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1.
A. Faggionato D. Gabrielli M. Ribezzi Crivellari 《Journal of statistical physics》2009,137(2):259-304
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states (x,σ)∈Ω×Γ, Ω being a region in ℝ
d
or the d-dimensional torus, Γ being a finite set. The continuous variable x follows a piecewise deterministic dynamics, the discrete variable σ evolves by a stochastic jump dynamics and the two resulting evolutions are fully-coupled. We study stationarity, reversibility
and time-reversal symmetries of the process. Increasing the frequency of the σ-jumps, the system behaves asymptotically as deterministic and we investigate the structure of its fluctuations (i.e. deviations
from the asymptotic behavior), recovering in a non Markovian frame results obtained by Bertini et al. (Phys. Rev. Lett. 87(4):040601,
2001; J. Stat. Phys. 107(3–4):635–675, 2002; J. Stat. Mech. P07014, 2007; Preprint available online at , 2008), in the context of Markovian stochastic interacting particle systems. Finally, we discuss a Gallavotti–Cohen-type symmetry
relation with involution map different from time-reversal. 相似文献
2.
We examine the entropy of stationary nonequilibrium measures of boundary driven symmetric simple exclusion processes. In contrast
with the Gibbs–Shannon entropy (Bahadoran in J. Stat. Phys. 126(4–5):1069–1082, 2007; Derrida et al. in J. Stat. Phys. 126(4–5):1083–1108, 2007), the entropy of nonequilibrium stationary states differs from the entropy of local equilibrium states. 相似文献
3.
We slightly extend the fluctuation theorem obtained in (Lebowitz and Spohn in J. Stat. Phys. 95:333–365, 1999) for sums of generators, considering continuous-time Markov chains on a finite state space whose underlying graph has multiple
edges and no loop. This extended frame is suited when analyzing chemical systems. As simple corollary we derive by a different
method the fluctuation theorem of D. Andrieux and P. Gaspard for the fluxes along the chords associated to a fundamental set
of oriented cycles (Andrieux and Gaspard in J. Stat. Phys. 127:107–131, 2007). 相似文献
4.
Gérard?Le?Ca?r 《Journal of statistical physics》2010,140(4):728-751
A constrained diffusive random walk of n steps in ℝ
d
and a random flight in ℝ
d
, which are equivalent, were investigated independently in recent papers (J. Stat. Phys. 127:813, 2007; J. Theor. Probab. 20:769, 2007, and J. Stat. Phys. 131:1039, 2008). The n steps of the walk are independent and identically distributed random vectors of exponential length and uniform orientation.
Conditioned on the sum of their lengths being equal to a given value l, closed-form expressions for the distribution of the endpoint of the walk were obtained altogether for any n for d=1,2,4. Uniform distributions of the endpoint inside a ball of radius l were evidenced for a walk of three steps in 2D and of two steps in 4D. 相似文献
5.
Mykhaylo Tyomkyn 《Journal of statistical physics》2012,148(6):1072-1075
We analyze the abelian sandpile model on ℤ d for the starting configuration of n particles in the origin and 2d−2 particles otherwise. We give a new short proof of the theorem of Fey, Levine and Peres (J. Stat. Phys. 198:143–159, 2010) that the radius of the toppled cluster of this configuration is O(n 1/d ). 相似文献
6.
This short note complements the recent paper of the authors (Alonso, Gamba in J. Stat. Phys. 137(5–6):1147–1165, 2009). We revisit the results on propagation of regularity and stability using L
p
estimates for the gain and loss collision operators which had the exponent range misstated for the loss operator. We show
here the correct range of exponents. We require a Lebesgue’s exponent α>1 in the angular part of the collision kernel in order to obtain finiteness in some constants involved in the regularity
and stability estimates. As a consequence the L
p
regularity associated to the Cauchy problem of the space inhomogeneous Boltzmann equation holds for a finite range of p≥1 explicitly determined. 相似文献
7.
We analyze the large-time behavior of various kinetic models for the redistribution of wealth in simple market economies introduced
in the pertinent literature in recent years. As specific examples, we study models with fixed saving propensity introduced
by Chakraborti and Chakrabarti (Eur. Phys. J. B 17:167–170, 2000), as well as models involving both exchange between agents and speculative trading as considered by Cordier et al. (J. Stat.
Phys. 120:253–277, 2005) We derive a sufficient criterion under which a unique non-trivial stationary state exists, and provide criteria under which
these steady states do or do not possess a Pareto tail. In particular, we prove the absence of Pareto tails in pointwise conservative
models, like the one in (Eur. Phys. J. B 17:167–170, 2000), while models with speculative trades introduced in (J. Stat. Phys. 120:253–277, 2005) develop fat tails if the market is “risky enough”. The results are derived by a Fourier-based technique first developed
for the Maxwell-Boltzmann equation (Gabetta et al. in J. Stat. Phys. 81:901–934, 1995; Bisi et al. in J. Stat. Phys. 118(1–2):301–331, 2005; Pareschi and Toscani in J. Stat. Phys. 124(2–4):747–779, 2006) and from a recursive relation which allows to calculate arbitrary moments of the stationary state. 相似文献
8.
