共查询到20条相似文献,搜索用时 31 毫秒
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The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interestingly rich phase structure. In this setting, we derive moderate deviations principles for the random total magnetization S n , which is the partial sum of (dependent) spins. A typical result is that under appropriate assumptions on the distribution of the local external fields there exist a real number m, a positive real number ??, and a positive integer k such that (S n ?nm)/n ?? satisfies a moderate deviations principle with speed n 1?2k(1???) and rate function ??x 2k /(2k)!, where 1?1/(2(2k?1))<??<1. 相似文献
3.
The exact solutions of the rate equations of the n-polymer stochastic aggregation involving two types of clusters, active and passive for the kernel \dprnk=1s(ik)(s(ik)=ik) and \dsumnk=1s(ik)(s(ik)=ik), are obtained. The large-mass behaviours of the final mass distribution of the active and passive clusters have scaling-like forms, although the models exhibit different properties. Respectively, they have different decay exponents γ=\dfrac{2n+1}{2(n-1)} and γ=q+\dfrac{2n+1}{2(n-1)} for \dprnk=1}s(ik)(s(ik)=ik) and γ=\dfrac 3{2(n-1)} and γ=q+\dfrac 3{2(n-1)} for \dsumnk=1}s(ik)(s(ik)=ik), which include exponents of two-polymer stochastic aggregation. We also find that gelation is suppressed for kernel \dprnk=1s(ik)(s(ik)=ik) which is different from the deterministic aggregation. 相似文献
4.
W.K. Theumann 《Physica A》1975,80(1):25-45
The order-parameter correlation function is calculated in the critical region of momentum space in terms of a second-moment correlation length ξ1 by means of perturbation expansion to order 1/n, for an n-vector system with short-range interactions, in zero field above Tc, for 2 < d < 4. The scaling function of the dependence is obtained in closed form with a precisely identified cutoff-dependent factor which is the amplitude of the correlation-length dependence of the susceptibility. Both the exponents and the coefficients of the expansion for fixed q as t = (T?Tc)/Tc → 0 are given explicitly and the former are shown to be in accordance with the operator product expansion. The coefficients of order 1/n in the terms associated with a tk(1?α) dependence of the energy density, for integer k ≥ 1, are expected to be explicitly cutoff-dependent and this is verified by the detailed calculations for k = 1. The behaviour for fixed t and q → 0 is shown to be markedly different from the Ornstein-Zernike approximation. Detailed comparison is provided with the scaling function of the t dependence of the correlations appearing in parallel work. 相似文献
5.
The afterglow of a discharge in helium with a small admixture of hydrogen is studied spectroscopically (p=40 Torr, [e]≤1011 cm?3). The time-resolved measurements of intensities of the first four lines of the Balmer series are performed. The concentrations of metastable helium atoms and molecules are evaluated from the relative intensity of the absorption lines. The ratios of excitation transfer rates from atoms He(2 3 S 1) k 1(n) and molecules of helium He2(a 2sσ 3Σ u + ) k 2(n) to atomic hydrogen H*(n) are measured to be k 1(n=3)/k 2(n=3)=0.04±0.02 and k 1(n=4)/k 2(n=4)=0.01±0.02. The ratios of excitation rate constants k 2(n) corresponding to different states H(n) are measured to be k 1(n=4)/k 2(n=3)=0.023±0.01; k 1(n=5)/k 2(n=3)≤0.013; and k 1(n=6)/k 2(n=3)≤0.007. 相似文献
6.
Xian Gao 《Physics letters. [Part B]》2011,702(1):12-15
We investigate the effects of the presence of relic classical superhorizon inhomogeneities during inflation. This superhorizon inhomogeneity appears as a gradient locally and picks out a preferred direction. Quantum fluctuations on this slightly inhomogeneous background are generally statistical anisotropic. We find a quadrupole modification to the ordinary isotropic spectrum. Moreover, this deviation from statistical isotropy is scale-dependent, with a ∼−1/k2 factor. This result implies that the statistical anisotropy mainly appears on large scales, while the spectrum on small scales remains highly isotropic. Moreover, due to this −1/k2 factor, the power on large scales is suppressed. Thus, our model can simultaneously explain the observed anisotropic alignments of the low-? multipoles and their low power. 相似文献
7.
