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We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an entanglement-boundary law. These results apply to any ground state of a gapped model resulting from dynamics generated by a local Hamiltonian, as well as, dually, to states that are generated via a sudden quench of an interaction as recently studied in the case of dynamics of quantum phase transitions. We achieve these results by exploiting ideas from quantum information theory and tools provided by Lieb-Robinson bounds. We also show that there exist noncritical fermionic systems and equivalent spin chains with rapidly decaying interactions violating this entanglement-boundary law. Implications for the classical simulatability are outlined.  相似文献   

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The variation in dynamic stiffness due to a geometrical shift of a cylindrical vibration isolator is predicted by a scaling law and compared to the results of a waveguide solution. The simple scaling law fails to model satisfactorily the stiffness variation due to a single length or radius shift, while predicting successfully the results of an isolator shape invariant shift. The small deviations arise from a disregarded material property shift.  相似文献   

4.
Bastea S 《Physical review letters》2004,93(19):199603; author reply 199604
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We find prominent similarities in the features of the time series for the (model earthquakes or) overlap of two Cantor sets when one set moves with uniform relative velocity over the other and time series of stock prices. An anticipation method for some of the crashes have been proposed here, based on these observations.   相似文献   

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Scaling laws relating the critical indices in different dimensionalities with the same long range (1/rx) interactions are derived. Critical exponents are then generated from the short range values and from recent near-mean-field expansions.  相似文献   

8.
H. Rapp 《Physics letters. A》1973,43(5):420-422
In order to establish scaling laws and characteristic curves of a plasma focus device, the neutron output was measured as a function of the deuterium filling pressure, accelerator length and capacitor energy.  相似文献   

9.
Widely cited evidence for scaling (self-similarity) of the returns of stocks and other securities is inconsistent with virtually all currently-used models for price movements. In particular, state-of-the-art models provide for ubiquitous, irregular, and oftentimes high-frequency fluctuations in volatility (“stochastic volatility”), both intraday and across the days, weeks, and years over which data is aggregated in demonstrations of self-similarity of returns. Stochastic volatility renders these models, which are based on variants and generalizations of random walks, incompatible with self-similarity. We show here that empirical evidence for self-similarity does not actually contradict the analytic lack of self-similarity in these models. The resolution of the mismatch between models and data can be traced to a statistical consequence of aggregating large amounts of non-stationary data.  相似文献   

10.
In this Letter we present a numerical study of the effect of noise on a chaotic scattering problem in open Hamiltonian systems. We use the second order Heun method for stochastic differential equations in order to integrate the equations of motion of a two-dimensional flow with additive white Gaussian noise. We use as a prototype model the paradigmatic Hénon-Heiles Hamiltonian with weak dissipation which is a well-known example of a system with escapes. We study the behavior of the scattering particles in the scattering region, finding an abrupt change of the decay law from algebraic to exponential due to the effects of noise. Moreover, we find a linear scaling law between the coefficient of the exponential law and the intensity of noise. These results are of a general nature in the sense that the same behavior appears when we choose as a model a two-dimensional discrete map with uniform noise (bounded in a particular interval and zero otherwise), showing the validity of the algorithm used. We believe the results of this work be useful for a better understanding of chaotic scattering in more realistic situations, where noise is presented.  相似文献   

11.
Scaling laws for large virtual photon mass (q2) in electroproduction and annihilation are studied in the framework of a simple planar dual model. We find, as has recently been conjectured, that the scaling behaviour depends on the number of space-time dimensions spanned by large momenta. In particular, for a certain range of parameters in the model, we find that the annihilation cross section is dominated by the one-dimensional configuration and increases with q2 relative to its canonical behaviour while the electroproduction total cross section is dominated by the two-dimensional configuration and has the canonical Bjorken scaling behavior. In general the scaling laws and therefore the structure of events in the model are distinctively different from the conventional parton model. The problem of consistency of planar dual tree diagrams with unitarity sum rules is discussed.  相似文献   

12.
Double power laws in income and wealth distributions   总被引:1,自引:0,他引:1  
Close examination of wealth distributions reveal the existence of two distinct power law regimes. The Pareto exponents of the super-rich, identified, for example in rich lists such as provided by Forbes, are smaller than the Pareto exponents obtained for top earners in income data sets. Our extension of the Slanina model of wealth is able to reproduce these double power law features.  相似文献   

13.
From a geometric picture of hadrons as extended objects we arrive at some universal features of high energy collisions. In this approach the mean multiplicity, as a function of s, and the KNO scaling function are universal, and asymptotically the ratio σelastictotal is expected to be the same for all processes.  相似文献   

14.
The decay of mounds about a dozen layers high on the Si(111)-(7x7) surface has been measured quantitatively by scanning tunneling microscopy and compared with analytic predictions for the power-law dependence on time predicted for a step-mediated decay mechanism. Conformably, we find an exponent 1/4 associated with the (3D) decay of the mound height and exponent 1/3 associated with the (2D) decay of top-layer islands. Using parameters from a continuum step model, we capture the essence of the kinetics. Qualitative features distinguish these mounds from multilayer islands found on metals.  相似文献   

15.
D. Jou 《Physics letters. A》2011,375(42):3664-3667
An effective non-equilibrium temperature is defined for (locally) polarized and dense turbulent superfluid vortex bundles, related to the average energy of the excitations (Kelvin waves) of vortex lines. In the quadratic approximation of the excitation energy in terms of the wave amplitude A, a previously known scaling relation between amplitude and wavelength k of Kelvin waves in polarized bundles, namely Ak−1/2, follows from the homogeneity of the effective temperature. This result is analogous to that of the well-known equipartition result in equilibrium systems.  相似文献   

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The sizes of snow slab failure that trigger snow avalanches are power-law distributed. Such a power-law probability distribution function has also been proposed to characterize different landslide types. In order to understand this scaling for gravity-driven systems, we introduce a two-threshold 2D cellular automaton, in which failure occurs irreversibly. Taking snow slab avalanches as a model system, we find that the sizes of the largest avalanches just preceding the lattice system breakdown are power-law distributed. By tuning the maximum value of the ratio of the two failure thresholds our model reproduces the range of power-law exponents observed for land, rock, or snow avalanches. We suggest this control parameter represents the material cohesion anisotropy.  相似文献   

19.
The passage of a polymer through a narrow pore is associated with the crossing of a significant free energy barrier. Both in nature and in single molecule experiments the polymer is typically driven through the pore. We here address two such driving modes: (i) the driving by binding proteins that prevent (partial) back-sliding through the pore; and (ii) the driving by a trans-membrane force. In case (i) we derive the effective force and show finite size effects due to the size of the binding proteins. In case (ii) we demonstrate the crossover from a slow, equilibrium driving to a non-equilibrium behaviour at fast driving.  相似文献   

20.
The topography evolution of simultaneously rotated and Ar (+) ion sputtered InP surfaces was studied using scanning force microscopy. For certain sputter conditions, the formation of a highly regular hexagonal pattern of close-packed mounds was observed with a characteristic spatial wavelength which increases with sputter time t according to lambda approximately t(gamma) with gamma approximately 0.26. Based on the analysis of the dynamic scaling behavior of the surface roughness, the evolution of the surface topography will be discussed within the limits of existing models for surface erosion by ion sputtering.  相似文献   

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