Stability mapping of bipartite tight-binding graphs with losses and gain: PTPT-symmetry and beyond.

We consider bipartite tight-binding graphs composed by N nodes split into two sets of equal size: one set containing nodes with on-site loss, the other set having nodes with on-site gain. The nodes are connected randomly with probability p. Specifically, we measure the connectivity between the two sets with the parameter α, which is the ratio of current adjacent pairs over the total number of possible adjacent pairs between the sets. For general undirected-graph setups, the non-Hermitian Hamiltonian H(γ,α,N) of this model presents pseudo-Hermiticity, where γ is the loss/gain strength. However, we show that for a given graph setup H(γ,α,N) becomes PT-symmetric. In both scenarios (pseudo-Hermiticity and PT-symmetric), depending on the parameter combination, the spectra of H(γ,α,N) can be real even when it is non-Hermitian. Then we demonstrate, for both setups, that there is a well-defined sector of the γα-plane (which grows with N) where the spectrum of H(γ,α,N) is predominantly real.

Scarring in Rough Rectangular Billiards.

We study the mechanism of scarring of eigenstates in rectangular billiards with slightly corrugated surfaces and show that it is very different from that known in Sinai and Bunimovich billiards. We demonstrate that there are two sets of scar states. One set is related to the bouncing ball trajectories in the configuration space of the corresponding classical billiard. A second set of scar-like states emerges in the momentum space, which originated from the plane-wave states of the unperturbed flat billiard. In the case of billiards with one rough surface, the numerical data demonstrate the repulsion of eigenstates from this surface. When two horizontal rough surfaces are considered, the repulsion effect is either enhanced or canceled depending on whether the rough profiles are symmetric or antisymmetric. The effect of repulsion is quite strong and influences the structure of all eigenstates, indicating that the symmetric properties of the rough profiles are important for the problem of scattering of electromagnetic (or electron) waves through quasi-one-dimensional waveguides. Our approach is based on the reduction of the model of one particle in the billiard with corrugated surfaces to a model of two artificial particles in the billiard with flat surfaces, however, with an effective interaction between these particles. As a result, the analysis is conducted in terms of a two-particle basis, and the roughness of the billiard boundaries is absorbed by a quite complicated potential.

Disorder-Enhanced and Disorder-Independent Transport with Long-Range Hopping: Application to Molecular Chains in Optical Cavities.

Overcoming the detrimental effect of disorder at the nanoscale is very hard since disorder induces localization and an exponential suppression of transport efficiency. Here we unveil novel and robust quantum transport regimes achievable in nanosystems by exploiting long-range hopping. We demonstrate that in a 1D disordered nanostructure in the presence of long-range hopping, transport efficiency, after decreasing exponentially with disorder at first, is then enhanced by disorder [disorder-enhanced transport (DET) regime] until, counterintuitively, it reaches a disorder-independent transport (DIT) regime, persisting over several orders of disorder magnitude in realistic systems. To enlighten the relevance of our results, we demonstrate that an ensemble of emitters in a cavity can be described by an effective long-range Hamiltonian. The specific case of a disordered molecular wire placed in an optical cavity is discussed, showing that the DIT and DET regimes can be reached with state-of-the-art experimental setups.

Normalized Sombor Indices as Complexity Measures of Random Networks.

We perform a detailed computational study of the recently introduced Sombor indices on random networks. Specifically, we apply Sombor indices on three models of random networks: Erdös-Rényi networks, random geometric graphs, and bipartite random networks. Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the network, scale with the average degree. Moreover, we discuss the application of average Sombor indices as complexity measures of random networks and, as a consequence, we show that selected normalized Sombor indices are highly correlated with the Shannon entropy of the eigenvectors of the adjacency matrix.

An investigation of the parameter space for a family of dissipative mappings.

The parameter plane investigation for a family of two-dimensional, nonlinear, and area contracting map is made. Several dynamical features in the system such as tangent, period-doubling, pitchfork, and cusp bifurcations were found and discussed together with cascades of period-adding, period-doubling, and the Feigeinbaum scenario. The presence of spring and saddle-area structures allow us to conclude that cubic homoclinic tangencies are present in the system. A set of complex sets such as streets with the same periodicity and the period-adding of spring-areas are observed in the parameter space of the mapping.

