Optimal paths in disordered complex networks

We study the optimal distance in networks, l(opt), defined as the length of the path minimizing the total weight, in the presence of disorder. Disorder is introduced by assigning random weights to the links or nodes. For strong disorder, where the maximal weight along the path dominates the sum, we find that l(opt) approximately N(1/3) in both Erdos-Rényi (ER) and Watts-Strogatz (WS) networks. For scale-free (SF) networks, with degree distribution P(k) approximately k(-lambda), we find that l(opt) scales as N((lambda-3)/(lambda-1)) for 3 or =4. Thus, for these networks, the small-world nature is destroyed. For 2相似文献   

Quantum phase slips in the presence of finite-range disorder

To study the effect of disorder on quantum phase slips (QPSs) in superconducting wires, we consider the plasmon-only model where disorder can be incorporated into a first-principles instanton calculation. We consider weak but general finite-range disorder and compute the form factor in the QPS rate associated with momentum transfer. We find that the system maps onto dissipative quantum mechanics, with the dissipative coefficient controlled by the wave (plasmon) impedance Z of the wire and with a superconductor-insulator transition at Z = 6.5 k. We speculate that the system will remain in this universality class after resistive effects at the QPS core are taken into account.     

Scale-free networks are ultrasmall

We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) proportional, variant k(-lambda), i.e., the probability of having k links outgoing from a site. In contrast to the diameter of regular random networks or small-world networks, which is known to be d approximately ln(N, we show, using analytical arguments, that scale-free networks with 23, d approximately ln(N. We also show that, for any lambda>2, one can construct a deterministic scale-free network with d approximately ln(ln(N, which is the lowest possible diameter.     

Fluctuation conductivity in layered d-wave superconductors near critical disorder

We consider the fluctuation conductivity in the critical region of a disorder induced quantum phase transition in layered d-wave superconductors. We specifically address the fluctuation contribution to the systems conductivity in the limit of large (quasi-two-dimensional system) and small (quasi-three-dimensional system) separation between adjacent layers of the system. Both in-plane and c-axis conductivities were discussed near the point of insulator-superconductor phase transition. The value of the dynamical critical exponent, z = 2, permits a perturbative treatment of this quantum phase transition under the renormalization group approach. We discuss our results for the system conductivities in the critical region as function of temperature and disorder.Received: 10 October 2003, Published online: 23 December 2003PACS: 74.40. + k Fluctuations (noise, chaos, nonequilibrium superconductivity, localization, etc.) - 73.43.Nq Quantum phase transitions     

Disorder induced quantum phase transition in random-exchange spin-1/2 chains

We investigate the effect of quenched bond disorder on the anisotropic antiferromagnetic spin-1/2 (XXZ) chain as a model for disorder-induced quantum phase transitions. We find nonuniversal behavior of the average correlation functions for weak disorder, followed by a quantum phase transition into a strongly disordered phase with only short-range xy correlations. We find no evidence for the universal strong-disorder fixed point predicted by the real-space renormalization group, suggesting a qualitatively different view of the relationship between quantum fluctuations and disorder.     

Scale-free networks on lattices

We suggest a method for embedding scale-free networks, with degree distribution Pk approximately k(-lambda), in regular Euclidean lattices accounting for geographical properties. The embedding is driven by a natural constraint of minimization of the total length of the links in the system. We find that all networks with lambda>2 can be successfully embedded up to a (Euclidean) distance xi which can be made as large as desired upon the changing of an external parameter. Clusters of successive chemical shells are found to be compact (the fractal dimension is df=d), while the dimension of the shortest path between any two sites is smaller than 1: dmin=(lambda-2)/(lambda-1-1/d), contrary to all other known examples of fractals and disordered lattices.     

Effects of average degree of network on an order-disorder transition in opinion dynamics

We have investigated the influence of the average degree \langle k \rangle of network on the location of an order--disorder transition in opinion dynamics. For this purpose, a variant of majority rule (VMR) model is applied to Watts--Strogatz (WS) small-world networks and Barab\'{a}si--Albert (BA) scale-free networks which may describe some non-trivial properties of social systems. Using Monte Carlo simulations, we find that the order--disorder transition point of the VMR model is greatly affected by the average degree \langle k \rangle of the networks; a larger value of \langle k \rangle results in a more ordered state of the system. Comparing WS networks with BA networks, we find WS networks have better orderliness than BA networks when the average degree \langle k \rangle is small. With the increase of \langle k \rangle, BA networks have a more ordered state. By implementing finite-size scaling analysis, we also obtain critical exponents \beta/\nu, \gamma/\nu and 1/\nu for several values of average degree \langle k \rangle. Our results may be helpful to understand structural effects on order--disorder phase transition in the context of the majority rule model.     

