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1.
On the properties of small-world network models 总被引:7,自引:0,他引:7
A. Barrat M. Weigt 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,13(3):547-560
We study the small-world networks recently introduced by Watts and Strogatz [Nature 393, 440 (1998)], using analytical as well as numerical tools. We characterize the geometrical properties resulting from the
coexistence of a local structure and random long-range connections, and we examine their evolution with size and disorder
strength. We show that any finite value of the disorder is able to trigger a “small-world” behaviour as soon as the initial
lattice is big enough, and study the crossover between a regular lattice and a “small-world” one. These results are corroborated
by the investigation of an Ising model defined on the network, showing for every finite disorder fraction a crossover from
a high-temperature region dominated by the underlying one-dimensional structure to a mean-field like low-temperature region.
In particular there exists a finite-temperature ferromagnetic phase transition as soon as the disorder strength is finite.
[0.5cm]
Received 29 March 1999 and Received in final form 21 May 1999 相似文献
2.
Yu. Kh. Vekilov I. A. Gordeev É. I. Isaev 《Journal of Experimental and Theoretical Physics》1999,89(5):995-999
The electronic spectrum and wave functions of a new quasicrystal structure—a two-dimensional Fibonacci lattice—are investigated
in the tight-binding approximation using the method of the level statistics. This is a self-similar structure consisting of
three elementary structural units. The “central” and “nodal” decoration of this structure are examined. It is shown that the
electronic energy spectrum of a two-dimensional Fibonacci lattice contains a singular part, but in contrast to a one-dimensional
Fibonacci lattice the spectrum does not contain a hierarchical gap structure. The measure of allowed states (Lebesgue measure)
of the spectrum is different from zero, and for “central” decoration it is close to 1. The character of the localization of
the wave functions is investigated, and it is found that the wave functions are “critical.”
Zh. éksp. Teor. Fiz. 116, 1834–1842 (November 1999) 相似文献
3.
We investigate, using numerical simulations and analytical arguments, a simple one-dimensional model for the swelling or the
collapse of a closed polymer chain of size N, representing the dynamical evolution of a polymer in a Θ-solvent that is rapidly changed into a good solvent (swelling)
or a bad solvent (collapse). In the case of swelling, the density profile for intermediate times is parabolic and expands
in space as t
1/3, as predicted by a Flory-like continuum theory. The dynamics slows down after a time ∝N
2 when the chain becomes stretched, and the polymer gets stuck in metastable “zig-zag” configurations, from which it escapes
through thermal activation. The size of the polymer in the final stages is found to grow as . In the case of collapse, the chain very quickly (after a time of order unity) breaks up into clusters of monomers (“pearls”).
The evolution of the chain then proceeds through a slow growth of the size of these metastable clusters, again evolving as
the logarithm of time. We enumerate the total number of metastable states as a function of the extension of the chain, and
deduce from this computation that the radius of the chain should decrease as 1/ln(ln t). We compute the total number of metastable states with a given value of the energy, and find that the complexity is non-zero
for arbitrary low energies. We also obtain the distribution of cluster sizes, that we compare to simple “cut-in-two” coalescence
models. Finally, we determine the aging properties of the dynamical structure. The subaging behaviour that we find is attributed
to the tail of the distribution at small cluster sizes, corresponding to anomalously “fast” clusters (as compared to the average).
We argue that this mechanism for subaging might hold in other slowly coarsening systems.
Received 23 October 2000 相似文献
4.
S. G. Bilchinskaya O. Ya. Butkovskii Yu. A. Kravtsov I. A. Rychka E. D. Surovyatkina 《Journal of Experimental and Theoretical Physics》2002,95(1):175-180
The problem of transition of a noisy dynamical system to a periodic oscillatory regime through a zone of chaos is considered. Using the noisy logistics map as an example, domains of attraction of energetically equivalent regimes of period three are found for various transition rates and various noise levels. The fine structure of the domains of attraction under the condition of fast transitions is revealed. It is discovered that the settling time of the stable cycle of period three heavily depends on the initial conditions, i.e., on the structure of the domains of attraction. The critical transition rate that separates the region of the probabilistic symmetry of final states from the region of the dynamic behavior of trajectories is estimated. 相似文献
5.
The probabilities of transitions between the Fock states of two electromagnetic field modes under the influence of coupling
between modes of finite duration are investigated. It is shown that the transition probability is a strongly oscillating function
of the mode numbers of the photons. Under conditions in which the coupling frequency exceeds the geometric mean of the mode
frequencies (strong coupling), large numbers of photons are excited in the mode with the lower frequency. The excitation of
a two-dimensional radiation field oscillator and the “red” asymmetry of the transition probabilities can be attributed to
instability of the classical two-dimensional oscillator with strong mode coupling.
Zh. éksp. Teor. Fiz. 112, 128–136 (July 1997) 相似文献
6.
