Related papers: Energy Decay of Damped Systems

We show that the central finite difference formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators using, as a basis…

We calculate the leading perturbative and power corrections to the hadronic invariant mass and energy spectra in semileptonic heavy hadron decays. We apply our results to the $B$ system. Moments of the invariant mass spectrum, which vanish…

We prove that the scattering matrix at a fixed quasi--energy determines uniquely a time--periodic potential that decays exponentially at infinity. We consider potentials that for each fixed time belong to $L^{3/2}$ in space. The exponent…

In this work we propose a mechanism for converting the spectral problem of vertex models transfer matrices into the solution of certain linear partial differential equations. This mechanism is illustrated for the…

We establish a procedure to find the extremal density matrices for any finite Hamiltonian of a qudit system. These extremal density matrices provide an approximate description of the energy spectra of the Hamiltonian. In the case of…

A new derivation is given for the representation, under certain conditions, of the integral dispersion relations of scattering theory through local forms. The resulting expressions have been obtained through an independent procedure to…

We consider the $2$-spin spherical Sherrington--Kirkpatrick model whose disorder is given by a deformed Wigner matrix of the form $W+\lambda V$, where $W$ is a Wigner matrix and $V$ is a random diagonal matrix with i.i.d. entries. Assuming…

We establish global pointwise bounds for the Green's matrix for divergence form, second order elliptic systems in a domain under the assumption that weak solutions of the system vanishing on a portion of the boundary satisfy a certain local…

We investigate the long-time behavior of solutions of quasilinear hyperbolic systems with transparent boundary conditions when small source terms are incorporated in the system. Even if the finite-time stability of the system is not…

A boundary value problem on an unbounded domain, associated to difference equations with the Euclidean mean curvature operator is considered. The existence of solutions which are positive on the whole domain and decaying at infinity is…

Model-independent bounds are presented for the form-factors describing the semileptonic decay $\Lambda_b\to\Lambda_ce\bar\nu_e$ at the end-point of the lepton energy spectrum. For the axial-vector form-factor $f_1^A(1)$ we obtain…

We consider two different collective spin systems subjected to strong dissipation -- on the same scale as interaction strengths and external fields -- and show that either continuous or discontinuous dissipative quantum phase transitions…

We consider a broad class of second-order dynamical systems and study the impact of damping as a system parameter on the stability, hyperbolicity, and bifurcation in such systems. We prove a monotonic effect of damping on the hyperbolicity…

We obtain some important fundamental inequalities concerning the long time behavior of high order derivatives for solutions of some dissipative systems in terms of their $L^2$ algebraic decay. Some of these inequalities have not been…

The time decay of fully discrete finite-volume approximations of porous-medium and fast-diffusion equations with Neumann or periodic boundary conditions is proved in the entropy sense. The algebraic or exponential decay rates are computed…

We present an infinite lattice DMRG sweeping procedure which can be used as a replacement for the standard infinite lattice blocking schemes. Although the scheme is generally applicable to any system, its main advantages are the correct…

We consider a class of abstract second order evolution equations with a restoring force that is strictly superlinear at infinity with respect to the position, and a dissipation mechanism that is strictly superlinear at infinity with respect…

We show the exponential decay of eigenfunctions of second-order geometric many-body type Hamiltonians at non-threshold energies. Moreover, in the case of first order and small second order perturbations we show that there are no…

We study the energy decay rate of the Kelvin-Voigt damped wave equation with piecewise smooth damping on the multi-dimensional domain. Under suitable geometric assumptions on the support of the damping, we obtain the optimal polynomial…

We propose a second order exponential scheme suitable for two-component coupled systems of stiff evolutionary advection--diffusion--reaction equations in two and three space dimensions. It is based on a directional splitting of the involved…