Phase transitions for information diffusion in random clustered networks

We study the conditions for the phase transitions of information diffusion in complexnetworks. Using the random clustered network model, a generalisation of the Chung-Lurandom network model incorporating clustering, we examine the effect of clustering underthe Susceptible-Infected-Recovered (SIR) epidemic diffusion model with heterogeneouscontact rates. For this purpose, we exploit the branching process to analyse informationdiffusion in random unclustered networks with arbitrary contact rates, and provide noveliterative algorithms for estimating the conditions and sizes of global cascades,respectively. Showing that a random clustered network can be mapped into a factor graph,which is a locally tree-like structure, we successfully extend our analysis to randomclustered networks with heterogeneous contact rates. We then identify the conditions forphase transitions of information diffusion using our method. Interestingly, for variouscontact rates, we prove that random clustered networks with higher clustering coefficientshave strictly lower phase transition points for any given degree sequence. Finally, weconfirm our analytical results with numerical simulations of both synthetically-generatedand real-world networks.     

Rounding by disorder of first-order quantum phase transitions: emergence of quantum critical points

We give a heuristic argument for disorder rounding of a first-order quantum phase transition into a continuous phase transition. From both weak and strong disorder analysis of the N-color quantum Ashkin-Teller model in one spatial dimension, we find that, for N > or =3, the first-order transition is rounded to a continuous transition and the physical picture is the same as the random transverse field Ising model for a limited parameter regime. The results are strikingly different from the corresponding classical problem in two dimensions where the fate of the renormalization group flows is a fixed point corresponding to N-decoupled pure Ising models.     

Failure tolerance of spike phase synchronization in coupled neural networks

Neuronal synchronization plays an important role in the various functionality of nervous system such as binding, cognition, information processing, and computation. In this paper, we investigated how random and intentional failures in the nodes of a network influence its phase synchronization properties. We considered both artificially constructed networks using models such as preferential attachment, Watts-Strogatz, and Erdo?s-Re?nyi as well as a number of real neuronal networks. The failure strategy was either random or intentional based on properties of the nodes such as degree, clustering coefficient, betweenness centrality, and vulnerability. Hindmarsh-Rose model was considered as the mathematical model for the individual neurons, and the phase synchronization of the spike trains was monitored as a function of the percentage∕number of removed nodes. The numerical simulations were supplemented by considering coupled non-identical Kuramoto oscillators. Failures based on the clustering coefficient, i.e., removing the nodes with high values of the clustering coefficient, had the least effect on the spike synchrony in all of the networks. This was followed by errors where the nodes were removed randomly. However, the behavior of the other three attack strategies was not uniform across the networks, and different strategies were the most influential in different network structure.     

Quantum critical behavior near a density-wave instability in an isotropic fermi liquid

We study the quantum critical behavior in an isotropic Fermi liquid in the vicinity of a zero-temperature density-wave transition at a finite wave vector qc. We show that, near the transition, the Landau damping of the soft bosonic mode yields a crossover in the fermionic self-energy from Sigma(k,omega) approximately Sigma(k) to Sigma(k,omega) approximately Sigma(omega), where k and omega are momentum and frequency. Because of this self-generated locality, the fermionic effective mass diverges right at the quantum critical point, not before; i.e., the Fermi liquid survives up to the critical point.     

Disorder promotes ferromagnetism: rounding of the quantum phase transition in Sr(1-x)Ca(x)RuO3

The subtle interplay of randomness and quantum fluctuations at low temperatures gives rise to a plethora of unconventional phenomena in systems ranging from quantum magnets and correlated electron materials to ultracold atomic gases. Particularly strong disorder effects have been predicted to occur at zero-temperature quantum phase transitions. Here, we demonstrate that the composition-driven ferromagnetic-to-paramagnetic quantum phase transition in Sr(1-x)Ca(x)RuO3 is completely destroyed by the disorder introduced via the different ionic radii of the randomly distributed Sr and Ca ions. Using a magneto-optical technique, we map the magnetic phase diagram in the composition-temperature space. We find that the ferromagnetic phase is significantly extended by the disorder and develops a pronounced tail over a broad range of the composition x. These findings are explained by a microscopic model of smeared quantum phase transitions in itinerant magnets. Moreover, our theoretical study implies that correlated disorder is even more powerful in promoting ferromagnetism than random disorder.     

Resonant localized states and quantum percolation on random chains with power-law-diluted long-range couplings

We investigate the nature of one-electron eigenstates in power-law-diluted chains for which the probability of occurrence of a bond between sites separated by a distance r decays as p(r) = p/r(1+σ). Using an exact diagonalization scheme and a phenomenological finite-size scaling analysis, we determine the quantum percolation transition phase diagram in the full parameter space (p,σ). We show that the density of states displays singularities at some resonance energies associated with degenerate eigenstates localized in a pair of sites with special symmetries. This model is shown to present an intermediate phase for which there is classical percolation but no quantum percolation. Quantum percolation only takes place for σ < 0.78, a value larger than the corresponding one for the Anderson transition in long-ranged coupled chains with random diagonal disorder. The fractality of critical wavefunctions is also characterized.     