S. A. Gavrilov V. V. Gusev V. S. Dneprovskii E. A. Zhukov A. N. Syrnikov I. V. Yaminskii E. A. Muljarov 《JETP Letters》1999,70(3):216-221
The characteristic features of the luminescence spectra of CdS semiconductor nanocrystals, crystallized in hollow channels
in a dielectric template, are explained in terms of excitonic transitions in semiconductor-insulator quantum wires. The excitonic
transition energies agree with the values calculated taking into account the effects of size quantization and the “dielectric
enhancement of excitons” — the large increase in the electron-hole attraction as a result of the difference between the permittivities
of the semiconductor and insulator. The theoretically computed binding energies of excitons in CdS quantum wires with a diameter
of 10 nm reach 170 meV. It is shown that the excitonic transition energy is constant for a wide range of wire diameters.
Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 216–220 (10 August 1999) 相似文献
7.
M. Holthaus S. Stenholm 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,20(3):451-467
We discuss the dynamics of two weakly coupled Bose-Einstein condensates in a double-well potential, contrasting the mean-field
picture to the exact N-particle evolution. On the mean-field level, a self-trapping transition occurs when the scaled interaction strength exceeds
a critical value; this transition essentially persists in small condensates comprising about 1000 atoms. When the double-well
is modulated periodically in time, Floquet-type solutions to the nonlinear Schr?dinger equation take over the role of the
stationary mean-field states. These nonlinear Floquet states can be classified as “unbalanced” or “balanced”, depending on
whether or not they entail long-time confinement of most particles to one well. Since the emergence of unbalanced Floquet
states depends on the amplitude and frequency of the modulating force, we predict that the onset of self-trapping can efficiently
be controlled by varying these parameters. This prediction is verified numerically by both mean-field and N-particle calculations.
Received 5 November 2000 and Received in final form 16 February 2001 相似文献
8.
Recent experiments on unzipping of RNA helix-loop structures by force have shown that ≈40-base molecules can undergo kinetic
transitions between two well-defined “open” and “closed” states, on a timescale ≈1 sec [Liphardt et al., Science 297, 733-737 (2001)]. Using a simple dynamical model, we show that these phenomena result from the slow kinetics
of crossing large free energy barriers which separate the open and closed conformations. The dependence of barriers on sequence
along the helix, and on the size of the loop(s) is analyzed. Some DNA and RNA sequences that could show dynamics on different
time scales, or three(or more)-state unzipping, are proposed. Our dynamical model is also applied to the unzipping of long
(kilo-basepair) DNA molecules at constant force.
Received 29 July 2002 / Received in final form 5 February 2003 Published online: 16 April 2003
RID="a"
ID="a"e-mail: cocco@ldfc.u-strasbg.fr
RID="b"
ID="b"e-mail: jmarko@uic.edu
RID="c"
ID="c"e-mail: monasson@lpt.ens.fr 相似文献
9.
The intermode anharmonic interaction in the theory of ultrafast (t∼10−13 s) vibronic phase transitions induced on semiconductor surfaces (Si, GaAs) by femtosecond laser pulses is calculated. The
conditions for plasma-induced transitions either to a state of chaotic disorder in the positions of the atoms (“cold liquid”)
or into a state with crystal symmetry different from the initial symmetry (a new crystalline phase) are determined. It is
shown that a NaCl-type structure is realized in GaAs for a transition of the second type, the transition being due to the
instability of the longitudinal optical phonon branch. The corresponding numerical estimates are made for Si and GaAs.
Fiz. Tverd. Tela (St. Petersburg) 41, 1462–1466 (August 1999) 相似文献
10.
Kh. Moumanis R. P. Seisyan M. É. Sasin A. V. Kavokin S. I. Kokhanovskii H. M. Gibbs G. Khitrova 《Physics of the Solid State》1998,40(5):731-733
Additional localization of holes due to Coulomb attraction to the electron located in a quantum well is important for light-hole
excitons in the heterostructure (In, Ga)As/GaAs. The fine structure of the optical and magneto-optical spectra of these quantum
wells is examined in detail with the formation of a “Coulomb well” and deformations taken into account.
Fiz. Tverd. Tela (St. Petersburg) 40, 797–799 (May 1998) 相似文献
11.
12.
A. A. Klochikhin S. A. Permogorov A. N. Reznitskii T. Breitkopf R. Westphäling C. Klingshirn 《Physics of the Solid State》1998,40(5):821-822
It is shown that, with strong pulsed excitation, the intensity of the exciton recombination band in the fluctuation tail of
the density of states in the limit of large times in the presence of traps is described by the asymptote of a solution to
the diffusion equation. The critical diffusion index corresponds to a “normal” process in the CdS-Se solid solution and to
“anomalous” diffusion in the case of ZnSe-Te.
Fiz. Tverd. Tela (St. Petersburg) 40, 892–893 (May 1998) 相似文献
13.
The conditions for the existence of resonance electronic states near the critical points of volume bands are obtained. It
is shown that resonances of this type are qualitatively different from surface resonances associated with states induced by
an image potential. The manifestation of such “volume” resonances in the scattering of very slow electrons by a TiS2 surface is studied.