Information Entropy of Tight-Binding Random Networks with Losses and Gain: Scaling and Universality.

We study the localization properties of the eigenvectors, characterized by their information entropy, of tight-binding random networks with balanced losses and gain. The random network model, which is based on Erdos-Rényi (ER) graphs, is defined by three parameters: the network size N, the network connectivity α , and the losses-and-gain strength γ . Here, N and α are the standard parameters of ER graphs, while we introduce losses and gain by including complex self-loops on all vertices with the imaginary amplitude i γ with random balanced signs, thus breaking the Hermiticity of the corresponding adjacency matrices and inducing complex spectra. By the use of extensive numerical simulations, we define a scaling parameter ξ ≡ ξ ( N , α , γ ) that fixes the localization properties of the eigenvectors of our random network model; such that, when ξ < 0.1 ( 10 < ξ ), the eigenvectors are localized (extended), while the localization-to-delocalization transition occurs for 0.1 < ξ < 10 . Moreover, to extend the applicability of our findings, we demonstrate that for fixed ξ , the spectral properties (characterized by the position of the eigenvalues on the complex plane) of our network model are also universal; i.e., they do not depend on the specific values of the network parameters.

Transmission through surface-corrugated unidirectional waveguides.

We study wave transmission G through quasi-one-dimensional waveguides with constant cross section. Constant cross section means that an infinite set of lines of the same length (that do not intersect each other) which are perpendicular to one boundary of the waveguide are also perpendicular to the other boundary. This makes the sign of the tangential velocity for all collision points of an arbitrary particle trajectory to stay constant, so that the classical or ray dynamics in the waveguide is unidirectional. In particular, we report the systematic enhancement of transmission in unidirectional corrugated waveguides when contrasting their transmission properties with those for equivalent constant-width waveguides (for which the classical dynamics is not unidirectional since particles moving in one direction along the waveguide can change its direction of motion). Also, we verify the universality of the distribution of transmissions P(G) in the diffusive ( ⟨G⟩>1) and localized ( ⟨G⟩≪1) regimes of transport. Moreover, we show that in the transition regime, ⟨G⟩∼1, P(G) is well described by the DMPK approach (the Fokker-Planck approach of Dorokhov, Mello, Pereyra, and Kumar) to bulk-disordered wires.

Information-Length Scaling in a Generalized One-Dimensional Lloyd's Model.

We perform a detailed numerical study of the localization properties of the eigenfunctions of one-dimensional (1D) tight-binding wires with on-site disorder characterized by long-tailed distributions: For large ϵ , P ( ϵ ) ∼ 1 / ϵ 1 + α with α ∈ ( 0 , 2 ] ; where ϵ are the on-site random energies. Our model serves as a generalization of 1D Lloyd's model, which corresponds to α = 1 . In particular, we demonstrate that the information length ß of the eigenfunctions follows the scaling law ß = γ x / ( 1 + γ x ) , with x = ξ / L and γ ≡ γ ( α ) . Here, ξ is the eigenfunction localization length (that we extract from the scaling of Landauer's conductance) and L is the wire length. We also report that for α = 2 the properties of the 1D Anderson model are effectively reproduced.

Beyond Anderson localization in 1D: anomalous localization of microwaves in random waveguides.

Experimental evidence demonstrating that anomalous localization of waves can be induced in a controllable manner is reported. A microwave waveguide with dielectric slabs randomly placed is used to confirm the presence of anomalous localization. If the random spacing between slabs follows a distribution with a power-law tail (Lévy-type distribution), unconventional properties in the microwave-transmission fluctuations take place revealing the presence of anomalous localization. We study both theoretically and experimentally the complete distribution of the transmission through random waveguides characterized by α=1/2 ("Lévy waveguides") and α=3/4, α being the exponent of the power-law tail of the Lévy-type distribution. As we show, the transmission distributions are determined by only two parameters, both of them experimentally accessible. Effects of anomalous localization on the transmission are compared with those from the standard Anderson localization.

