共查询到20条相似文献,搜索用时 15 毫秒
1.
E. Bogomolny U. Gerland C. Schmit 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,19(1):121-132
We propose a plasma model for spectral statistics displaying level repulsion without long-range spectral rigidity, i.e. statistics intermediate between random matrix and Poisson statistics similar to the ones found numerically at the critical
point of the Anderson metal-insulator transition in disordered systems and in certain dynamical systems. The model emerges
from Dysons one-dimensional gas corresponding to the eigenvalue distribution of the classical random matrix ensembles by restricting
the logarithmic pair interaction to a finite number k of nearest neighbors. We calculate analytically the spacing distributions and the two-level statistics. In particular we
show that the number variance has the asymptotic form Σ2(L) ∼χL for large L and the nearest-neighbor distribution decreases exponentially when s→∞, P(s) ∼ exp(- Λs) with Λ = 1/χ = kβ + 1, where β is the inverse temperature of the gas (β = 1, 2 and 4 for the orthogonal, unitary and symplectic symmetry class
respectively). In the simplest case of k = β = 1, the model leads to the so-called Semi-Poisson statistics characterized by particular simple correlation functions
e.g.
P(s) = 4s exp(- 2s). Furthermore we investigate the spectral statistics of several pseudointegrable quantum billiards numerically and compare
them to the Semi-Poisson statistics.
Received 13 September 2000 相似文献
2.
Potts Models in the Continuum. Uniqueness and Exponential Decay in the Restricted Ensembles 总被引:1,自引:1,他引:0
Anna De Masi Immacolata Merola Errico Presutti Yvon Vignaud 《Journal of statistical physics》2008,133(2):281-345
In this paper we study a continuum version of the Potts model, where particles are points in ℝ
d
, d≥2, with a spin which may take S≥3 possible values. Particles with different spins repel each other via a Kac pair potential of range γ
−1, γ>0. In mean field, for any inverse temperature β there is a value of the chemical potential λ
β
at which S+1 distinct phases coexist. We introduce a restricted ensemble for each mean field pure phase which is defined so that the
empirical particles densities are close to the mean field values. Then, in the spirit of the Dobrushin-Shlosman theory (Dobrushin
and Shlosman in J. Stat. Phys. 46(5–6):983–1014, 1987), we prove that while the Dobrushin high-temperatures uniqueness condition does not hold, yet a finite size condition is
verified for γ small enough which implies uniqueness and exponential decay of correlations. In a second paper (De Masi et al. in Coexistence
of ordered and disordered phases in Potts models in the continuum, 2008), we will use such a result to implement the Pirogov-Sinai scheme proving coexistence of S+1 extremal DLR measures. 相似文献
3.
Quantum Gravitational Corrections to the Real Klein-Gordon Field in the Presence of a Minimal Length
S. K. Moayedi M. R. Setare H. Moayeri 《International Journal of Theoretical Physics》2010,49(9):2080-2088
The (D+1)-dimensional (β,β′)-two-parameter Lorentz-covariant deformed algebra introduced by Quesne and Tkachuk (J. Phys., A Math. Gen. 39, 10909, 2006), leads to a nonzero minimal uncertainty in position (minimal length). The Klein-Gordon equation in a (3+1)-dimensional space-time
described by Quesne-Tkachuk Lorentz-covariant deformed algebra is studied in the case where β′=2β up to first order over deformation parameter β. It is shown that the modified Klein-Gordon equation which contains fourth-order derivative of the wave function describes
two massive particles with different masses. We have shown that physically acceptable mass states can only exist for
b < \frac18m2c2\beta<\frac{1}{8m^{2}c^{2}} which leads to an isotropic minimal length in the interval 10−17 m<(ΔX
i
)0<10−15 m. Finally, we have shown that the above estimation of minimal length is in good agreement with the results obtained in previous
investigations. 相似文献
4.
5.
