We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution has generically a stretched-exponential form, but can assume also an algebraic decay, in the family of models which we call “GARCH”-type. The intermediate r...

By using some very simple mathematical arguments, it is possible to prove that quantum mechanics forbids a strictly exponential form for the decay. Examining more closely the derivation of the approximate exponential decay from Fermi’s Golden rule reveals a clear physical interpretation of this strange result. Closely linked to this field is the topic of the quantum Zeno effect and how the obse...

We prove that the q-state Potts antiferromagnet on a lattice of maximum coordination number r exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) whenever q > 2r. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay for q 7), triangular lattice (q 11), hexagonal lattice (q 4), and Kagom e l...

This work discusses the asymptotic behavior of a transmission problem on star-shaped networks of interconnected elastic and thermoelastic rods. Elastic rods are undamped, of conservative nature, while the thermoelastic ones are damped by thermal effects. We analyze the overall decay rate depending of the number of purely elastic components entering on the system and the irrationality properties...

Diffusion of metal atoms onto a molecular monolayer attached to a conducting surface permits electronic contact to the molecules with minimal heat transfer or structural disturbance. Surface-mediated metal deposition (SDMD) involves contact between "cold" diffusing metal atoms and molecules, due to shielding of the molecules from direct exposure to metal vapor. Measurement of the current throug...

This paper presents a method for designing state observers with exponential error decay for nonlinear systems whose output measurements are affected by known time-varying delays. A modular approach is followed, where sub-observers are connected in cascade to achieve a desired exponential convergence rate (chain observer). The observer employs delay-dependent time-varying gains to achieve the de...

This paper presents a method for designing state observers with exponential error decay for nonlinear systems whose output measurements are affected by known time-varying delays. A modular approach is followed, where subobservers are connected in cascade to achieve a desired exponential convergence rate (chain observer). When the delay is small, a single-step observer is sufficient to carry out...

The possibility of the magnetic monopole decay in the constant electric field is investigated and the exponential factor in the probability is obtained. Corrections due to Coulomb interaction are calculated. The relation between masses of particles for the process to exist is obtained.

In this paper, we study the global existence and exponential decay for a dynamic contact problem between a Timoshenko beam with second sound and two rigid obstacles, of which the heat flux is given by Cattaneo’s law instead of the usual Fourier’s law. The main difficulties arise from the irregular boundary terms, from the low regularity of the weak solution and from the weaker dissipative effec...

Using Monte Carlo simulations, we show that the autocorrelation function C(t) in the d = 3 Ising model with a plaquette interaction has a stretched-exponential decay in a supercooled liquid phase. Such a decay characterizes also some ground-state probability distributions obtained from the numerically exact counting of up to 10(450) configurations. A related model with a strongly degenerate gro...