We analyze the long time behavior of transport equations for a class of dissi-pative quantum systems with Fokker-planck type scattering operator, subject to connning potentials of harmonic oscillator type. We establish the conditions under which there exists a thermal equilibrium state and prove exponential decay towards it, using (classical) entropy-methods. Additionally, we give precise dispe...

the main contribution of the present work is to investigate the capability of exponential-type constitutive equationto model the warm deformation flow curves of a eutectoid steel in the temperature range of 620-770 °c andat the strain rates in the range of 0.01-10 s-1 conducted on a gleeble-1500 thermomechanical simulator. warmdeformation in this temperature range facilitates the occurrence of ...

We consider a class of viscous damped vibrating systems. We prove that, under the assumption that the damping term ensures the exponential decay for the corresponding inviscid system, then the exponential decay rate is uniform for the viscous one, regardless what the value of the viscosity parameter is. Our method is mainly based on a decoupling argument of low and high frequencies. Low frequen...

We use the properties of subharmonic functions to prove the following results, First, for any lattice system with finite-range forces there is a gap in the spectrum of the transfer matrix, which persists in the thermodynamic limit, if the fugacity z lies in a region E of the complex plane that contains the origin and is free of zeros of the grand partition function (with periodic boundary condi...

We give simple bounds for the exponential decay of a strongly continuous semigroup V (t) = exp(At) in a Hilbert space. The bounds are expressed by means of the solution X of the Ljapunov equation A X + XA = ?I and the quantity sup 0th kV (t)k for small h. Our main bound is attained on any normal semigroup and can therefore not be improved in general. Let V (t) be a strongly continuous semigroup...

The present paper generalizes the analysis [18, 2] of the correlations for a lattice system of real-valued spins at low temperature. The Gibbs measure is assumed to be generated by a fairly general pair potential (Hamiltonian function). The novelty, as compared to [18, 2], is that the single-site (self-) energies of the spins are not required to have only a single local minimum and no other ext...

We give a proof of dynamical localization in the form of exponential decay of spatial correlations in the time evolution for the one-dimensional continuum Anderson model via the fractional moments method. This follows via exponential decay of fractional moments of the Green function, which is shown to hold at arbitrary energy and for any single-site distribution with bounded, compactly supporte...

We consider a class of  systems of nonlinear  differential equations  neu tral type with distributed delay and periodic coefficients in the linear part. Using Lyapunov–Krasovskii functional, sufficient conditions for exponential stability zero solution are established estimates characterizing rate decay solutions at infinity, as well set attraction, obtained.

The framework to describe natural phenomena at their basics being quantum mechanics, there exist a large number of common global phenomena occurring in different branches of natural sciences. One such global phenomenon is spontaneous quantum decay. However, its long time behaviour is experimentally poorly known. Here we show, that by combining two genuine quantum mechanical results, it is possi...

We consider the Bresse system with frictional dissipative terms acting in all the equations. We show the exponential decay of the solution by using a method developed by Z. Liu and S. Zheng and their collaborators in past years. The numerical computations were made by using the finite difference method to prove the theoretical results. In particular, the finite difference method in our case is ...