Blinking of single molecules and nanocrystals is modeled as a two-state renewal process with on (fluorescent) and off (non-fluorescent)
states. The on and off-times may have power-law or exponential distributions. A fractional generalization of the exponential
function is used to develop a unified treatment of the blinking statistics for both types of distributions. In the framework
of the two-state model, an equation for the probability density p(t
on|t) of the total on-time is derived. As applied to power-law blinking, the equation contains derivatives of fractional orders
α and β equal to the exponents of the on and off-time power-law distributions, respectively. In the limit case of α = β =
1, the distributions become exponential and the fractional differential equation reduces to an integer order differential
equation. Solutions to these equations are expressed in terms of fractional stable distributions. The Poisson transform of
p(t
on|t) is the photon number distribution that determines the photon counting statistics. It is shown that the long-time asymptotic
behavior of Mandel’s Q parameter follows a power law: M(t) ∝ t
γ
. The function γ(α, β) is defined on the (α, β) plane. An analysis of the relative variance of the total on-time shows that it decays only
when α = β = 1 or α < β. Otherwise, relative fluctuations either exhibit asymptotic power-law growth or approach a constant
level. Analytical calculations are in good agreement with the results of Monte Carlo simulations. 相似文献
6.
Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space
should in most circumstances be the same as in the random energy model. We review some rigorous results confirming the validity
of this conjecture. In the context of the SK models, we analyse the limits of the validity of the conjecture for energy levels
growing with the volume of the system. In the case of the Generalised Random energy model, we give a complete analysis for
the behaviour of the local energy statistics at all energy scales. In particular, we show that, in this case, the REM conjecture
holds exactly up to energies E
N
< β
c
N, where β
c
is the critical temperature. We also explain the more complex behaviour that sets in at higher energies.
Research supported in part by the DFG in the Dutch-German Bilateral Research Group “Mathematics of Random Spatial Models from
Physics and Biology” and by the European Science Foundation in the Programme RDSES. 相似文献
7.
M. Loulidi 《Journal of statistical physics》2008,132(1):109-127
A one-dimensional disordered particle hopping rate asymmetric exclusion process (ASEP) with open boundaries and a random sequential
dynamics is studied analytically. Combining the exact results of the steady states in the pure case with a perturbative mean
field-like approach the broken particle-hole symmetry is highlighted and the phase diagram is studied in the parameter space
(α,β), where α and β represent respectively the injection rate and the extraction rate of particles. The model displays, as in the pure case,
high-density, low-density and maximum-current phases. All critical lines are determined analytically showing that the high-density
low-density first order phase transition occurs at α≠β. We show that the maximum-current phase extends its stability region as the disorder is increased and the usual
-decay of the density profile in this phase is universal. Assuming that some exact results for the disordered model on a ring
hold for a system with open boundaries, we derive some analytical results for platoon phase transition within the low-density
phase and we give an analytical expression of its corresponding critical injection rate α
*. As it was observed numerically (Bengrine et al. J. Phys. A: Math. Gen. 32:2527, [1999]), we show that the quenched disorder induces a cusp in the current-density relation at maximum flow in a certain region
of parameter space and determine the analytical expression of its slope. The results of numerical simulations we develop agree
with the analytical ones.
Regular associate of ICTP. 相似文献
8.
Robert V. Harlander Luminita Mihaila Matthias Steinhauser 《The European Physical Journal C - Particles and Fields》2009,63(3):383-390
A number of
[` DR]\overline {\mbox {\textsc{D}R}}
renormalization constants in softly broken SUSY- QCD are evaluated to three-loop level: the wave function renormalization constants for quarks, squarks, gluons, gluinos, ghosts,
and ε-scalars, and the renormalization constants for the quark and gluino mass as well as for all cubic vertices. The latter allow
us to derive the corresponding β functions through three loops, all of which we find to be identical to the expression for the gauge β function obtained by Jack et al. (Phys. Lett. B 386:138, 1996, ) (see also Pickering et al. in Phys. Lett. B 510, 347, 2001, ). This explicitly demonstrates the consistency of DRED with SUSY and gauge invariance, an important pre-requisite for precision calculations in supersymmetric theories. 相似文献
9.
