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1.
P. H. Chavanis 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,53(4):487-501
Systems with long-range interactions can reach a Quasi
Stationary State (QSS) as a result of a violent collisionless
relaxation. If the system mixes well (ergodicity), the QSS can be
predicted by the statistical theory of Lynden-Bell (1967) based on
the Vlasov equation. When the initial condition takes only two
values, the Lynden-Bell distribution is similar to the Fermi-Dirac
statistics. Such distributions have recently been observed in
direct numerical simulations of the HMF model (Antoniazzi et al. 2006). In this paper, we determine the caloric curve
corresponding to the Lynden-Bell statistics in relation with the
HMF model and analyze the dynamical and thermodynamical stability
of spatially homogeneous solutions by using two general criteria
previously introduced in the literature. We express the critical
energy and the critical temperature as a function of a degeneracy
parameter fixed by the initial condition. Below these critical
values, the homogeneous Lynden-Bell distribution is not a maximum
entropy state but an unstable saddle point. Known stability
criteria corresponding to the Maxwellian distribution and the
water-bag distribution are recovered as particular limits of our
study. In addition, we find a critical point below which the
homogeneous Lynden-Bell distribution is always stable. We apply
these results to the situation considered in Antoniazzi et
al. For a given energy, we find a critical initial
magnetization above which the homogeneous Lynden-Bell distribution
ceases to be a maximum entropy state. For an energy U=0.69, this
transition occurs above an initial magnetization Mx=0.897. In
that case, the system should reach an inhomogeneous Lynden-Bell
distribution (most mixed) or an incompletely mixed state (possibly
fitted by a Tsallis distribution). Thus, our theoretical study
proves that the dynamics is different for small and large initial
magnetizations, in agreement with numerical results of Pluchino et
al. (2004). This new dynamical phase transition may reconcile the
two communities by showing that they study different regimes. 相似文献
2.
P. H. Chavanis 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,52(1):61-82
We study the relaxation of a test particle immersed
in a bath of field particles interacting via weak long-range
forces. To order 1/N in the N→+∞ limit, the
velocity distribution of the test particle satisfies a
Fokker-Planck equation whose form is related to the Landau and
Lenard-Balescu equations in plasma physics. We provide explicit
expressions for the diffusion coefficient and friction force in the
case where the velocity distribution of the field particles is
isotropic. We consider (i) various dimensions of space d=3,2 and
1; (ii) a discret spectrum of masses among the particles; (iii)
different distributions of the bath including the Maxwell
distribution of statistical equilibrium (thermal bath) and the step
function (water bag). Specific applications are given for
self-gravitating systems in three dimensions, Coulombian systems in
two dimensions and for the HMF model in one dimension. 相似文献
3.
P. H. Chavanis 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,52(1):47-59
We present first elements of kinetic theory appropriate
to the inhomogeneous phase of the Hamiltonian Mean Field (HMF)
model. In particular, we investigate the case of strongly
inhomogeneous distributions for T→0 and exhibit
curious behaviour of the force auto-correlation function and
friction coefficient. The temporal correlation function of the
force has an oscillatory behaviour which averages to zero over a
period. By contrast, the effects of friction accumulate with time
and the friction coefficient does not satisfy the Einstein
relation. On the contrary, it presents the peculiarity to increase
linearly with time. Motivated by this result, we provide analytical
solutions of a simplified kinetic equation with a time dependent
friction. Analogies with self-gravitating systems and other systems
with long-range interactions are also mentioned. 相似文献
4.
G.-H. Mu W. Chen J. Kertész W.-X. Zhou 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,68(1):145-152
The distributions of trade sizes and trading volumes are investigated based on the limit order book data of 22 liquid Chinese
stocks listed on the Shenzhen Stock Exchange in the whole year 2003. We observe that the size distribution of trades for individualstocks
exhibits jumps, which is caused by the number preference of traders when placing orders. We analyze the applicability of the
“q-Gamma” function for fitting the distribution by the Cramér-von Mises criterion. The empirical PDFs of tradingvolumes at
different timescales Δt ranging from 1 min to 240 min can be well modeled. The applicability of the q-Gamma functions for
multiple trades is restricted to the transaction numbers Δn≤ 8. We find that all the PDFs have power-law tails for large volumes.
Using careful estimation of the average tail exponents α of the distributions of trade sizes and trading volumes, we get α>
2, well outside the Lévy regime. 相似文献
5.