P. Collet J. -P. Eckmann V. Glaser A. Martin 《Communications in Mathematical Physics》1984,94(3):353-370
We study the iterations of the mapping $$\mathcal{N}[F(s)] = \frac{{(F(s))^2 - (F(0))^2 }}{s} + (F(0))^2 ,$$ with the constraintsF(1)=1,F(s)=∑a nsn,a n≧0, and find that, except ifF(s)≡s,N[F(s)] approaches either 0 or 1 for |s|<1 ask→∞. 相似文献
8.
Statistics of fluctuations in a spatially distributed system describing the interaction of nonequilibrium phase transitions is studied. It is shown that for a certain value of the intensity of external white noise acting on phase transitions, the time and spatial spectra of fluctuations exhibit power dependences S(f) ~ f ?α and S(k) ~ k ?γ. The dependence of exponents α and γ on the diffusion coefficient determining the spatial interaction of fluctuations is determined. Extremal low-frequency fluctuations are singled out and the distribution functions of their duration (P(τ) ~ τ?β) and size (P(s) ~ s?ν)) are constructed. It is found that exponent α in the time spectral dependence and exponent β in the duration of fluctuations are connected via the relation α + β = 2. Exponents γ and ν in the spatial spectral dependence and in the size distribution function are connected via an analogous relation (γ + ν = 2). 相似文献
9.
The thermal expansion, spontaneous volume magnetostriction ωs, forced volume magnetostriction and Young's modulus of amorphous Fe-B, Fe-P, Co-B and (Fe-M)77Si10B13 (M = Cr, Mn, Co, Ni) alloys have been measured to make clear the magnetovolume effect in transition metal-metalloid amorphous alloys. The thermal expansion coefficient α, ωs and are dependent on the number of d-electrons per transition metal atom neff calculated based on the charge transfer model. The neff vs. α, ωs and curves are quite similar to the corresponding curves in fcc alloys. The maxima in those curves are, however, found at neff ≈ 8.2 for the amorphous alloys in contrast with neff ≈ 8.7 for the fcc Fe-Ni alloys. On the other hand, Young's modulus measured under the saturation of magnetization is governed by the molar volume, irrespective of neff. The magnetovolume effect in transition metal-metalloid amorphous alloys is discussed in connection with the instability of ferromagnetism of amorphous Fe. 相似文献
10.
The formation and decay kinetics of chain linked triplet radical pairs derived from photo-induced electron transfer reactions in a series of 21 zinc porphyrin-flexible spacer-viologen (ZnP-Sp n -Vi2+) dyads containing 2–138 atoms (n) in the spacer, have been examined by nanosecond laser flash photolysis techniques in an external magnetic field. In non-viscous polar solvents (acetone and CHCl3 plus CH3OH = 1:1 v/v), the effect of the spacer length on the rate constant of forward electron transfer can be described by the equation: k et = k 0 et(n + 6)?1.5, with k 0 et = 3 × 1010 s?1 and 1.2 × 1010 s?1 for electron transfer from the singlet and triplet states of ZnP, respectively. In zero magnetic field, the value of the triplet radical pair recombination rate constant, k r(0) = 0.7 × 106-8 × 106 s?1, is significantly smaller than k et. The dependence of k r(0) on n has an extremum with the maximum near n = 20. In a strong magnetic field (B = 0.21 T), significant retardation of triplet radical pair recombination is observed. In strong magnetic fields the effect of the chain length on triplet radical pair recombination rates is rather small and k r(B) may vary in the range 0.3 × 106-1 × 107 s?1. The phenomena observed are discussed in terms of the interplay of molecular and spin dynamics in the limits of slow and fast encounters, taking into account the exchange-interaction. 相似文献
11.