Peter Nyman 《International Journal of Theoretical Physics》2010,49(1):1-9
In this paper we continue to study so-called “inverse Born’s rule problem”: to construct a representation of probabilistic
data of any origin by a complex probability amplitude which matches Born’s rule. The corresponding algorithm—quantum-like
representation algorithm (QLRA)—was recently proposed by A. Khrennikov (Found. Phys. 35(10):1655–1693, 2005; Physica E 29:226–236, 2005; Dokl. Akad. Nauk 404(1):33–36, 2005; J. Math. Phys. 46(6):062111–062124, 2005; Europhys. Lett. 69(5):678–684, 2005). Formally QLRA depends on the order of conditioning. For two observables (of any origin, e.g., physical or biological) a and b, b|a- and a|b conditional probabilities produce two representations, say in Hilbert spaces H
b|a
and H
a|b
. In this paper we prove that under “natural assumptions” (which hold, e.g., for quantum observables represented by operators
with nondegenerate spectra) these two representations are unitary equivalent. This result proves the consistency of QLRA. 相似文献
10.
We study the local semicircle law for Gaussian β-ensembles at the edge of the spectrum. We prove that at the almost optimal level of n-2/3+e{n^{-2/3+\epsilon}}, the local semicircle law holds for all β ≥ 1 at the edge. The proof of the main theorem relies on the calculation of the moments of the tridiagonal model of Gaussian
β-ensembles up to the p
n
-moment, where pn = O(n2/3-e){p_n = O(n^{2/3-\epsilon})}. The result is analogous to the result of Sinai and Soshnikov (Funct Anal Appl 32(2), 1998) for Wigner matrices, but the combinatorics involved in the calculations are different. 相似文献
11.
In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov
(Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic,
Norwell, 2004; Fuzzy Sets Syst. 155:4–17, 2005; Biosystems 84:225–241, 2006; Found. Phys. 35(10):1655–1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105–117, 2009), it was pointed out that statistics collected in such the experiments have “quantum-like” properties, which can not be explained
in classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process
in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical
frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33–59, 1999). 相似文献
12.
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
13.
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
14.
I.M. Sokolov 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,22(3):369-373
We consider two-particle dispersion in a velocity field, where the relative two-point velocity scales according to v
2(r) ∝r
α and the corresponding correlation time scales as τ(r) ∝r
β, and fix α = 2/3, as typical for turbulent flows. We show that two generic types of dispersion behavior arize: For α/2 +
β < 1 the correlations in relative velocities decouple and the diffusion approximation holds. In the opposite case, α/2 +
β > 1, the relative motion is strongly correlated. The case of Kolmogorov flows corresponds to a marginal, nongeneric situation.
In this case, depending on the particular parameters of the flow, the dispersion behavior can be rather diffusive or rather
ballistic.
Received 13 March 2001 相似文献
15.
P. Deift D. Gioev T. Kriecherbauer M. Vanlessen 《Journal of statistical physics》2007,129(5-6):949-1053
We give a proof of the Universality Conjecture for orthogonal (β=1) and symplectic (β=4) random matrix ensembles of Laguerre-type
in the bulk of the spectrum as well as at the hard and soft spectral edges. Our results are stated precisely in the Introduction
(Theorems 1.1, 1.4, 1.6 and Corollaries 1.2, 1.5, 1.7). They concern the appropriately rescaled kernels K
n, β, correlation and cluster functions, gap probabilities and the distributions of the largest and smallest eigenvalues. Corresponding
results for unitary (β=2) Laguerre-type ensembles have been proved by the fourth author in Ref. 23. The varying weight case
at the hard spectral edge was analyzed in Ref. 13 for β=2: In this paper we do not consider varying weights.
Our proof follows closely the work of the first two authors who showed in Refs. 7, 8 analogous results for Hermite-type ensembles.
As in Refs. 7, 8 we use the version of the orthogonal polynomial method presented in Refs. 22, 25, to analyze the local eigenvalue
statistics. The necessary asymptotic information on the Laguerre-type orthogonal polynomials is taken from Ref. 23. 相似文献
16.