V. Schwämmle F. D. Nobre C. Tsallis 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,66(4):537-546
The stability of q-Gaussian distributions as particular solutions of the
linear diffusion equation and its generalized nonlinear form, , the porous-medium equation, is investigated through both numerical
and analytical approaches. An analysis of the kurtosis of the distributions strongly suggests that an initial q-Gaussian, characterized by an index qi, approaches asymptotically the
final, analytic solution of the porous-medium equation, characterized by an index q, in such a way that the relaxation rule for
the kurtosis evolves in time according to a q-exponential, with a relaxation index qrel ≡qrel(q). In some cases, particularly when one attempts to transform an infinite-variance distribution (qi ≥ 5/3) into a finite-variance
one (q < 5/3), the relaxation towards the asymptotic solution may occur very slowly in time. This fact might shed some light
on the slow relaxation, for some long-range-interacting many-body Hamiltonian systems, from long-standing quasi-stationary
states to the ultimate thermal equilibrium
state. 相似文献
6.
Vasily E. Tarasov 《Annals of Physics》2005,316(2):393-413
We consider the class of non-Hamiltonian and dissipative statistical systems with distributions that are determined by the Hamiltonian. The distributions are derived analytically as stationary solutions of the Liouville equation for non-Hamiltonian systems. The class of non-Hamiltonian systems can be described by a non-holonomic (non-integrable) constraint: the velocity of the elementary phase volume change is directly proportional to the power of non-potential forces. The coefficient of this proportionality is determined by Hamiltonian. The constant temperature systems, canonical-dissipative systems, and Fermi-Bose classical systems are the special cases of this class of non-Hamiltonian systems. 相似文献
7.
A. Rossani 《Physica A》2009,388(12):2354-2366
The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to external electric and/or magnetic fields. We construct a Fokker-Planck approximation to the kinetic equations and derive the most general class of distributions for the given problem by discussing in detail some physically meaningful cases. The equivalence with the transport theory of electrons in a phonon background is also discussed. 相似文献
8.
P.-H. Chavanis A. Campa 《The European Physical Journal B - Condensed Matter and Complex Systems》2010,76(4):581-611
We study the maximization of the Tsallis functional at
fixed mass and energy in the Hamiltonian Mean Field (HMF) model. We
give a thermodynamical and a dynamical interpretation of this
variational principle. This leads to q-distributions known as
stellar polytropes in astrophysics. We study phase transitions
between spatially homogeneous and spatially inhomogeneous
equilibrium states. We show that there exists a particular index
q
c
= 3 playing the role of a canonical tricritical point
separating first and second order phase transitions in the
canonical ensemble and marking the occurence of a negative specific
heat region in the microcanonical ensemble. We apply our results to
the situation considered by Antoni and Ruffo [Phys. Rev. E 52,
2361 (1995)] and show that the anomaly displayed on their caloric
curve can be explained naturally by assuming that, in this region,
the QSSs are polytropes with critical index q
c
= 3. We
qualitatively justify the occurrence of polytropic (Tsallis)
distributions with compact support in terms of incomplete
relaxation and inefficient mixing (non-ergodicity). Our paper
provides an exhaustive study of polytropic distributions in the HMF
model and the first plausible explanation of the surprising result
observed numerically by Antoni and Ruffo (1995). In the course of
our analysis, we also report an interesting situation where the
caloric curve presents both microcanonical first and second order
phase transitions. 相似文献
9.
J. Ke P.-P. Li X.-S. Chen Z. Lin Y. Z. Zheng 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,70(2):211-215
We propose a growing network model with link
constraint, in which new nodes are continuously introduced into
the system and immediately connected to preexisting nodes, and any
arbitrary node cannot receive new links when it reaches a maximum
number of links km. The connectivity of the network model is
then investigated by means of the rate equation approach. For the
connection kernel A(k)=kγ, the degree distribution nk
takes a power law if γ≥1 and decays stretched
exponentially if 0≤γ< 1. We also consider a network
system with the connection kernel A(k)=kα(km-k)β.
It is found that nk approaches a power law in the α> 1
case and has a stretched exponential decay in the 0≤α<
1 case, while it can take a power law with exponential truncation
in the special α=β=1 case. Moreover, nk may have a
U-type structure if α> β. 相似文献
10.
S. Duhot R. Mélin 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,51(2):257-266
The three-dimensional bimodal random-field Ising model
is investigated using the N-fold version of the Wang-Landau
algorithm. The essential energy subspaces are determined by the
recently developed critical minimum energy subspace technique, and
two implementations of this scheme are utilized. The random fields
are obtained from a bimodal discrete (±Δ) distribution,
and we study the model for various values of the disorder strength
Δ, Δ=0.5,1,1.5 and 2, on cubic lattices with
linear sizes L=4–24. We extract information for the probability
distributions of the specific heat peaks over samples of random
fields. This permits us to obtain the phase diagram and present
the finite-size behavior of the specific heat. The question of
saturation of the specific heat is re-examined and it is shown
that the open problem of universality for the random-field Ising
model is strongly influenced by the lack of self-averaging of the
model. This property appears to be substantially depended on the
disorder strength. 相似文献
11.
