Search results for "Initial value problem"
showing 10 items of 96 documents
Quantum walks in weak electric fields and Bloch oscillations
2020
Bloch oscillations appear when an electric field is superimposed on a quantum particle that evolves on a lattice with a tight-binding Hamiltonian (TBH), i.e., evolves via what we will call an electric TBH; this phenomenon will be referred to as TBH Bloch oscillations. A similar phenomenon is known to show up in so-called electric discrete-time quantum walks (DQWs); this phenomenon will be referred to as DQW Bloch oscillations. This similarity is particularly salient when the electric field of the DQW is weak. For a wide, i.e., spatially extended initial condition, one numerically observes semi-classical oscillations, i.e., oscillations of a localized particle, both for the electric TBH and …
Nonunitary generation of nonclassical states of a bidimensional harmonic oscillator
2000
A scheme for generating quantum superpositions of macroscopically distinguishable states of the vibrational motion of a bidimensionally trapped ion is reported. We show that these states possess highly nonclassical properties controllable by an adjustable parameter simply related to the initial condition of the confined system
Stabilization by dissipation and stochastic resonant activation in quantum metastable systems
2018
In this tutorial paper we present a comprehensive review of the escape dynamics from quantum metastable states in dissipative systems and related noise-induced effects. We analyze the role of dissipation and driving in the escape process from quantum metastable states with and without an external driving force, starting from a nonequilibrium initial condition. We use the Caldeira–Leggett model and a non-perturbative theoretical technique within the Feynman–Vernon influence functional approach in strong dissipation regime. In the absence of driving, we find that the escape time from the metastable region has a nonmonotonic behavior versus the system-bath coupling and the temperature, produci…
Chaos and nonlinearities in high harmonic generation
2016
Linearity is a fundamental postulate of quantum mechanics which is occasionally the subject of debate. This paper investigates the possibility of checking this assumption by using a laser field. We study the corrections caused by the presence of a small nonlinearity in the Hamiltonian of a quantum system. As a model we use a simplified two-level quantum system whose states are coupled by a small off-diagonal term proportional to the population of the upper level. The nonlinearity causes spontaneous decay of the upper level, shift and broadening of the line and the sensitive dependence of the final state on the initial condition. The presence of a strong laser field, resonant with the atomic…
Thermalization in the initial stage of heavy ion collisions
2017
The high density non-abelian matter produced in heavy ion collisions is extremely anisotropic. Prethermal dynamics for the anisotropic and weakly coupled matter is discussed. Thermalization is realized with the effective kinetic theory in the leading order accuracy of the weakly coupled expansion. With the initial condition from color glass condensate, hydrodynamization time for the LHC energies is realized to be about 1 fm/c, while the thermalization happens much later than the hydrodynamization. peerReviewed
A note on cooperative versus non-cooperative strategies in international pollution control
2002
Abstract In this note, we evaluate the scope of Dockner and Long’s [Journal of Environment Economics and Management 24 (1993) 13] conclusion on the efficiency of the non-cooperative outcome in a differential game of international pollution control. We also complete the study of the different equilibria the differential game can present. Our results show that their conclusion requires that the initial value of the stock of pollution be higher than the Pareto-efficient pollution stock so that the equilibrium path of emissions involves a decreasing stock of pollution. Our results also show that the application of the procedure proposed by Tsutsui and Mino [Journal of Economic Theory 52 (1990) …
The asymptotic behavior of the solutions of the Cauchy problem generated by ϕ-accretive operators
2005
Abstract The purpose of this paper is to study the asymptotic behavior of the solutions of certain type of differential inclusions posed in Banach spaces. In particular, we obtain the abstract result on the asymptotic behavior of the solution of the boundary value problem { u t − Δ p ( u ) + | u | γ − 1 u = f on ] 0 , ∞ [ × Ω , − ∂ u ∂ η ∈ β ( u ) on [ 0 , ∞ [ × ∂ Ω , u ( 0 , x ) = u 0 ( x ) in Ω , where Ω is a bounded open domain in R n with smooth boundary ∂Ω, f ( t , x ) is a given L 1 -function on ] 0 , ∞ [ × Ω , γ ⩾ 1 and 1 ⩽ p ∞ . Δ p represents the p-Laplacian operator, ∂ ∂ η is the associated Neumann boundary operator and β a maximal monotone graph in R × R with 0 ∈ β ( 0 ) .
On the Cauchy problem for microlocally symmetrizable hyperbolic systems with log-Lipschitz coefficients
2017
International audience; The present paper concerns the well-posedness of the Cauchy problem for microlocally symmetrizable hyperbolic systems whose coefficients and symmetrizer are log-Lipschitz continuous, uniformly in time and space variables. For the global in space problem we establish energy estimates with finite loss of derivatives, which is linearly increasing in time. This implies well-posedness in H ∞ , if the coefficients enjoy enough smoothness in x. From this result, by standard arguments (i.e. extension and convexification) we deduce also local existence and uniqueness. A huge part of the analysis is devoted to give an appropriate sense to the Cauchy problem, which is not evide…
Exclusive heavy vector meson production at next-to-leading order in the dipole picture
2021
We calculate exclusive production of a longitudinally polarized heavy vector meson at next-to-leading order in the dipole picture. The large quark mass allows us to separately include both the first QCD correction proportional to the coupling constant $\alpha_s$, and the first relativistic correction suppressed by the quark velocity $v^2$. Both of these corrections are found to be numerically important in $\mathrm{J}/\psi$ production. The results obtained are directly suitable for phenomenological calculations. We also demonstrate how vector meson production provides complementary information to structure function analyses when one extracts the initial condition for the energy evolution of …
Flow analysis with 3-dim ultra-relativistic hydro
2009
We review how flow observables of ultra-relativistic heavy-ion collisions are influenced by the initial condition, the description of the fluid dynamical (FD) stage and freeze-out (FO). We discuss the effects of the resolution of the FD treatment, the arising smoothing and numerical viscosity, as well as the consequences of final FO. This final FO stage includes confinement and simultaneous formation of constituent quarks. From the energy and momentum conservation at the FO stage pressure change and flow velocity may occur, which further modifies the observables.