We consider the continuous time version of the Random Walk Pinning Model (RWPM), studied in (Berger and Toninelli (Electron. J. Probab., to appear) and Birkner and Sun (Ann. Inst. Henri Poincaré
Probab. Stat. 46:414–441, 2010; ). Given a fixed realization of a random walk Y on ℤ
d
with jump rate ρ (that plays the role of the random medium), we modify the law of a random walk X on ℤ
d
with jump rate 1 by reweighting the paths, giving an energy reward proportional to the intersection time Lt(X,Y)=ò0t 1Xs=Ys dsL_{t}(X,Y)=\int_{0}^{t} \mathbf {1}_{X_{s}=Y_{s}}\,\mathrm {d}s: the weight of the path under the new measure is exp (βL
t
(X,Y)), β∈ℝ. As β increases, the system exhibits a delocalization/localization transition: there is a critical value β
c
, such that if β>β
c
the two walks stick together for almost-all Y realizations. A natural question is that of disorder relevance, that is whether the quenched and annealed systems have the same behavior. In this paper we investigate how the disorder modifies the shape of the free energy curve:
(1) We prove that, in dimension d≥3, the presence of disorder makes the phase transition at least of second order. This, in dimension d≥4, contrasts with the fact that the phase transition of the annealed system is of first order. (2) In any dimension, we prove
that disorder modifies the low temperature asymptotic of the free energy. 相似文献
17.
A Fredholm Determinant Representation in ASEP 总被引:3,自引:2,他引:1
In previous work (Tracy and Widom in Commun. Math. Phys. 279:815–844, 2008) the authors found integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice
ℤ. The dynamics are uniquely determined once the initial state is specified. In this note we restrict our attention to the
case of step initial condition with particles at the positive integers ℤ+ and consider the distribution function for the mth particle from the left. In Tracy and Widom (Commun. Math. Phys. 279:815–844, 2008) an infinite series of multiple integrals was derived for the distribution. In this note we show that the series can be summed
to give a single integral whose integrand involves a Fredholm determinant. We use this determinant representation to derive
(non-rigorously, at this writing) a scaling limit. 相似文献
18.
Helge Krüger 《Communications in Mathematical Physics》2010,295(3):853-875
I study the Lyapunov exponent and the integrated density of states for general Jacobi operators. The main result is that questions
about these can be reduced to questions about ergodic Jacobi operators. I use this to show that for finite gap Jacobi operators,
regularity implies that they are in the Cesàro–Nevai class, proving a conjecture of Barry Simon. Furthermore, I use this to
study Jacobi operators with coefficients a(n) = 1 and b(n) = f(n
ρ
(mod 1)) for ρ > 0 not an integer. 相似文献
19.
O. S. Kirsebom H. O. U. Fynbo A. Jokinen M. Madurga K. Riisager A. Saastamoinen O. Tengblad J. Äystö 《The European Physical Journal A - Hadrons and Nuclei》2011,47(10):130
We report on a new measurement of the β-delayed proton spectrum of 23Al. Higher statistics compared to previous measurements allow us to identify new proton lines in the energy range 1–2 MeV.
A statistical analysis of the observed β strength shows that the B (GT) values are fully consistent with having a Porter-Thomas distribution. This is indicative of chaotic behaviour and implies
that only the average β strength carries physical meaning. 相似文献
20.
Haisheng Li 《Communications in Mathematical Physics》2011,308(3):703-741
We develop a theory of f{\phi} -coordinated (quasi-) modules for a general nonlocal vertex algebra where f{\phi} is what we call an associate of the one-dimensional additive formal group. By specializing f{\phi} to a particular associate, we obtain a new construction of weak quantum vertex algebras in the sense of Li (Selecta Mathematica
(New Series) 11:349–397, 2005). As an application, we associate weak quantum vertex algebras to quantum affine algebras, and we also associate quantum
vertex algebras and f{\phi} -coordinated modules to a certain quantum βγ-system explicitly. 相似文献