We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist of (a) justifying the use of relative entropy as the uniquely natural criterion to select a preferred approximation from within a family of trial parameterized distributions, and (b) to obtain the optimal approximation by marginalizing over parameters using the method of maximum entropy and information geometry. As an illustration we apply our method to simple fluids. The “exact” canonical distribution is approximated by that of a fluid of hard spheres. The proposed method first determines the preferred value of the hard-sphere diameter, and then obtains an optimal hard-sphere approximation by a suitably weighed average over different hard-sphere diameters. This leads to a considerable improvement in accounting for the soft-core nature of the interatomic potential. As a numerical demonstration, the radial distribution function and the equation of state for a Lennard-Jones fluid (argon) are compared with results from molecular dynamics simulations. 相似文献
12.
M. Treiber D. Helbing 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,68(4):607-618
This contribution presents a derivation of the steady-state distribution of velocities and
distances of driven particles on a onedimensional periodic ring, using a Fokker-Planck formalism. We will compare two different
situations: (i) symmetrical interaction forces fulfilling Newton’s law
of “actio = reactio” and (ii) asymmetric, forwardly directed interactions as, for example
in vehicular traffic. Surprisingly, the steady-state velocity and distance distributions
for asymmetric interactions and driving terms agree with the equilibrium distributions of
classical many-particle systems with symmetrical interactions, if the system is large enough.
This analytical result is confirmed by computer simulations and
establishes the possibility of approximating the steady state
statistics in driven many-particle systems by Hamiltonian systems. Our finding is also
useful to understand the various departure time distributions of queueing systems as a possible
effect of interactions among the elements in the respective queue [Physica A 363, 62 (2006)]. 相似文献
13.
C. Monthus T. Garel 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,53(1):39-45
The directed polymer in a 1+3 dimensional
random medium is known to present a disorder-induced phase
transition. For a polymer of length L, the high temperature
phase is characterized by a diffusive behavior for the end-point
displacement R2 ∼L and by free-energy fluctuations of order
ΔF(L) ∼O(1). The low-temperature phase is characterized by
an anomalous wandering exponent R2/L ∼Lω and
by free-energy fluctuations of order ΔF(L) ∼Lω
where ω∼0.18. In this paper, we first study the scaling
behavior of various properties to localize the critical temperature
Tc. Our results concerning R2/L and ΔF(L) point towards
0.76 < Tc ≤T2=0.79, so our conclusion is that Tc is equal
or very close to the upper bound T2 derived by Derrida and
coworkers (T2 corresponds to the temperature above which the ratio
remains finite as L ↦
∞). We then present histograms for the free-energy, energy and
entropy over disorder samples. For T ≫Tc, the free-energy
distribution is found to be Gaussian. For T ≪Tc, the free-energy
distribution coincides with the ground state energy distribution, in
agreement with the zero-temperature fixed point picture. Moreover the
entropy fluctuations are of order ΔS ∼L1/2 and follow a
Gaussian distribution, in agreement with the droplet predictions,
where the free-energy term ΔF ∼Lω is a near
cancellation of energy and entropy contributions of order L1/2. 相似文献
14.
We present a new approach to determine velocity distributions in granular gases to improve the Sonine polynomial expansion of the velocity distribution function, at higher inelasticities, for the homogeneous cooling regime of inelastic hard spheres. The perturbative consistency is recovered using a new set of dynamical variables based on the characteristic function and we illustrate our approach by computing the first four Sonine coefficients for moderate and high inelasticities. The analytical coefficients are compared with molecular dynamics simulations results and with a previous approach by Huthmann et al. 相似文献
15.
M. Gomes Angsula Ghosh 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,66(4):461-466
The asymmetric gap superconductivity is considered in orthorhombic high Tc cuprates. Recent experiments predict an anisotropy in the gap where |Δ(0,π)|> |Δ(π,0)| and the gap node deviates from the
diagonal direction toward the kx axis. The temperature dependencies of the specific heat and penetration depth along the a and b directions are calculated
for the anisotropic gap superconductors. However, the anisotropy in the penetration depth can be consistent with the experimental
observations only after the inclusion of the plane and chain coupling. The d-density wave (DDW) phase that explains the pseudogap
has also been considered to study the phase diagrams of the cuprates. 相似文献
16.