Fiz. Tverd. Tela (St. Petersburg) 40, 2003–2007 (November 1998) 相似文献
14.
R. I. Bogdanov M. P. Bogdanov 《Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques》2010,4(2):269-275
New calculated data on estimation of the density of particle fluxes are presented. These particles move freely in a surrounding
medium during the constant transit time and are then rescattered under the potential force field weakly perturbed by generalized
viscosity forces. An anharmonic potential on a phase straight line is taken as a potential, and the generalized viscosity
force corresponds to a small viscosity coefficient affinely dependent on the phase coordinate. The word “small’ here means
that the order of the generalized viscosity forces is less than two. The particle fluxes correspond to the periodic motion
of particles, asymptotically stable (unstable) states (“in” and “out” states) as t → (−) + ∞ that have basins of attraction (repulsion) with a positive measure. 相似文献
15.
Retrieval of the quasi-optimal signal activating the excitable systems using preceding noise samples
We propose a method for obtaining a signal leading to the activation of an excitable dynamic system for a signal energy close
to minimal. The efficiency of this technique, which is based on recording and processing of noise samples preceding the activation
was tested using the FitzHugh–Nagumo, Hodgkin–Huxley, and Luo–Rudy models as examples. It is shown that the proposed procedure
gives good results when the noise intensity is smaller than or close to the system activation energy. The criteria of “low”
and “high” intensities of fluctuations are proposed. The method of increasing the stability of the excitable system with respect
to “low-intensity” noise by filtering or another way of suppression of the spectral components that make the main contribution
to the energetically optimal activation signal is justified. The relation between eigenvalues of the linearized system of
the Hamiltonian equations, which describe the optimal trajectories and the activation signal, and eigenvalues of the excitable
system linearized near the initial equilibroum state is found. 相似文献
16.
M. Z. Smirnov 《Journal of Experimental and Theoretical Physics》1997,85(3):441-446
An open quantum system, which consists of a “dressed” two-level atom, i.e., an atom interacting with a classical multifrequency
field, and a single quantized mode of an electromagnetic field, is examined. It is shown that when the frequency of the quantized
mode coincides with one of the transition frequencies between the quasienergy levels, two interaction mechanisms, which differ
in the dynamics of the populations of the quasienergy states, can be realized.
Zh. éksp. Teor. Fiz. 112, 818–827 (September 1997) 相似文献
17.
William Arveson 《Communications in Mathematical Physics》2000,211(1):63-83
A mathematical notion of interaction is introduced for noncommutative dynamical systems, i.e., for one parameter groups of
*-automorphisms of endowed with a certain causal structure. With any interaction there is a well-defined “state of the past” and a well-defined
“state of the future”. We describe the construction of many interactions involving cocycle perturbations of the CAR/CCR flows
and show that they are nontrivial. The proof of nontriviality is based on a new inequality, relating the eigenvalue lists
of the “past” and “future” states to the norm of a linear functional on a certain C
*-algebra.
To the memory of Irving Segal
Received: 12 October 1999 / Accepted: 21 October 1999 相似文献
18.
We report the results of theoretical investigations of tunneling current noise spectra in a wide range of applied bias voltage.
Localized states of individual impurity atoms play an important role in tunneling current noise formation. It was found that
switching “on” and “off” of Coulomb interaction of conduction electrons with two charged localized states results in power
law singularity of low-frequency tunneling current noise spectrum (1/f
α) and also results on high frequency component of tunneling current spectra (singular peaks appear).
The article is published in the original. 相似文献
19.
E. Z. Kuchinskii N. A. Kuleeva I. A. Nekrasov M. V. Sadovskii 《Journal of Experimental and Theoretical Physics》2010,110(2):325-335
The density of states, the dynamic (optical) conductivity, and the phase diagram of the paramagnetic two-dimensional Anderson-Hubbard
model with strong correlations and disorder are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation).
Strong correlations are accounted by the DMFT, while disorder is taken into account via the appropriate generalization of
the self-consistent theory of localization. We consider the two-dimensional system with the rectangular “bare” density of
states (DOS). The DMFT effective single-impurity problem is solved by numerical renormalization group (NRG). The “correlated
metal,” Mott insulator, and correlated Anderson insulator phases are identified from the evolution of the density of states,
optical conductivity, and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in
two-dimensional systems of finite size, allowing us to construct the complete zero-temperature phase diagram of the paramagnetic
Anderson-Hubbard model. The localization length in our approximation is practically independent of the strength of Hubbard
correlations. But the divergence of the localization length in a finite-size two-dimensional system at small disorder signifies
the existence of an effective Anderson transition. 相似文献
20.
N. Mukunda 《Pramana》1998,51(5):643-649
The conventional separation of states of the quantised radiation field into “classical” and “nonclassical” types is expressed
in a dual operator form and then refined. This is based on new features of the normal ordering rule for passage from classical
to quantum dynamical variables. The cases of single and two-mode radiation fields are discussed 相似文献