共查询到20条相似文献,搜索用时 46 毫秒
1.
We investigate the effects of renormalization on the localization of the quasiparticle excitations of one-dimensional Bose-Einstein condensate in a random potential. Starting with a set of linearized equations of motion for the phases of superfluid grains coupled by Josephson interactions, we use mode-counting techniques to calculate the inverse localization length for large (108) arrays. Employing distributions for the interaction parameters that are the same as the initial (pre-renormalization) distributions used by Gurarie et al. (Phys. Rev. Lett. 101 (2008) 170407), we compare the initial-interaction results for the localization length with those obtained using renormalization group techniques. 相似文献
2.
Complex networks renormalization: flows and fixed points 总被引:1,自引:0,他引:1
Recently, it has been claimed that some complex networks are self-similar under a convenient renormalization procedure. We present a general method to study renormalization flows in graphs. We find that the behavior of some variables under renormalization, such as the maximum number of connections of a node, obeys simple scaling laws, characterized by critical exponents. This is true for any class of graphs, from random to scale-free networks, from lattices to hierarchical graphs. Therefore, renormalization flows for graphs are similar as in the renormalization of spin systems. An analysis of classic renormalization for percolation and the Ising model on the lattice confirms this analogy. Critical exponents and scaling functions can be used to classify graphs in universality classes, and to uncover similarities between graphs that are inaccessible to a standard analysis. 相似文献
3.
Chandre C Jauslin HR 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》2000,61(2):1320-1328
We analyze the stability of invariant tori for Hamiltonian systems with two degrees of freedom by constructing a transformation that combines Kolmogorov-Arnold-Moser theory and renormalization-group techniques. This transformation is based on the continued fraction expansion of the frequency of the torus. We apply this transformation numerically for arbitrary frequencies that contain bounded entries in the continued fraction expansion. We give a global picture of renormalization flow for the stability of invariant tori, and we show that the properties of critical (and near critical) tori can be obtained by analyzing renormalization dynamics around a single hyperbolic strange attractor. We compute the fractal diagram, i.e., the critical coupling as a function of the frequencies, associated with a given one-parameter family. 相似文献
4.
László Gulyás George Kampis Richard O. Legendi 《The European physical journal. Special topics》2013,222(6):1311-1333
Inspecting the dynamics of networks opens a new dimension in understanding the interactions among the components of complex systems. Our goal is to understand the baseline properties expected from elementary random changes over time, in order to be able to assess the various effects found in longitudinal data. We created elementary dynamic models from classic random and preferential networks. Focusing on edge dynamics, we defined several processes for changing networks of a fixed size. We applied simple rules, including random, preferential and assortative modifications of existing edges – or a combination of these. Starting from initial Erdos-Rényi networks, we examined various basic network properties (e.g., density, clustering, average path length, number of components, degree distribution, etc.) of both snapshot and cumulative networks (for various lengths of aggregation time windows). Our results provide a baseline for changes to be expected in dynamic networks. We found universalities in the dynamic behavior of most network statistics. Furthermore, our findings suggest that certain network properties have a strong, non-trivial dependence on the length of the sampling window. 相似文献
5.
Achille Giacometti Amos Maritan Hisao Nakanishi 《Journal of statistical physics》1994,75(3-4):669-706
The dependence of the universality class on the statistical weight of unrestricted random paths is explicitly shown both for deterministic and statistical fractals such as the incipient infinite percolation cluster. Equally weighted paths (ideal chain) and kinetically generated paths (random walks) belong, in general, to different universality classes. For deterministic fractals exact renormalization group techniques are used. Asymptotic behaviors for the end-to-end distance ranging from power to logarithmic (localization) laws are observed for the ideal chain. In all these cases, random walks in the presence of nonperfect traps are shown to be in the same universality class of the ideal chain. Logarithmic behavior is reflected insingular renormalization group recursions. For the disordered case, numerical transfer matrix techniques are exploited on percolation clusters in two and three dimensions. The two-point correlation function scales with critical exponents not obeying standard scaling relations. The distribution of the number of chains and the number of chains returning to the starting point are found to be well approximated by a log-normal distribution. The logmoment of the number of chains is found to have an essential type of singularity consistent with the log-normal distribution. A non-self-averaging behavior is argued to occur on the basis of the results. 相似文献
6.
