Time-dependent external field

The time-dependent external field in the simulation comprises two laser pulses, an XUV pump pulse followed by an intense IR probe pulse, both with a Gaussian envelope. In order to consider a realistic case, we use parameters not too far from those used in experiments, compare with Ref. [154], but the XUV pulse is in our simulation centered around the first doubly excited states with 1P° symmetry ( 60 eV). The XUV-pump pulse is 385 ats long (full width at half maximum of the intensity), with the energy peaked at 60.69 eV, and an intensity of 2 1013 W/cm2 the probe is a Tirsapphire 800 nm (1.55 eV) pulse, 3.77 fs long (fwhm), with an intensity of 1012 W/cm2. 

The random matrix was first introduced by E. P. Wigner as a model to mimic unknown interactions in nuclei, and it has been studied to describe statistical natures of spectral fluctuations in quantum chaos systems [17]. Here, we introduce a random matrix system driven by a time-dependent external field E(t), which is considered as a model of highly excited atoms or molecules under an electromagnetic field. We write the Hamiltonian... 

One-electron atoms subjected to a time-dependent external field provide physically realistic examples of scattering systems with chaotic classical dynamics. Recent work on atoms subjected to a sinusoidal external field or to a periodic sequence of instantaneous kicks is reviewed with the aim of exposing similarities and differences to frequently studied abstract model systems. Particular attention is paid to the fractal structure of the set of trapped unstable trajectories and to the long time behavior of survival probabilities which determine the ionization rates of the atoms. Corresponding results for unperturbed two-electron atoms are discussed. 

The total magnetic field H - acting on the ferrofluid particle (the Neel mechanism being been blocked) is made up of a large constant field term H representing the DC bias field, a small time-dependent external field H(t) and a random field term h(r) so that... 

The definition (9.1) of the ET rate constant assumes that the kinetics is exponential. In general, of course, it is not, particularly at low temperatures. Possible sources of nonexponential behavior are complex spectral density and, as a result, complex relaxation dynamics of the participating bath modes [45, 47], fluctuating tunneling matrix element [59-61], time-dependent external field modulating the energy gap [66, 67], and nonequilibrium... 

According to the Boltzmann superposition principle [2], the response of a system to a time-dependent external field can be expressed by the superposition of responses of fields at different times. Each response is only dependent on the magnitude of... 

Consider a time-dependent external field h t) applied to a system in equilibrimn imder a potential V x). For the sake of simplicity, x has been used to denote the whole set of coordinates xi appearing in the Smolu-chowsky equation. Because the applied field perturbs the system, the average values of physical quantities in the system change from those in the equilibrium state. If the field is weak, the change in any physical quantity is a linear functional of h t) as expressed by... 

We next introduce a perturbation which displaces the solute position. This perturbation disturbs the spatial correlation between the solute and the solvent, and can be formulated in terms of the time-dependent external field 4>ext(r,t) that couples to p A(r). Thus the Hamiltonian which represents the perturbation takes the form... 

Here 4(o ) is the Fourier transform of the time-dependent external field defined as... 

Abstract. This article reviews from both theoretical and numerical aspects three non-equivalent complete second-order formulations of quantum dissipation theory, in which both the reduced dynamics and the initial canonical thermal equilibrium are properly treated in the weak system-bath coupling limit. Two of these formulations are rather familiar as the time-local and the memory-kernel prescriptions, while another which can be termed as correlated driving-dissipation equations of motion will be shown to have the combined merits of the two conventional formulations. By exploiting the exact solutions to the driven Brownian oscillator system, we demonstrate that the time-local and correlated driving-dissipation equations of motion formulations are usually better than their memory-kernel counterparts, in terms of their applicability to a broad range of system-bath coupling, non-Markovian, and temperature parameters. Numerical algorithms are detailed for an efficient evaluation of both the reduced canonical thermal equilibrium state and the non-Markovian evolution at any temperature, in the presence of arbitrary time-dependent external fields. 

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