linear, isotropic and homogeneous. We derive the Fresnel coefficients of the system and the Poynting vectors at the interface, in order to compute the reflectance and transmittance of the system. We use a particular parametrisation of the referred Fresnel coefficients so as to make a connection with the ones obtained for refraction by an interface between two lossless media. This analysis allows the discussion of an actual application, namely the Fresnel polarisation of infra-red radiation by elemental bismuth, based on the concept of pseudo Brewster's angle. [ABSTRACT FROM AUTHOR]

Localization phenomena of non-interacting electrons are critically investigated in a quantum network where site energies and/or hopping integrals are correlated in the form of Aubry-André-Harper (AAH) model. In presence of diagonal hopping between neighboring strands of the network an energy zone, consists of extended and localized states, appears whose width can be adjusted by tuning the physical parameters describing the system. It gives an important signature towards the detection of mobility edge which we justify by analyzing the energy band spectra. Finally, we study the interplay between the diagonal and off-diagonal disorders, and explore the robust delocalizing effect. Our analysis may lead to important aspects of electronic localization in coupled AAH chains. [ABSTRACT FROM AUTHOR]

We investigate statistical aspects of the entanglement production for open chaotic mesoscopic billiards in contact with superconducting parts, known as Andreev billiards. The complete distributions of concurrence and entanglement of formation are obtained by using the Altland-Zirnbauer symmetry classes of circular ensembles of scattering matrices, which complements previous studies in chaotic universal billiards belonging to other classes of random matrix theory. Our results show a unique and very peculiar behavior: the realization of entanglement in a Andreev billiard always results in non-separable state, regardless of the time reversal symmetry. The analytical calculations are supported by a numerical Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

Using the Green's function technique, we respectively investigate the electron transport properties of two spin components through the system of a T-shaped double quantum dot structure coupled to a Majorana bound state, in which only one quantum dot is connected with two metallic leads. We explore the interplay between the Fano effect and the MBSs for different dot-MBS coupling strength λ, dot-dot coupling strength t, and MBS-MBS coupling strength ε in the noninteracting case. Then the Coulomb interaction and magnetic field effect on the conductance spectra are investigated. Our results indicate that G( ω) is not affected by the Majorana bound states, but a '0.5' conductance signature occurs in the vicinities of Fermi level of G( ω). This robust property persists for a wide range of dot-dot coupling strength and dot-MBS coupling strength, but it can be destroyed by Coulomb interaction in quantum dots. By adjusting the size and direction of magnetic field around the quantum dots, the '0.5' conductance signature damaged by U can be restored. At last, the spin magnetic moments of two dots by applying external magnetic field are also predicted. [ABSTRACT FROM AUTHOR]

Energy spectra and transport properties of armchair nanotubes with curvature induced spin-orbit interaction are investigated thoroughly. The spin-orbit interaction consists of two terms: the first one preserves the spin symmetry in rotating frame, while the second one breaks it. It is found that the both terms are equally important: (i) at scattering on the potential step which mimics a long-range potential in the nanotubes; (ii) at transport via nanotube quantum dots. It is shown that an armchair nanotube with the first spin-orbit term works as an ideal spin-filter, while the second term produces a parasitic inductance. [ABSTRACT FROM AUTHOR]

In the original article, the first author's name was mistakenly written as S. Seyyare Aksul. It must be corrected to S. Seyyare Aksu. The publisher apologizes for the mistake. [ABSTRACT FROM AUTHOR]

We address the electronic properties of quantum dots in the two-dimensional α − 𝒯3 lattice when subjected to a perpendicular magnetic field. Implementing an infinite mass boundary condition, we first solve the eigenvalue problem for an isolated quantum dot in the low-energy, long-wavelength approximation where the system is described by an effective Dirac-like Hamiltonian that interpolates between the graphene (pseudospin 1/2) and Dice (pseudospin 1) limits. Results are compared to a full numerical (finite-mass) tight-binding lattice calculation. In a second step we analyse charge transport through a contacted α − 𝒯3 quantum dot in a magnetic field by calculating the local density of states and the conductance within the kernel polynomial and Landauer-Büttiker approaches. Thereby the influence of a disordered environment is discussed as well. [ABSTRACT FROM AUTHOR]

Based on the structural and energetic properties of an atomistic cluster a method to measure the degree of amorphousness of the cluster is proposed. The proposed method is applied to gold-copper nanoalloys with sizes of 38, 55, 365, 933 atoms, and with structural and energetic properties obtained through molecular dynamics simulation and the Gupta potential model. Results show that structures with a low degree of amorphousness have perfect or distorted geometries which are fully identified as Mackay icosahedron, truncated octahedron, pancake, or fcc, while those with a high degree of amorphousness are also fully identified as amorphous, in agreement with results reported in the literature. The proposed method should be a promising tool to easily identify how ordered or disordered an atomistic cluster is, as well as for the easily identification of the local environment of the core or surface atoms of the cluster, among others. [ABSTRACT FROM AUTHOR]

A theoretical study was undertaken of the effects of single and multiple vacancies created at different surface sites of a non-passivated silicon nanowire (SiNW) with diameter ~11.0 Å, grown in the [001] direction. The results showed that vacancies at vertex site were most energetically favorable, due to the surface dimerization process, which was responsible for metallic or semi-metallic behavior in the perfect [001] SiNW. Modifications at wavefunction localization due surface dimerization and their consequences at electronic properties were also investigated and provided helpful information on application of these materials as gas-sensing nanodevices. [ABSTRACT FROM AUTHOR]