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1.
Numerical simulations are done of Langevin dynamics for a uniform-orderparameter, field-swept Landau model,= –|a/2|m 2+|b/4|m 4mh(t) , to study hysteresis effects. The field is swept at a constant rateh(t)=h(0)+ht. The stochastic jump values of the field {hJ from an initially prepared metastable minimumm(0) are recorded, on passage to a global minimum m(). The results are: (a) The mean jump¯h J(h) increases (hysteresis loop widens) with h, confirming a previous theoretical criterion based on rate competition between field-sweep and inverse mean first-passage time (FPT); (b) The broad jump distribution(h J,h) is related to intrinsically large FPT fluctuations ( 22)/ 2 O(1), and can be quantitatively understood. Possible experimental tests of the ideas are indicated.  相似文献   

2.
We investigate the influence of long range interactions on the relaxation behaviour of a lattice model with an on-site potential of 4-type and infinite range harmonic interactions. For finite number of particlesN, it is shown that the autocorrelation functions <E n(t)E n > of the fluctuations of the one-particle energiesE n(t) decays exponentially. The corresponding relaxation time is proportional toN and is given by (T, N) =N0(T). The temperature dependent time scale 0 can explicitly be related to the dynamics of a one-particle correlator of the noninteracting system. The results are derived using Mori-Zwanzig projection formalism. The corresponding memory kernel is calculated within a mode coupling approximation and by a perturbative approach. Both results agree in leading order in 1/N. It is speculated that any interaction of range generates a timescale .  相似文献   

3.
A qualitative change in the topology of the joint probability densityP(,x), which occurs for strongly colored noise in multistable systems, has recently been observed first by analog simulation (F. Moss and F. Marchesoni,Phys. Lett. A 131:322 (1988)) and confirmed by matrix continued fraction methods (Th. Leiber and H. Riskin, unpublished), and by analytic theory (P. Hänggi, P. Jung, and F. Marchesoni,J. Stat. Phys., this issue). Systems studied were of the classx=–U(x)/x+(t,), whereU(x) is a multistable potential and (t, ) is a colored, Gaussian noise of intensityD, for which =0, and (t) (s)=(D/)exp(–t–s/). When the noise correlation time is smaller than some critical value 0, which depends onD, the two-dimensional densityP(,x) has the usual topology [P. Jung and H. Risken,Z. Phys. B 61:367 (1985); F. Moss and P. V. E. McClintock,Z. Phys. B 61:381 (1985)]: a pair of local maxima ofP(,x), which correspond to a pair of adjacent local minima ofU(x), are connected by a single saddle point which lies on thex axis. When >0, however,the single saddle disappears and is replaced by a pair of off-axis saddles. A depression, or hole, which is bounded by the saddles and the local maxima thus appears. The most probable trajectory connecting the two potential wells therefore does not pass through the origin for >0, but instead must detour around the local barrier. This observation implies that successful mean-first-passage-time theories of strongly colored noise driven systems must necessarily be two dimensional (Hänggiet al.). We have observed these holes for several potentialsU(x): (1)a soft, bistable potential by analog simulation (Moss and Marchesoni); (2) a periodic potential [Th. Leiber, F. Marchesoni, and H. Risken,Phys. Rev. Lett. 59:1381 (1987)] by matrix continued fractions; (3) the usual hard, bistable potential,U(x)=–ax 2/2+bx 4/4, by analog simulations only; and (4) a random potential for which the forcingf(x)=–U(x)/x is an approximate Gaussian with nonzero correlation length, i.e., colored spatiotemporal noise, by analog simulation. There is a critical curve 0(D) in the versusD plane which divides the two topological behaviors. For a fixed value ofD, this curve is shifted toward larger values of 0 for progressively weaker barriers between the wells. Therefore, strong barriers favor the observation of this topological transformation at smaller values of . Recently, an analytic expression for the critical curve, valid asymptotically in the small-D limit, has been obtained (Hänggiet al.).This paper will appear in a forthcoming issue of theJournal of Statistical Physics.  相似文献   

4.
We consider a semi-infinite 3-dimensional Ising system with a rough wall to describe the effect of the roughness r of the substrate on wetting. We show that the difference of wall free energies (r)= AW(r)– BW(r) of the two phases behaves like (r)r(1), where r=1 characterizes a purely flat surface, confirming at low enough temperature and small roughness the validity of Wenzel's law, cos (r)r cos (1), which relates the contact angle of a sessile droplet to the roughness of the substrate  相似文献   

