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1.
We model a resistor by a stochastic lattice gas: Charge carriers jump randomly to neighboring lattice sites and interact by the constraint of single site occupancy. In contrast to independently moving charge carriers, the excess noise to quadratic order in the driving force for this model behaves for small frequencies as -1/2, |log|, d/2-1 for dimensionsd=1,2,3,..., respectively. We show that for this model the relationship between the excess noise and the four point current correlation function in equilibrium as proposed by Stanton and Nelkin becomes exact. This supports the view that the 1/f-noise may be related to the long time tail in the four point current correlation function.  相似文献
2.
In the literature one finds several different Markov approximations for a quantum system weakly coupled to a thermal reservoir. We want to point out that, in general, only the rigorous approximation given by E.B. Davies preserves positivity.  相似文献
3.
We consider the ferromagnetic Ising model with Glauber spin flip dynamics in one dimension. The external magnetic field vanishes and the couplings are i.i.d. random variables. If their distribution has compact support, the disorder averaged spin auto-correlation function has an exponential decay in time. We prove that, if the couplings are unbounded, the decay switches to either a power law or a stretched exponential, in general.  相似文献
4.
We consider the scalar field φ t with a reversible stochastic dynamics which is defined by the standard Dirichlet form relative to the Gibbs measure with formal energy . The potential V is even and strictly convex. We prove that under a suitable large scale limit the φ t -field becomes deterministic such that locally its normal velocity is proportional to its mean curvature, except for some anisotropy effects. As an essential input we prove that for every tilt there is a unique shift invariant, ergodic Gibbs measure for the -field. Received: 1 February 1996 / Accepted: 2 July 1996  相似文献
5.
We generalize the surface growth model of Gates and Westcott to arbitrary inclination. The exact steady growth velocity is of saddle type with principal curvatures of opposite sign. According to Wolf, this implies logarithmic height correlations, which we prove by mapping the steady state of the surface to world lines of free fermions with chiral boundary conditions.  相似文献
6.
We study Onsager's theory of large, coherent vortices in turbulent flows in the approximation of the point-vortex model for two-dimensional Euler hydrodynamics. In the limit of a large number of point vortices with the energy perpair of vortices held fixed, we prove that the entropy defined from the microcanonical distribution as a function of the (pair-specific) energy has its maximum at a finite value and thereafter decreases, yielding the negative-temperature states predicted by Onsager. We furthermore show that the equilibrium vorticity distribution maximizes an appropriate entropy functional subject to the constraint of fixed energy, and, under regularity assumptions, obeys the Joyce-Montgomery mean-field equation. We also prove that, under appropriate conditions, the vorticity distribution is the same as that for the canonical distribution, a form of equivalence of ensembles. We establish a large-fluctuation theory for the microcanonical distributions, which is based on a level-3 large-deviations theory for exchangeable distributions. We discuss some implications of that property for the ergodicity requirements to justify Onsager's theory, and also the theoretical foundations of a recent extension to continuous vorticity fields by R. Robert and J. Miller. Although the theory of two-dimensional vortices is of primary interest, our proofs actually apply to a very general class of mean-field models with long-range interactions in arbitrary dimensions.  相似文献
7.
We investigate interface dynamics in 1+1 dimensions, respecting reflection symmetry. In the continuum approach of Kardar, Parisi, and Zhang, the leading nonlinearity is then of the form (h t)3. On the basis of Monte Carlo simulations for a driven lattice gas, we argue that the nonlinearity is marginally irrelevant. Thus, the universality class is the one of equilibrium interfaces with a purely relaxational bulk dynamics.  相似文献
8.
We investigate the behavior of a two-level quantum system in contact with a classical heat bath, e.g., a solute particle with internal degrees of freedom immersed in a solvent of massive particles. Using a combination of analytical and numerical methods, we obtain precise information about localization, time-displaced correlation functions, and the frequency-dependent susceptibility of such solute particles. We find that these quantities can have a strong dependence on the density of the solvent fluid, with the maximum changes from the behavior of the corresponding isolated quantum system occurring in many cases at very low densities. We compare the exact results with those obtained by path integral Monte Carlo. There is good agreement with the imaginary time correlations, but analytic continuation to real time proves elusive: even with the best numerical data on the former, we can only get very gross features of the latter.  相似文献
9.
We show that the problem of a directed polymer on a tree with disorder can be reduced to the study of nonlinear equations of reaction-diffusion type. These equations admit traveling wave solutions that move at all possible speeds above a certain minimal speed. The speed of the wavefront is the free energy of the polymer problem and the minimal speed corresponds to a phase transition to a glassy phase similar to the spin-glass phase. Several properties of the polymer problem can be extracted from the correspondence with the traveling wave: probability distribution of the free energy, overlaps, etc.  相似文献
10.
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