Martin Gaume 《Mathematical Physics, Analysis and Geometry》2010,13(3):205-217
In this paper, we consider a class of two-particle tight-binding Hamiltonians, describing pairs of interacting quantum particles
on the lattice ℤ
d
, d ≥ 1, subject to a common external potential V(x) which we assume quasi-periodic and depending on auxiliary parameters. Such parametric families of ergodic deterministic
potentials (“grands ensembles”) have been introduced earlier in Chulaevsky (2007), in the framework of single-particle lattice systems, where it was proved that a non-uniform analog of the Wegner bound
holds true for a class of quasi-periodic grands ensembles. Using the approach proposed in Chulaevsky and Suhov (Commun Math
Phys 283(2):479–489, 2008), we establish volume-dependent Wegner-type bounds for a class of quasi-periodic two-particle lattice systems with a non-random
short-range interaction. 相似文献
9.
We apply a PDE-based method to deduce the critical time and the size of the giant component of the “triangle percolation”
on the Erdős-Rényi random graph process investigated by Derényi, Palla and Vicsek in (Phys. Rev. Lett. 94:160202, [2005]; J. Stat. Phys. 128:219–227, [2007]). 相似文献
10.
We give a new proof of universality properties in the bulk of spectrum of the hermitian matrix models, assuming that the potential
that determines the model is globally C
2 and locally C
3 function (see Theorem 3.1). The proof as our previous proof in (Pastur and Shcherbina in J. Stat. Phys. 86:109–147, 1997) is based on the orthogonal polynomial techniques but does not use asymptotics of orthogonal polynomials. Rather, we obtain
the sin -kernel as a unique solution of a certain non-linear integro-differential equation that follows from the determinant
formulas for the correlation functions of the model. We also give a simplified and strengthened version of paper (Boutet de
Monvel, et al. in J. Stat. Phys. 79:585–611, 1995) on the existence and properties of the limiting Normalized Counting Measure of eigenvalues. We use these results in the
proof of universality and we believe that they are of independent interest. 相似文献
11.
Dmitry Panchenko 《Journal of statistical physics》2008,130(5):831-842
In Talagrand (J. Stat. Phys. 126(4–5):837–894, 2007) the large deviations limit
for the moments of the partition function Z
N
in the Sherrington-Kirkpatrick model (Sherrington and Kirkpatrick in Phys. Rev. Lett. 35:1792–1796, 1972) was computed for all real a≥0. For a≥1 this result extends the classical physicist’s replica method that corresponds to integer values of a. We give a new proof for a≥1 in the case of the pure p-spin SK model that provides a strong exponential control of the overlap.
This work is partially supported by NSF grant. 相似文献
12.
For a quantum spin chain or 1D fermionic system, we prove that the Drude weight
D verifies the universal Luttinger liquid relation vs2=D/kv_{s}^{2}=D/\kappa, where κ is the susceptibility and v
s
is the Fermi velocity. This result is proved by rigorous Renormalization Group methods and is true for any weakly interacting system, regardless
its integrability. This paper, combined with Benfatto and Mastropietro (in J. Stat. Phys. 138, 1084–1108, 2010), completes the proof of the Luttinger liquid conjecture for such systems. 相似文献
13.
Domingos H. U. Marchetti William R. P. Conti Leonardo F. Guidi 《Journal of statistical physics》2008,132(5):811-838
A continuous version of the hierarchical spherical model at dimension d=4 is investigated. Two limit distributions of the block spin variable X
γ
, normalized with exponents γ=d+2 and γ=d at and above the critical temperature, are established. These results are proven by solving certain evolution equations corresponding
to the renormalization group (RG) transformation of the O(N) hierarchical spin model of block size L
d
in the limit L
↓1 and N→∞. Starting far away from the stationary Gaussian fixed point the trajectories of these dynamical system pass through two
different regimes with distinguishable crossover behavior. An interpretation of this trajectories is given by the geometric
theory of functions which describe precisely the motion of the Lee–Yang zeroes. The large-N limit of RG transformation with L
d
fixed equal to 2, at the criticality, has recently been investigated in both weak and strong (coupling) regimes by Watanabe
(J. Stat. Phys. 115:1669–1713, 2004) . Although our analysis deals only with N=∞ case, it complements various aspects of that work.
D.H.U. Marchetti partially supported by CNPq and FAPESP.
W.R.P. Conti supported by FAPESP under grant 05/57416-8. 相似文献
14.
We show how to extract Cardy’s Formula for a general class of domains given the requisite interior analyticity statement.
This is accomplished by a careful study of the interplay between discretization schemes and extraction of limiting boundary
values. Of particular importance to the companion work (Binder et al. in J. Stat. Phys., 2010) we establish these results for slit domains and for the critical percolation models introduced in Chayes and Lei (Rev. Math.
Phys. 19:511–565, 2007). 相似文献
15.