[Profile of free fatty acids (FFA) in serum of young Colombians with obesity and metabolic syndrome]. / Perfil de ácidos grasos libres (AGL) en suero de jóvenes colombianos con obesidad y síndrome metabólico.

Obesity produces greater circulation of free fatty acids (FFA). In adults, the FFA composition changes in states of obesity; in adolescents, the results are contradictory. This study compare the FFA profile of obese youth with and without Metabolic Syndrome (MetS) and explore the association between FFA and metabolic alterations of obesity and MetS. A cross-sectional study with 96 young people between 10 and 18 years old was divided into three groups: 1) obese youth with MetS, 2) obese youth without MetS; and 3) adequate weight (AW), matched according to age, gender, pubertal maturation and socioeconomic stratum. The nutritional status was classified according to the body-mass index (BMI), according to the World Health Organization 2007 (WHO, 2007); the waist circumference (WC), adiposity, lipid profile, highly-sensitive reactive C protein (hsRCP), glucose, insulin and insulin resistance (IR), according to the homeostatic model assessment (HOMA Calculator Version 2.2.2). The FFA serum concentration was determined by gas chromatography. Both obese groups had higher adiposity, inflamation (hsRCP), FFA totals and frequency palmitoleic-16:Jn7, compared to AW. The obese with MetS presented more metabolic alterations, a greater amount of dihomo-γ-linolenic (DHGL-20:3n6) and a 20:3n6/18:2n6 relation, indicative of increased activity of A6 desaturase (D6D). The FFA totals, palmitoleic-l6:1n7, DHGL-20:3n6, D6D activity and hsRCP significantly correlated with variables of adiposity, IR and triglicerides. The results in obese with MetS corroborate the association among central obesity, inflammation and increased lipolysis in visceral adipose tissue and metabolic alterations.

Topological and spectral properties of random digraphs.

We investigate some topological and spectral properties of Erdos-Rényi (ER) random digraphs of size n and connection probability p, D(n,p). In terms of topological properties, our primary focus lies in analyzing the number of nonisolated vertices V_{x}(D) as well as two vertex-degree-based topological indices: the Randic index R(D) and sum-connectivity index χ(D). First, by performing a scaling analysis, we show that the average degree 〈k〉 serves as a scaling parameter for the average values of V_{x}(D), R(D), and χ(D). Then, we also state expressions relating the number of arcs, largest eigenvalue, and closed walks of length 2 to (n,p), the parameters of ER random digraphs. Concerning spectral properties, we observe that the eigenvalue distribution converges to a circle of radius sqrt[np(1-p)]. Subsequently, we compute six different invariants related to the eigenvalues of D(n,p) and observe that these quantities also scale with sqrt[np(1-p)]. Additionally, we reformulate a set of bounds previously reported in the literature for these invariants as a function (n,p). Finally, we phenomenologically state relations between invariants that allow us to extend previously known bounds.

Scaling properties of the action in the Riemann-Liouville fractional standard map.

The Riemann-Liouville fractional standard map (RL-fSM) is a two-dimensional nonlinear map with memory given in action-angle variables (I,θ). The RL-fSM is parameterized by K and α∈(1,2], which control the strength of nonlinearity and the fractional order of the Riemann-Liouville derivative, respectively. In this work we present a scaling study of the average squared action 〈I^{2}〉 of the RL-fSM along strongly chaotic orbits, i.e., for K≫1. We observe two scenarios depending on the initial action I_{0}, I_{0}≪K or I_{0}≫K. However, we can show that 〈I^{2}〉/I_{0}^{2} is a universal function of the scaled discrete time nK^{2}/I_{0}^{2} (n being the nth iteration of the RL-fSM). In addition, we note that 〈I^{2}〉 is independent of α for K≫1. Analytical estimations support our numerical results.

Localization properties of harmonic chains with correlated mass and spring disorder: Analytical approach.