W. X. Wang B. Y. Lin C. L. Tang G. R. Chen 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,60(4):529-536
We propose a Finite-Memory Naming Game (FMNG) model with
respect to the bounded rationality of agents or finite resources for
information storage in communication systems. We study its dynamics
on several kinds of complex networks, including random networks,
small-world networks and scale-free networks. We focus on the
dynamics of the FMNG affected by the memory restriction as well as
the topological properties of the networks. Interestingly, we found
that the most important quantity, the convergence time of reaching
the consensus, shows some non-monotonic behaviors by varying the
average degrees of the networks with the existence of the fastest
convergence at some specific average degrees. We also investigate
other main quantities, such as the success rate in negotiation, the
total number of words in the system and the correlations between
agents of full memory and the total number of words, which clearly
explain the nontrivial behaviors of the convergence. We provide some
analytical results which help better understand the dynamics of the
FMNG. We finally report a robust scaling property of the convergence
time, which is regardless of the network structure and the memory
restriction. 相似文献
7.
Theory of rumour spreading in complex social networks 总被引:1,自引:0,他引:1
We introduce a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular, those mediated by the Internet). We use analytical and numerical solutions of these equations to examine the threshold behaviour and dynamics of the model on several models of such networks: random graphs, uncorrelated scale-free networks and scale-free networks with assortative degree correlations. We show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumour spreading rate below which a rumour cannot propagate in the system. In the case of scale-free networks, on the other hand, this threshold becomes vanishingly small in the limit of infinite system size. We find that the initial rate at which a rumour spreads is much higher in scale-free networks than in random graphs, and that the rate at which the spreading proceeds on scale-free networks is further increased when assortative degree correlations are introduced. The impact of degree correlations on the final fraction of nodes that ever hears a rumour, however, depends on the interplay between network topology and the rumour spreading rate. Our results show that scale-free social networks are prone to the spreading of rumours, just as they are to the spreading of infections. They are relevant to the spreading dynamics of chain emails, viral advertising and large-scale information dissemination algorithms on the Internet. 相似文献
8.
The renormalization group is not only a powerful method for describing universal properties of phase transitions, but it is
also useful for evaluating non-universal thermodynamic properties beyond mean-field theory. In this contribution we concentrate
on these latter aspects of the renormalization group approach. We introduce its main underlying ideas in the familiar context
of the ideal Bose gas and then apply them to the case of an interacting, confined Bose gas within the framework of the random
phase approximation. We model confinement by periodic boundary conditions and demonstrate how confinement modifies the flow
equations of the renormalization group, thus changing the thermodynamic properties of the gas.
Received: 20 July 2001 / Revised version: 20 August 2001 / Published online: 23 November 2001 相似文献
9.
We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse field Ising model, which is a prototype of random quantum magnets. With this algorithm we can renormalize an N-site cluster within a time NlogN, independently of the topology of the graph, and we went up to N ~ 4 × 10(6). We have studied regular lattices with dimension D ≤ 4 as well as Erd?s-Rényi random graphs, which are infinite dimensional objects. In all cases the quantum critical behaviour is found to be controlled by an infinite disorder fixed point, in which disorder plays a dominant role over quantum fluctuations. As a consequence the renormalization procedure as well as the obtained critical properties are asymptotically exact for large systems. We have also studied Griffiths singularities in the paramagnetic and ferromagnetic phases and generalized the numerical algorithm for other random quantum systems. 相似文献
10.
We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization. 相似文献
11.
Z.-G. Huang X.-J. Xu Z.-X. Wu Y.-H. Wang 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,51(4):549-553
We carry out comparative studies of random walks on deterministic
Apollonian networks (DANs) and random Apollonian networks (RANs).