Gast?o?A.?Braga Leandro?M.?Cioletti Rémy?Sanchis 《Journal of statistical physics》2009,136(1):195-198
In this short note we present some explicit conditions under which the Theorem of Braga et al. (J. Stat. Phys. 129:587–591,
2007) can be extended to spin-spin correlation functions of mixed short-range/long-range ferromagnetic vector spin models in the
disordered phase. 相似文献
16.
A. Romannikov 《Foundations of Physics》2011,41(8):1331-1337
A relation between physical consequences of the so-called Ehrenfest’s Paradox and the radial electric field E
r
(r) in the classical quasi-neutral tokamak plasma is shown. Basic author’s approach to the relativistic nature of the tokamak
E
r
(r) has been described in Romannikov (J. Exp. Theor. Phys. 108:340–348, 2009). The experiment which can resolve the Ehrenfest’s Paradox is presented. 相似文献
17.
Johannes Blümlein Dieter Robaschik Bodo Geyer 《The European Physical Journal C - Particles and Fields》2009,61(2):279-298
The quantum field theoretic treatment of inclusive deep-inelastic diffractive scattering given in a previous paper (Blümlein
et al. in Nucl. Phys. B 755:112–136, 2006) is discussed in detail using an equivalent formulation with the aim to derive a representation suitable for data analysis.
We consider the off-cone twist-2 light-cone operators to derive the target-mass and finite t corrections to diffractive deep-inelastic scattering and deep-inelastic scattering. The corrections turn out to be at most
proportional to x|t|/Q
2, xM
2/Q
2, x=x
BJ or x
ℙ, which suggests an expansion in these parameters. Their contribution varies in size considering diffractive scattering or
meson-exchange processes. Relations between different kinematic amplitudes which are determined by one and the same diffractive
GPD or its moments are derived. In the limit t,M
2→0 one obtains the results of (Blümlein and Robaschik in Phys. Lett. B 517:222, 2001) and (Blümlein and Robaschik in Phys. Rev. D 65:096002, 2002). 相似文献
18.
Yaacov Kopeliovich 《Letters in Mathematical Physics》2010,94(3):313-333
Let X be a general cyclic cover of
\mathbbCP1{\mathbb{CP}^{1}} ramified at m points, λ1... λ
m
. we define a class of non-positive divisors on X of degree g −1 supported in the pre images of the branch points on X, such that the Riemann theta function does not vanish on their image in J(X). We generalize the results of Bershadsky and Radul (Commun Math Phys 116:689–700, 1988), Nakayashiki (Publ Res Inst Math Sci 33(6):987–1015, 1997) and Enolskii and Grava (Lett Math Phys 76(2–3):187–214, 2006) and prove that up to a certain determinant of the non-standard periods of X, the value of the Riemann theta function at these divisors raised to a high enough power is a polynomial in the branch point
of the curve X. Our approach is based on a refinement of Accola’s results for 3 cyclic sheeted cover (Accola, in Trans Am Math Soc 283:423–449,
1984) and a generalization of Nakayashiki’s approach explained in Nakayashiki (Publ Res Inst Math Sci 33(6):987–1015, 1997) for general cyclic covers. 相似文献
19.
Federico Bassetti Lucia Ladelli Giuseppe Toscani 《Journal of statistical physics》2011,142(4):686-709
We introduce a class of Kac-like kinetic equations on the real line, with general random collisional rules which, in some
special cases, identify models for granular gases with a background heat bath (Carrillo et al. in Discrete Contin. Dyn. Syst.
24(1):59–81, 2009), and models for wealth redistribution in an agent-based market (Bisi et al. in Commun. Math. Sci. 7:901–916, 2009). Conditions on these collisional rules which guarantee both the existence and uniqueness of equilibrium profiles and their
main properties are found. The characterization of these stationary states is of independent interest, since we show that
they are stationary solutions of different evolution problems, both in the kinetic theory of rarefied gases (Cercignani et al.
in J. Stat. Phys. 105:337–352, 2001; Villani in J. Stat. Phys. 124:781–822, 2006) and in the econophysical context (Bisi et al. in Commun. Math. Sci. 7:901–916, 2009). 相似文献
20.
We propose a new method for the problems of computing free energy and surface pressure for various statistical mechanics models
on a lattice ℤ
d
. Our method is based on representing the free energy and surface pressure in terms of certain marginal probabilities in a
suitably modified sublattice of ℤ
d
. Then recent deterministic algorithms for computing marginal probabilities are used to obtain numerical estimates of the
quantities of interest. The method works under the assumption of Strong Spatial Mixing (SSP), which is a form of a correlation
decay.
We illustrate our method on the hard-core and monomer-dimer models, on which we improve several earlier estimates. For example
we show that the exponential of the monomer-dimer coverings of ℤ3 belongs to the interval [0.78595,0.78599], improving best previously known estimate of [0.7850,0.7862] obtained in (Friedland
and Peled in Adv. Appl. Math. 34:486–522, 2005; Friedland et al. in J. Stat. Phys., 2009). Moreover, we show that given a target additive error ε>0, the computational effort of our method for these two models is (1/ε)
O(1)
both for the free energy and surface pressure values. In contrast, prior methods, such as the transfer matrix method, require
exp ((1/ε)
O(1)) computation effort. 相似文献