We study the dynamics defined by the Boltzmann equation set in the Euclidean space R in the vicinity of global Maxwellians with finite mass. A global Maxwellian is a special solution of the Boltzmann equation for which the collision integral vanishes identically. In this setting, the dispersion due to the advection operator quenches the dissipative effect of the Boltzmann collision integral. As...

We consider a class of semi-linear dissipative hyperbolic equations in which the operator associated to the linear part has a nontrivial kernel. Under appropriate assumptions on the nonlinear term, we prove that all solutions decay to 0, as t → +∞, at least as fast as a suitable negative power of t. Moreover, we prove that this decay rate is optimal in the sense that there exists a nonempty ope...

We prove an extension theorem for a small perturbation of the Ornstein-Uhlenbeck operator (L,D(L)) in the space of all uniformly continuous and bounded functions f : H → R, where H is a separable Hilbert space. We consider a perturbation of the form N0φ = Lφ + 〈Dφ,F 〉 where F : H → H is bounded and Fréchet differentiable with uniformly continuous and bounded differential. Hence, we prove that N...

We consider a quantum system coupled to a dissipative background with many degrees of freedom using the Monte Carlo wave function method. Instead of dealing with a density matrix which can be very highly dimensional, the method consists of integrating a stochastic Schrödinger equation with a non-Hermitian damping term in the evolution operator, and with random quantum jumps. The method is appli...

We analyze the order of convergence for operator splitting methods applied to conservation laws with stii source terms. We suppose that the source term q(u) is dissipative. It is proved that the L 1 error introduced by the time-splitting can be bounded by O((tkq(u 0)k L 1 (R)), which is an improvement of the O(Qt) upper bound, where t is the splitting time step, Q is the Lipschitz constant of q...

This paper proposes the use of optical flow from a moving robot to provide force feedback to an operator’s joystick to facilitate collision free teleoperation. Optical flow is measured by a pair of wide angle cameras on board the vehicle and used to generate a virtual environmental force that is reflected to the user through the joystick, as well as feeding back into the control of the vehicle....

We propose a Hamiltonian model that describes the interaction between a vortex line in superfluid He and the gas of elementary excitations. An equation of irreversible motion for the density operator of the vortex, regarded as a macroscopic quantum particle with a finite mass, is derived in the frame of Generalized Master Equations. This enables us to cast the effect of the coupling as a drag f...

Quantum jumps of a qubit are usually observed between its energy eigenstates, also known as its longitudinal pseudospin component. Is it possible, instead, to observe quantum jumps between the transverse superpositions of these eigenstates? We answer positively by presenting the first continuous quantum nondemolition measurement of the transverse component of an individual qubit. In a circuit Q...

Abstract In this paper, we consider the time decay of solutions to some problems arising in strain gradient thermoelasticity. We restrict two-dimensional case, and assume that two dissipative mechanisms are introduced, temperature mass dissipation. First, show problem is well-posed proving operator defining it generates a contractive semigroup linear operators. Then, assuming function involving...

In this paper, we investigate the stability of linear wave equation where one part boundary, which is seen as a lower-dimensional Riemannian manifold, governed by coupled equation, while other subject to dissipative Robin velocity feedback. We prove that closed-loop equations generate semi-uniformly stable semigroup contractions on suitable energy space. Furthermore, under multiplier-related ge...