We study the localization properties of normal modes in harmonic chains with mass and spring weak disorder. Using a perturbative approach, an expression for the localization length L_{loc} is obtained, which is valid for arbitrary correlations of the disorder (mass disorder correlations, spring disorder correlations, and mass-spring disorder correlations are allowed), and for practically the whole frequency band. In addition, we show how to generate effective mobility edges by the use of disorder with long range self-correlations and cross-correlations. The transport of phonons is also analyzed, showing effective transparent windows that can be manipulated through the disorder correlations even for relative short chain sizes. These results are connected to the problem of heat conduction in the harmonic chain; indeed, we discuss the size scaling of the thermal conductivity from the perturbative expression of L_{loc}. Our results may have applications in modulating thermal transport, particularly in the design of thermal filters or in manufacturing high-thermal-conductivity materials.

Scattering and transport properties of the three classical Wigner-Dyson ensembles at the Anderson transition.

An extensive numerical analysis of the scattering and transport properties of the power-law banded random matrix model (PBRM) at criticality in the presence of orthogonal, unitary, and symplectic symmetries is presented. Our results show a good agreement with existing analytical expressions in the metallic regime and with heuristic relations widely used in studies of the PBRM model in the presence of orthogonal and unitary symmetries. Moreover, our results confirm that the multifractal behavior of disordered systems at criticality can be probed by measuring scattering and transport properties, which is of paramount importance from the experimental point of view. Thus, a full picture of the scattering and transport properties of the PBRM model at criticality corresponding to the three classical Wigner-Dyson ensembles is provided.

Revan Sombor indices: Analytical and statistical study.

In this paper, we perform analytical and statistical studies of Revan indices on graphs $ G $: $ R(G) = \sum_{uv \in E(G)} F(r_u, r_v) $, where $ uv $ denotes the edge of $ G $ connecting the vertices $ u $ and $ v $, $ r_u $ is the Revan degree of the vertex $ u $, and $ F $ is a function of the Revan vertex degrees. Here, $ r_u = \Delta + \delta - d_u $ with $ \Delta $ and $ \delta $ the maximum and minimum degrees among the vertices of $ G $ and $ d_u $ is the degree of the vertex $ u $. We concentrate on Revan indices of the Sombor family, i.e., the Revan Sombor index and the first and second Revan $ (a, b) $-$ KA $ indices. First, we present new relations to provide bounds on Revan Sombor indices which also relate them with other Revan indices (such as the Revan versions of the first and second Zagreb indices) and with standard degree-based indices (such as the Sombor index, the first and second $ (a, b) $-$ KA $ indices, the first Zagreb index and the Harmonic index). Then, we extend some relations to index average values, so they can be effectively used for the statistical study of ensembles of random graphs.

Nonuniform random graphs on the plane: A scaling study.

We consider random geometric graphs on the plane characterized by a nonuniform density of vertices. In particular, we introduce a graph model where n vertices are independently distributed in the unit disk with positions, in polar coordinates (l,θ), obeying the probability density functions ρ(l) and ρ(θ). Here we choose ρ(l) as a normal distribution with zero mean and variance σ∈(0,∞) and ρ(θ) as a uniform distribution in the interval θ∈[0,2π). Then, two vertices are connected by an edge if their Euclidean distance is less than or equal to the connection radius ℓ. We characterize the topological properties of this random graph model, which depends on the parameter set (n,σ,ℓ), by the use of the average degree 〈k〉 and the number of nonisolated vertices V_{×}, while we approach their spectral properties with two measures on the graph adjacency matrix: the ratio of consecutive eigenvalue spacings r and the Shannon entropy S of eigenvectors. First we propose a heuristic expression for 〈k(n,σ,ℓ)〉. Then, we look for the scaling properties of the normalized average measure 〈X[over ¯]〉 (where X stands for V_{×}, r, and S) over graph ensembles. We demonstrate that the scaling parameter of 〈V_{×}[over ¯]〉=〈V_{×}〉/n is indeed 〈k〉, with 〈V_{×}[over ¯]〉≈1-exp(-〈k〉). Meanwhile, the scaling parameter of both 〈r[over ¯]〉 and 〈S[over ¯]〉 is proportional to n^{-γ}〈k〉 with γ≈0.16.

Analytical and computational properties of the variable symmetric division deg index.