Continuous-time quantum walks on Erdös-Rényi networks

We study the coherent exciton transport of continuous-time quantum walks (CTQWs) on Erdös-Rényi networks. We numerically investigate the transition probability between two nodes of the networks, and compare the classical and quantum transport efficiency on networks of different connectivity. In the long time limiting, we find that there is a high probability to find the exciton at the initial node. We also study how the network parameters affect such high return probability.     

Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks

Non-Hermitian topological edge states have many intriguing properties, however, to date, they have mainly been discussed in terms of bulk–boundary correspondence. Here, we propose using a bulk property of diffusion coefficients for probing the topological states and exploring their dynamics. The diffusion coefficient was found to show unique features with the topological phase transitions driven by parity–time (PT)-symmetric non-Hermitian discrete-time quantum walks as well as by Hermitian ones, despite the fact that artificial boundaries are not constructed by an inhomogeneous quantum walk. For a Hermitian system, a turning point and abrupt change appears in the diffusion coefficient when the system is approaching the topological phase transition, while it remains stable in the trivial topological state. For a non-Hermitian system, except for the feature associated with the topological transition, the diffusion coefficient in the PT-symmetric-broken phase demonstrates an abrupt change with a peak structure. In addition, the Shannon entropy of the quantum walk is found to exhibit a direct correlation with the diffusion coefficient. The numerical results presented herein may open up a new avenue for studying the topological state in non-Hermitian quantum walk systems.     

Dipolar excitons, spontaneous phase coherence, and superfluid-insulator transition in bilayer quantum Hall systems at nu = 1

The spontaneous interlayer phase coherent (111) state of a bilayer quantum Hall system at filling factor nu = 1 may be viewed as a condensate of interlayer particle-hole pairs or excitons. We show that when the layers are biased in such a way that these excitons are very dilute, they may be viewed as pointlike bosons. We calculate the exciton dispersion relation and show that the exciton-exciton interaction is dominated by the dipole moment they carry. In addition to the phase coherent state, we also find a Wigner crystal/glass phase in the presence/absence of disorder which is an insulating state for the excitons. The position of the phase boundary is estimated and the transition between these two phases is discussed.     

Search for Majorana fermions in multiband semiconducting nanowires

We study multiband semiconducting nanowires proximity-coupled with an s-wave superconductor. We show that, when an odd number of subbands are occupied, the system realizes a nontrivial topological state supporting Majorana modes. We study the topological quantum phase transition in this system and calculate the phase diagram as a function of the chemical potential and magnetic field. Our key finding is that multiband occupancy not only lifts the stringent constraint of one-dimensionality but also allows one to have higher carrier density in the nanowire, and as such multisubband nanowires are better suited for observing the Majorana particle. We study the robustness of the topological phase by including the effects of the short- and long-range disorder. We show that there is an optimal regime in the phase diagram ("sweet spot") where the topological state is to a large extent insensitive to the presence of disorder.     

Superfluid-insulator transition in a commensurate one-dimensional bosonic system with off-diagonal disorder

We study the nature of the superfluid-insulator quantum phase transition in a one-dimensional system of lattice bosons with off-diagonal disorder in the limit of a large integer filling factor. Monte Carlo simulations of two strongly disordered models show that the universality class of the transition in question is the same as that of the superfluid-Mott-insulator transition in a pure system. This result can be explained by disorder self-averaging in the superfluid phase and the applicability of the standard quantum hydrodynamic action. We also formulate the necessary conditions which should be satisfied by the stong-randomness universality class, if one exists.     

Density-matrix renormalization group study of the spin-Peierls instability in the antiferromagnetic Heisenberg ladder

The columnar dimerized antiferromagnetic S?=?1/2 spin ladder is numerically studied by the density-matrix renormalization-group (DMRG) method. The elastic lattice with spin-phonon coupling ?? and lattice elastic force k is introduced into the system. Thus the S?=?1?/?2 Heisenberg spin chain is unstable towards dimerization (the spin-Peierls transition). However, the dimerization should be suppressed if the rung coupling J _?? is sufficiently large, and a Columnar dimer to Rung singlet phase transition takes place. After a self-consistent calculation of the dimerization, we determine the quantum phase diagram by numerically computing the singlet-triplet gap, the dimerization amplitude, the order parameters, the rung spin correlation and quantum entropies. Our results show that the phase boundary between the Columnar dimer phase and Rung singlet phase is approximately of the form J _?? ~ \hbox{$(\frac{k}{\alpha^{2}})^{-\frac{5}{4}}$} ( k ?? 2 ) ? 5 4.