We perform computer simulations for the mean first-passage time,
the average return time, the mean-square displacement, and the
network coverage for the unrestricted random walk. The diffusions
both on DANs and RANs are proved to be sublinear. The effects of
the network structure on the dynamics and the search efficiencies
of walks with various strategies are also discussed. Contrary to
intuition, it is shown that the self-avoiding random walk, which
has been verified as an optimal local search strategy in networks,
is not the best strategy for the DANs in the large size limit. 相似文献
12.
Janssen HK Stenull O Oerding K 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》1999,59(6):R6239-R6242
We present an alternative view of Feynman diagrams for the field theory of random resistor networks, in which the diagrams are interpreted as being resistor networks themselves. This simplifies the field theory considerably as we demonstrate by calculating the fractal dimension D(B) of the percolation backbone to three loop order. Using renormalization group methods we obtain D(B)=2+epsilon/21-172epsilon(2)/9261+2epsilon(3)[-74 639+22 680zeta(3)]/4 084 101, where epsilon=6-d with d being the spatial dimension and zeta(3)=1.202 057... . 相似文献
13.
K. Anand T. Galla 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,68(4):587-600
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are characteristic of flow networks in economic, ecological and biological systems. Based on results from random matrix theory, we work out the phase diagram of such systems defined on extensively connected random graphs, and study in detail how the choice of control policies and the network structure affects stability. We also present results for more complex topologies of the underlying graph, focussing on finitely connected Erdös-Réyni graphs, Small-World Networks and Barabási-Albert scale-free networks. Results indicate that variability of input-output matrix elements, and random structures of the underlying graph tend to make the system less stable, while fast price dynamics or strong responsiveness to stock accumulation promote stability. 相似文献
14.
V. A. Avetisov A. Kh. Bikulov O. A. Vasilyev S. K. Nechaev A. V. Chertovich 《Journal of Experimental and Theoretical Physics》2009,109(3):485-504
The investigation of spectral properties of random block-hierarchical matrices as applied to dynamic and structural characteristics
of complex hierarchical systems with disorder is proposed for the first time. Peculiarities of dynamics on random ultrametric
energy landscapes are discussed and the statistical properties of scale-free and polyscale (depending on the topological characteristics
under investigation) random hierarchical networks (graphs) obtained by multiple mapping are considered. 相似文献
15.
16.
Deych LI 《Physical review letters》2005,95(4):043902
Semiclassical equations of lasing dynamics are rederived for a lasing medium in a cavity with a spatially nonuniform dielectric constant. The nonuniformity causes a radiative coupling between modes of the empty cavity, which results in a renormalization of self- and cross-saturation coefficients. Possible manifestations of these effects in random lasers are discussed. 相似文献
17.
Berkovits R 《Physical review letters》2012,108(17):176803
The properties of the entanglement entropy (EE) in one-dimensional disordered interacting systems are studied. Anderson localization leaves a clear signature on the average EE, as it saturates on the length scale exceeding the localization length. This is verified by numerically calculating the EE for an ensemble of disordered realizations using the density matrix renormalization group method. A heuristic expression describing the dependence of the EE on the localization length, which takes into account finite-size effects, is proposed. This is used to extract the localization length as a function of the interaction strength. The localization length dependence on the interaction fits nicely with the expectations. 相似文献
18.
We study one-dimensional disordered bosons at large commensurate filling. Using a real space renormalization group approach, we find a new random fixed point which controls a phase transition from a superfluid to an incompressible Mott glass. The transition can be tuned by changing the disorder distribution even with vanishing interactions. We derive the properties of the transition, which suggest that it is in the Kosterlitz-Thouless universality class. 相似文献
19.
20.
We introduce a unified formulation of variational methods for simulating ground state properties of quantum many-body systems. The key feature is a novel variational method over quantum circuits via infinitesimal unitary transformations, inspired by flow equation methods. Variational classes are represented as efficiently contractible unitary networks, including the matrix-product states of density matrix renormalization, multiscale entanglement renormalization (MERA) states, weighted graph states, and quantum cellular automata. In particular, this provides a tool for varying over classes of states, such as MERA, for which so far no efficient way of variation has been known. The scheme is flexible when it comes to hybridizing methods or formulating new ones. We demonstrate the functioning by numerical implementations of MERA, matrix-product states, and a new variational set on benchmarks. 相似文献