H. Yavari 《Brazilian Journal of Physics》2018,48(1):31-38
The thermal conductivity of a trapped dipolar Bose condensed gas is calculated as a function of temperature in the framework of linear response theory. The contributions of the interactions between condensed and noncondensed atoms and between noncondensed atoms in the presence of both contact and dipole-dipole interactions are taken into account to the thermal relaxation time, by evaluating the self-energies of the system in the Beliaev approximation. We will show that above the Bose-Einstein condensation temperature (T?>?T BEC ) in the absence of dipole-dipole interaction, the temperature dependence of the thermal conductivity reduces to that of an ideal Bose gas. In a trapped Bose-condensed gas for temperature interval k B T?<<?n 0 g B , E p ?<<?k B T (n 0 is the condensed density and g B is the strength of the contact interaction), the relaxation rates due to dipolar and contact interactions between condensed and noncondensed atoms change as \( {\tau}_{dd12}^{-1}\propto {e}^{-E/{k}_BT} \) and τ c12?∝?T ?5, respectively, and the contact interaction plays the dominant role in the temperature dependence of the thermal conductivity, which leads to the T ?3 behavior of the thermal conductivity. In the low-temperature limit, k B T?<<?n 0 g B , E p ?>>?k B T, since the relaxation rate \( {\tau}_{c12}^{-1} \) is independent of temperature and the relaxation rate due to dipolar interaction goes to zero exponentially, the T 2 temperature behavior for the thermal conductivity comes from the thermal mean velocity of the particles. We will also show that in the high-temperature limit (k B T?>?n 0 g B ) and low momenta, the relaxation rates \( {\tau}_{c12}^{-1} \) and \( {\tau}_{dd12}^{-1} \) change linearly with temperature for both dipolar and contact interactions and the thermal conductivity scales linearly with temperature. 相似文献
12.
F.W. Büsser L. Camilleri L. Di Lella G. Gladding A. Placci B.G. Pope A.M. Smith J.K. Yoh E. Zavattini B.J. Blumenfeld L.M. Lederman R.L. Cool L. Litt S.L. Segler 《Physics letters. [Part B]》1973,46(3):471-476
Invariant cross-sections are presented for the inclusive reaction p + p → πo + anything, Measurements of large transverse momentum πo's (2.5 GeV/c<p⊥<9 GeV/c) were made near 90° at the CERN ISR at five centre-of-mass energies (√s = 23.5, 30.6, 44.8, 52.7 and 62.4 GeV. At large p⊥, the invariant cross-sections are seem to vary with s and p⊥, in good agreement with a fit of the form Ap⊥?nF(p⊥/√s), with n≈8 and F(p⊥/√s)≈exp(?26p⊥/√s). 相似文献
13.
P. Cuff J. Ding O. Louidor E. Lubetzky Y. Peres A. Sly 《Journal of statistical physics》2012,149(3):432-477
We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with q??3 states and show that it undergoes a critical slowdown at an inverse-temperature ?? s (q) strictly lower than the critical ?? c (q) for uniqueness of the thermodynamic limit. The dynamical critical ?? s (q) is the spinodal point marking the onset of metastability. We prove that when ??<?? s (q) the mixing time is asymptotically C(??,q)nlogn and the dynamics exhibits the cutoff phenomena, a sharp transition in mixing, with a window of order n. At ??=?? s (q) the dynamics no longer exhibits cutoff and its mixing obeys a power-law of order n 4/3. For ??>?? s (q) the mixing time is exponentially large in n. Furthermore, as ?????? s with n, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of O(n ?2/3) around ?? s . These results form the first complete analysis of mixing around the critical dynamical temperature??including the critical power law??for a model with a first order phase transition. 相似文献
14.
The two photon exchange contribution to lepton-hadron scattering is considered. Under the assumptions of Lorentz covariance, gauge invariance, unitarity and analyticity, we prove a low momentum transfer theorem for the relevant amplitudes. Fixed energy dispersion relations tell us that their nonanalytic part, in the neighbourhood of t = 0, is given by the contribution of the two photon cut in the t-channel. The t-channel absorptive parts are obtained from unitarity. Their calculation has as input the two amplitudes corresponding to Compton scattering on the hadron with a pole contribution, and the continuum controlled at low t by the electromagnetic polarizabilities. By means of the dispersion integral, one proves the expansion for the continuum contribution, where k1(s) is the only unknown. Explicit expressions are obtained for the pole contribution as M → ∞, where M is the hadron mass, and for the continuum when (?t) <Λ and (?t) < 4m2, where m is the muon mass and Λ is a characteristic parameter of the hadron structure. 相似文献
15.