5.
A carrier transport model to explain the high-frequency response in high-speed MQW lasers is described. The ambipolar approximation, which is unsuitable for dealing with the high-speed carrier dynamics in MQW structures, was not adopted for small-signal analysis. The carrier transport effect can be characterized by four time constants: the electron transport time, bmn; the hole transport time, bmp; the electron escape time, wbn; and the hole escape time, wbp. The frequency response was interpreted as the sum of the constant response term due to the fast electron current and the roll-off term due to the slow hole transport time. The ratio of the electron contribution to the total response was proportional to the ratio of electron contribution to the total differential gain, , and reciprocally proportional to n0 = 1 + bmn/wbn. The value of was calculated to be about 0.5 for typical MQW lasers. The roll-off frequency is mainly determined by . The ratio p0 = 1 + bmp/wbp affects the resonant frequency and the damping rate in the high-bias condition.  相似文献   

6.
We study perturbative QCD at the five-loop level. In particular we considerR = tot(e + e hadrons)/(e + e + ) andR = ( v+hadrons)/( ev). We use our method to estimate the five-loop coefficients. As a result, we obtain s (M z ) = 0.1186(11) and s (34 GeV) = 0.1396(16), which are accurate at the 1% level. We also findR = 3.8350(18), which is consistent withR and is accurate to 0.05%.  相似文献   

7.
Let : [0, 1][0, 1] be a piecewise monotonie expanding map. Then admits an absolutely continuous invariant measure. A result of Kosyakin and Sandler shows that can be approximated by a sequence of absolutely continuous measures n invariant under piecewise linear Markov maps itn. Each itn is constructed on the inverse images of the turning points of . The easily computable measures n are used to estimate the Liapunov exponent of . The idea of using Markov maps for estimating the Liapunov exponent is applied to both expanding and nonexpanding maps.  相似文献   

8.
We prove exponential convergence to equilibrium (L 2 geometric ergodicity) for a random walk with inward drift on a sub-Cayley rooted tree. This randomwalk model generalizes a Monte Carlo algorithm for the self-avoiding walk proposed by Berretti and Sokal. If the number of vertices of levelN in the tree grows asC N ~ N N –1 , we prove that the autocorrelation time satisfies N2 N1+  相似文献   

9.
Let the Lie groups G and H act on the manifold P in such a way that P fibres as a principal G-bundle over P/G and as an H-bundle over P/H. We find that every pair (,) where is an H-invariant connection form in PP/G and is a G-invariant connection form in PP/H corresponds uniquely to a connection form in PP/(H×G) and a cross-section of a vector bundle with base P/(H×G).  相似文献   

10.
We consider bistable systems driven by stationary wideband Gaussian colored noise. We construct uniform asymptotic expansions of the stationary probability density function and of the activation rate, for small intensity and short correlation time of the noise. We find that for different values of the total power output / of the noise, different terms in the asymptotic expansions become dominant. For we recover previously derived results, while for =O() and new results are obtained.  相似文献   

11.
The electronic absorption coefficient (e) of meso-ultrasound (p –1 en, t, ee; ql 1, where p, en, t are the times of pulse relaxation, energy, and current carrier traps; ee –1 is the frequency of intraelectron collisions; , q are the frequency and wave vector of sound; l is the carrier mean free path) in the presence of a permanent external field E0 e 0 –1 q0T is calculated for anisotropic single-valley semiconductors with piezoelectrical and potential-deformation acoustoelectronic interaction. Considered arbitrary are: 1) the anisotropy of the tensors * and p (and other crystal parameters); 2) the degree of Fermi degeneration of the carriers; 3) the dependence of p on the carrier energy . The acoustoheat nonlinearity is neglected. The possibility of meso-ultrasound amplification by the transverse field (E0 - q) is predicted. By changing the orientation of the vector q relative to the crystal axes, the transverse threshold field (E thr ) can be controlled smoothly and within broad limits, This permits the production of a mechanical sound-amplification regulator or a modulator of its intensity. The ratio between E thr and E thr yields a measure of the relative anisotropy of the mobility.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 87–92, February, 1977.  相似文献   

12.
The Einstein universe is a simple model describing a static cosmological spacetime, having a constant radius and a constant curvature, and, as is well known, it does not describe our universe. We propose a model which is an extension of Einstein's. Our metric, havingR × S 3 topology, describes a nonisotropic homogeneous closed (finite) universe of Bianchi type IX. This metric is similar to that of Taub, but is simpler. Unlike the Taub solution (which is a cosmological extension of the NUT solution), however, the universe described by our metric contains matter. Like the Taub metric, our metric has two positive constants (, T). The gravitational red shift calculated from our metric is given. Similarly to the Schwarzschild metric, which has a singularity atr = 2m, this metric has the same kind of singularity att = 2. The maximal extension of the coordinates in our metric is fairly analogous to that of the Schwarzschild metric.  相似文献   