G. L. Ma S. Zhang Y. G. Ma X. Z. Cai J. H. Chen C. Zhong 《The European Physical Journal C - Particles and Fields》2008,57(3):589-593
Longitudinal broadening along the Δη direction on the near side in the two-dimensional (Δφ×Δη) di-hadron correlation distribution has been studied for central Au+Au collisions at
GeV, within a dynamical multi-phase transport model. It was found that longitudinal broadening is generated by a longitudinal
flow induced by a strong parton cascade in central Au+Au collisions, to be compared with p+p collisions at
GeV. The longitudinal broadening may shed light on the strongly interacting partonic matter at RHIC. 相似文献
17.
E.V. Votyakov A. De Martino D.H.E. Gross 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(4):593-603
We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation
for the density profiles maximizing the microcanonical entropy and solve it numerically. At low angular momenta, i.e. for a slowly rotating system, the well-known gravitational collapse “transition” is recovered. At higher angular momenta,
instead, rotational symmetry can spontaneously break down giving rise to more complex equilibrium configurations, such as
double-clusters (“double stars”). We analyze the thermodynamics of the system and the stability of the different equilibrium
configurations against rotational symmetry breaking, and provide the global phase diagram.
Received 8 July 2002 Published online 15 October 2002
RID="a"
ID="a"e-mail: demartino@hmi.de 相似文献
18.
J.N. Fuchs M. Holzmann F. Laloë 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,25(4):463-478
The purpose of this article is to discuss cluster expansions in dense quantum systems, as well as their interconnection with
exchange cycles. We show in general how the Ursell operators of order l≥ 3 contribute to an exponential which corresponds to a mean-field energy involving the second operator U2, instead of the potential itself as usual - in other words, the mean-field correction is expressed in terms of a modification
of a local Boltzmann equilibrium. In a first part, we consider classical statistical mechanics and recall the relation between
the reducible part of the classical cluster integrals and the mean-field; we introduce an alternative method to obtain the
linear density contribution to the mean-field, which is based on the notion of tree-diagrams and provides a preview of the
subsequent quantum calculations. We then proceed to study quantum particles with Boltzmann statistics (distinguishable particles)
and show that each Ursell operator Un with n≥ 3 contains a “tree-reducible part”, which groups naturally with U2 through a linear chain of binary interactions; this part contributes to the associated mean-field experienced by particles
in the fluid. The irreducible part, on the other hand, corresponds to the effects associated with three (or more) particles
interacting all together at the same time. We then show that the same algebra holds in the case of Fermi or Bose particles,
and discuss physically the role of the exchange cycles, combined with interactions. Bose condensed systems are not considered
at this stage. The similarities and differences between Boltzmann and quantum statistics are illustrated by this approach,
in contrast with field theoretical or Green's functions methods, which do not allow a separate study of the role of quantum
statistics and dynamics.
Received 18 October 2001 相似文献
19.
M. Wilkinson B. Mehlig K. Gustavsson E. Werner 《The European Physical Journal B - Condensed Matter and Complex Systems》2012,85(1):18
It might be expected that trajectories of a dynamical system which has no negative
Lyapunov exponent (implying exponential growth of small separations) will not cluster
together. However, clustering can occur such that the density
ρ(Δx) of trajectories within distance
|Δx| of a reference trajectory has a power-law divergence, so that
ρ(Δx) ∼ |Δx| −β
when |Δx| is sufficiently small, for some
0 < β < 1. We demonstrate this effect using a random map in
one dimension. We find no evidence for this effect in the chaotic logistic map, and argue
that the effect is harder to observe in deterministic maps. 相似文献
20.
G. Giardina V. A. Drozdov D. O. Eremenko S. Yu. Platonov O. V. Fotina O. A. Yuminov 《Bulletin of the Russian Academy of Sciences: Physics》2010,74(6):772-776
A large set of experimental observables for the 232Th(α, xnf)reaction was analyzed theoretically within the dynamic-statistical approach, making it possible to interconsistently consider
the manifestation of nuclear viscosity, the double-humped structure of the fission barrier, and the phenomenon of shell effect
damping with temperature. Analyses were performed for the energy dependence of the finite lifetime effect in the investigated
reaction, obtained using the crystal blocking technique; the fission probability isotopes produced in this reaction during
the development of a neutron emission cascade; and the anisotropy of angular distributions of fission fragments. It is shown
that this analysis allows us to obtain information regarding nuclear viscosity and its energy dependence at relatively low
excitation energies (<30 MeV). 相似文献