《Physica A》1996,229(2):244-254
Dynamic behaviours of the 2∞ attractor at the accumulation of period doubling in the logistic map are studied by the sum of the local expansion rates Sn(x1) of nearby orbits. The variance 〈[Sn(x)]2〉 and algebraic exponent ßn(x1) = Sn(x1)/ln(n) exhibits self-similar structures. The critical bifurcations such as intermittency, band merging and crisis-sudden widening of the chaotic attractor are studied in terms of a q-weighted average Λ(q), (− ∞ < q < ∞) of the coarse-grained local expansion rates Λ of nearby orbitals. 相似文献
16.
Sean O’Rourke 《Journal of statistical physics》2010,138(6):1045-1066
We study the fluctuations of eigenvalues from a class of Wigner random matrices that generalize the Gaussian orthogonal ensemble. We begin by considering an n×n matrix from the Gaussian orthogonal ensemble (GOE) or Gaussian symplectic ensemble (GSE) and let x k denote eigenvalue number k. Under the condition that both k and n?k tend to infinity as n→∞, we show that x k is normally distributed in the limit. We also consider the joint limit distribution of eigenvalues $(x_{k_{1}},\ldots,x_{k_{m}})$ from the GOE or GSE where k 1, n?k m and k i+1?k i , 1≤i≤m?1, tend to infinity with n. The result in each case is an m-dimensional normal distribution. Using a recent universality result by Tao and Vu, we extend our results to a class of Wigner real symmetric matrices with non-Gaussian entries that have an exponentially decaying distribution and whose first four moments match the Gaussian moments. 相似文献
17.
M. R. Setare D. Momeni V. Kamali R. Myrzakulov 《International Journal of Theoretical Physics》2016,55(2):1003-1018
We propose a generalised de Sitter scale factor for the cosmology of early and late time universe, including single scalar field is called as inflaton. This form of scale factor has a free parameter q is called as nonextensivity parameter. When q = 1, the scale factor is de Sitter. This scale factor is an intermediate form between power-law and de Sitter. We study cosmology of such families. We show that both kinds of dark components, dark energy and dark matter simultaneously are described by this family of solutions. As a motivated idea, we investigate inflation in the framework of q-de Sitter. We consider three types of scenarios for inflation. In a single inflation scenario, we observe that, inflation ended without any specific ending inflation ?end, the spectral index and the associated running of the spectral index are ns ? 1 ~ ?2??, αs ≡ 0. To end the inflation: we should have \(q=\frac {3}{4}\). We deduce that the inflation ends when the evolution of the scale factor is a(t) = e3/4(t). With this scale factor there is no need to specify ?end. As an alternative to have inflation with ending point, We will study q-inflation model in the context of warm inflation. We propose two forms of damping term Γ. In the first case when Γ = Γ0, we show the scale invariant spectrum, (Harrison-Zeldovich spectrum, i.e. ns = 1) may be approximately presented by (\(q=\frac {9}{10},~~N=70\)). Also there is a range of values of R and ns which is compatible with the BICEP2 data where \(q=\frac {9}{10}\). In case Γ = Γ1V(?), it is observed that small values of a number of e-folds are assured for small values of q parameter. Also in this case, the scale-invariant spectrum may be represented by \((q,N) = (\frac {9}{10},70)\). For \(q=\frac {9}{10}\) a range of values of R and ns is compatible with the BICEP2 data. Consequently, the proposal of q-de Sitter is consistent with observational data. We observe that the non-extensivity parameter q plays a significant role in inflationary scenario. 相似文献
18.
A. S. Kyuregyan 《Journal of Experimental and Theoretical Physics》2012,114(5):857-866
The transverse instability of a plane front of fast impact ionization waves in p +-n-n + semiconductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration ??b ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homogeneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum s M at k = k M, then decreases, and becomes negative at k > k 01. This behavior of the function s(k) for short-wavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and ??smearing?? of perturbation of concentrations owing to the transverse transport of charge carriers. The similarity laws for perturbations with k ? k M have been established: at fixed ??b values and the maximum field strength on the front E 0M, the growth rate s depends only on the ratio k/N and the boundary wavenumber k 01 ?? N. The parameters s M, k M, and k 01, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E 0M. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the operation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simulation results. The results have been confirmed by the numerical simulation of the evolution of small harmonic perturbations of the steady-state plane impact ionization wave. 相似文献
19.