The aim of this work is to obtain new inequalities for the variable symmetric division deg index $ SDD_\alpha(G) = \sum_{uv \in E(G)} (d_u^\alpha/d_v^\alpha+d_v^\alpha/d_u^\alpha) $, and to characterize graphs extremal with respect to them. Here, by $ uv $ we mean the edge of a graph $ G $ joining the vertices $ u $ and $ v $, and $ d_u $ denotes the degree of $ u $, and $ \alpha \in \mathbb{R} $. Some of these inequalities generalize and improve previous results for the symmetric division deg index. In addition, we computationally apply the $ SDD_\alpha(G) $ index on random graphs and we demonstrate that the ratio $ \langle SDD_\alpha(G) \rangle/n $ ($ n $ is the order of the graph) depends only on the average degree $ \langle d \rangle $.

Microwave graph analogs for the voltage drop in three-terminal devices with orthogonal, unitary, and symplectic symmetry.

Transmission measurements through three-port microwave graphs are performed, in analogy to three-terminal voltage drop devices with orthogonal, unitary, and symplectic symmetry. The terminal used as a probe is symmetrically located between two chaotic subgraphs, and each graph is connected to one port, the input and the output, respectively. The analysis of the experimental data clearly exhibits the weak localization and antilocalization phenomena. We find a good agreement with theoretical predictions, provided that the effects of dissipation and imperfect coupling to the ports are taken into account.

Leaking of orbits from the phase space of the dissipative discontinuous standard mapping.

We investigate the escape of particles from the phase space produced by a two-dimensional, nonlinear and discontinuous, area-contracting map. The mapping, given in action-angle variables, is parametrized by K and γ which control the strength of nonlinearity and dissipation, respectively. We focus on two dynamical regimes, K<1 and K≥1, known as slow and quasilinear diffusion regimes, respectively, for the area-preserving version of the map (i.e., when γ=0). When a hole of hight h is introduced in the action axis we find both the histogram of escape times P_{E}(n) and the survival probability P_{S}(n) of particles to be scale invariant, with the typical escape time n_{typ}=exp〈lnn〉; that is, both P_{E}(n/n_{typ}) and P_{S}(n/n_{typ}) define universal functions. Moreover, for γ≪1, we show that n_{typ} is proportional to h^{2}/D, where D is the diffusion coefficient of the corresponding area-preserving map that in turn is proportional to K^{5/2} and K^{2} in the slow and the quasilinear diffusion regimes, respectively.

[Does the use of fentanyl make Vater's ampulla cannulation difficult? A prospective and comparative study]. / ¿Dificulta la canulación del ámpula de Vater el uso de fentanilo? Un estudio prospectivo y comparativo.

BACKGROUND: Fentanyl is a synthetic opioid with excellent results in perioperative analgesia. It is commonly used for proximal and distal gastrointestinal endoscopic procedures, but its contracting action on the sphincter of Oddi, similar to that of morphine, makes its use for endoscopic cholangiopancreatography (ERCP) controversial. OBJECTIVE: To determinate if intravenous fentanyl as part of deep sedation hinders the cannulation of Vater's papilla during ERCP. MATERIAL AND METHODS: Prospective, comparative, randomized and double-blind trial that enrolled patients undergoing ERCP in 2008, > 18 years old, without previous endoscopic or surgical procedures related with Vater s papilla. Patients were randomized into two groups: patients in whom ERCP was performed with intravenous propofol (group A), and patients in whom the procedure was performed with intravenous fentanyl and propofol (group B). Gender, age, comorbid conditions, reasons for referral, difficulty of cannulation, diagnosis, therapeutic procedures, procedure time and endoscopic complications were all documented. RESULTS: 432 were included: 214 in group A and 218 in group B. Both groups were similar in relation with demographic characteristics, time of sedation and endoscopic procedure. Difficulty in cannulation had not a statistical significance (p = 0.163). The administered dose of propofol were less for group B (p < 0.001). No procedure-related mortality was documented. CONCLUSION: The combination of fentanyl and propofol may be used during ERCP, since it does not hinder the cannulation of Vater's papilla.