13.
For the Edwards-Anderson model we introduce an integral representation for the surface pressure (per unit surface) in terms of a quenched moment of the bond-overlap on the surface. We consider free , periodic and antiperiodic * boundary conditions (by symmetry ()=(*)), and prove the bounds We show moreover that at high temperatures () is close to 2/4 and () is close to 2/4 uniformly in the volume .  相似文献   

14.
Mori's scaling method is used to derive the kinetic equation for a dilute, nonuniform electron plasma in the kinetic region where the space-time cutoff (b, t c) satisfies Dbl f , D t c f , with D the Debye length, D –1= p the plasma frequency, andl f and f the mean free path and time, respectively. The kinetic equation takes account of the nonuniformity of the order ofl f and D for the single-and the two-particle distribution function, respectively. Thus the Vlasov term associated with the two-particle distribution function is retained. This kinetic equation is deduced from the kinetic equation in the coherent region obtained by Morita, Mori, and Tokuyama, where the space-time cutoff of the coherent region satisfies Dbr 0, Dt c 0, withr 0 the Landau length and 0 the corresponding time scale.  相似文献   

15.
The emissivity in the 2.7 m range is examined with a spectrometer having 25 cm–1 for 2.5, ,7.5 cm·atm,4 8cm·atm, 400T1000° K; 150P730 mm Hg. It is found that relation (1) is obeyed to within /0.1, though the calculated transmission is usually less than the measured value. It is shown that the relation is obeyed on account of the mutual position of the CO2 and H2O lines in the band, i.e., one gas may be considered as unselective relative to the other.  相似文献   

16.
In the study of the formulation of Maxwellian tails the nonlinear partial differential equation 2 u/x +u/x+u 2=0 arises. We determine the Lie point symmetry vector fields and calculate the similarity ansätze. Then we discuss the resulting ordinary differential equations. Finally, the existence of Lie Bäcklund vector fields is studied and a Painlevé analysis is performed.  相似文献   

17.
We derive the exact matrix field theory for a replicated grassmannian representation of a local pairing superconducting disorder ensemble including three superconducting order parameters and the spin-flip pairbreaking mechanism. Disorder is assumed to be gaussian distributed. We find by exactly solving the saddle-point equation the criterion for a vanishing gap –1 + –1 , where denotes the averaged superconducting order parameter, –1 the spin-flip scattering rate, and –1 the scattering rate corresponding to correlations of Re(–). Taken at =0, our field theory, which is exact in all orders of –1 , contains new terms in addition to those of theO( –1 ) model derived by Efetov et al. Our formulation transfers correctly to all orders the invariances of the action into symmetries of the matrix field theory. The saddle point approximation is outlined and it is shown how singular corrections to the saddle point density of states arise atE F in a gapless superconductor. Finally singular corrections in the two particle propagator, the density correlation function and the conductivity are calculated for =0 in one loop order. It turns out that these corrections can be entirely expressed by those of the single particle density of states.  相似文献   

18.
We show the existence of a constant (0, ) such that if n is the extinction time for a supercritical contact process on [1, n] d starting from full occupancy, then {log(E[ n])}/n d tend to as n tends to infinity.  相似文献   

19.
For a space-time which admits a closed timelike smooth curve it is estimated that 2 · 10–24 · l 2, where is the real time andl the spatial length associated with the timelike curve, and is the density of material.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 9, pp. 33–36, September, 1973.  相似文献   

20.
We consider the mechanism of macroscopic polarization of semiconducting plates owing to the interaction of free carriers with an impurity level, in which role the level of the residual impurity of compensated semiconductors may appear. This mechanism, in combination with the diffusion-drift mechanism of polarization, results in additional dispersion of the real () and imaginary () parts of the dielectric permittivity, this being particularly significant for semiconductors of thickness smaller than the screening length Ls of free carriers. The character of the behavior of and depends on the relation between the Maxwell relation time M and the times of carrier capture: c and ejection e by an impurity center. For cetm and (/Ls) e/c1 the dispersion of and is the same as for thick plates (/Ls1). For c m e and (/Ls)e/c1 the () curve has a characteristic kink in the region 1/e, indicating additional absorption associated with the ejection of carriers into the surface region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 11–13, October, 1981.  相似文献   

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