T V Ramakrishnan 《Pramana》1976,7(2):63-94
The possible instabilities of a 1-dimensional itinerant electron gas are discussed, assuming electron-electron interaction to play the dominant role. As is well known, in the RPA, a 1-dimensional metal is prone to spin density wave (SDW), charge density wave (CDW) and Cooper pair (CP) instabilities. The spin channel decomposition of the irreducible scattering amplitude I is made and the spin channel projections are evaluated in terms of the matrix elements of bare electron-electron interactionV(x) for momenta of interest. It is found that if the bare electron interactionV(x) is repulsive and decreases monotonically with separation, only the SDW instability will occur. If the small separation (x?(2k F )?1) part of the interaction is greatly reduced or is made attractive,V(x) is non-monotonic,V q (q?2k F ) is negative, and a CDW instability is preferred. A CP instability is possible if the electron interaction is attractive,i.e., if [V q (0<q<k F )+V q (q?2k F )]<0. The above RPA results serve only as rough indicators, since in general there are important two-electron configurations with two-electron momentum close to zero and with electron hole momentum close to 2k F , an example being the near Fermi energy configurationk 1?k F ,k 2??k F ,k 3??k F k 4?k F . Therefore as pointed out first by Bychkov, Gorkov and Dzhyaloshinskii (BGD), cross channel coupling is especially significant. It is shown that the cross channel coupling is constructive is some cases,eg., exchange of CD fluctuations leads to an effective electron-electron spin singlet attraction and vice-versa. A formalism for studying such effects is set up, and the particular example mentioned above is discussed. An RPA-like approximation is made for the form of the reducible singlet electron hole scattering amplitudeγ s d and the resulting induced Cooper pair attraction is calculated to be $$\begin{gathered} [I_s ^e ]_{ind.} \rho _{{}^\varepsilon F} = [ln(\lambda \beta \omega _c )]^{ - 1} ln\{ [1 + 2\pi ^{ - 1} ln(\lambda \beta \omega _c )^2 ]/ \hfill \\ 1 + [8\pi ^{ - 1} \gamma _s ^d (q = 2k_F )^{ - 1} )^2 ]\} \hfill \\ \end{gathered} $$ where λ=1.14,β=(k B T)?1 andω 0 is an electronic energy cut-off ~ε F . The induced electron hole attraction due to the exchange of virtual Cooper pairs has a similar expression, but with a factor of (1/4) and withγ s e (q=0) replacingγ s d (q=2k F ). The induced Cooper pair attraction is seen to be quite large over a broad range of temperatures close to but aboveT CDW [i.e., aboveT such thatγ s d (q=2k F )?1=0]. There is no requirement thatγ s d (q=2k F ) andγ s e (q=0) become singular at the same temperature, as found by BGD. The BGD prediction is seen to arise from the neglect of real particle hole and particle-particle excitations while calculatingγ s d andγ s e . The effect of impurities, of electron-phonon coupling, of interchain coupling and of interaction between thermal order parameter fluctuations is discussed. The results are then applied to a discussion of the properties of TTF-TCNQ, where it is suggested that a CDW instability occurs becauseV q (q=2k F )<0,i.e., because the small separation electron repulsion is strongly reduced by the highly polarizable TTF. Because of substantial interchain coupling, the bulk CDW instability occurs close to the RPA instability temperature. The giant conductivity observed by Colemanet al is attributed to superconductive fluctuations in a 1-dimensional system with large mean field superconductive transition temperatureT CP MF of order 300°K. Such a largeT CP MF is shown to result from the induced Cooper pair attraction due to CD fluctuation exchange. 相似文献
20.
J.V. Mantese W.I. Goldburg D.H. Darling H.G. Craighead U.J. Gibson R.A. Buhrman W.W. Webb 《Solid State Communications》1981,37(4):353-357
Granular composites consisting of 25% nickel as 8 nm diameter particles dispersed in an aluminium oxide matrix display excess conduction noise. Co-deposited films with resistance per square about 105 ohms and negative temperature coefficient show a noise power spectral density where α ? 1.10 ± 0.03 over the accessible spectral range of 0.1 Hz ? ? ? 5000 Hz. The amplitude 3 × 10?15 ? Sv(1) ? 5 × 10?12 V2Hz?1, appears to increase approximately quadratically as the applied voltage Vs up to Vs ? 2.5 V and as the first power of Vs for 2.5 ? Vs < 35 V. 相似文献