When an electronic system is irradiated by an intense laser field, the potential “seen” by electrons is modified, which affects significantly the bound-state energy levels, a feature that has been observed in transition energy experiments. For lasers for which the dipole approximation applies, a nonperturbative approach based upon the Kramers–Henneberger translation transformation, followed by Floquet series expansions, yields, for sufficiently high frequencies, the so-called “laser-dressed” potential, which is taken for composing a time-independent Schrödinger equation whose solutions are the desired quasistationary states. This approach, developed originally for atoms, has been verified to be useful also for carriers in semiconductor nanostructures under intense laser fields. In quantum wells, analytical expressions for the dressed potential have been proposed in literature for a nonresonant, intense laser field polarized perpendicularly to the interfaces. By noting that they apply only for α0≤L/2, where α0 is the laser-dressing parameter and L is the well width, we derive here an analytical expression valid for all values of α0. Interestingly, our model predicts the formation of a double-well potential for laser frequencies and intensities such that α0>L/2, which creates a possibility of generating resonant states into the channel. In addition, the rapid coalescence of the energy levels with the increase in α0 we found indicates the possibility of controlling the population inversion in quantum well lasers operating in the optical pumping scheme.

Quasistationary states of long-range interacting systems have been studied at length over the last 15 years. It is known that the collisional terms of the Balescu-Lenard and Landau equations vanish for one-dimensional systems in homogeneous states, thus requiring a new kinetic equation with a proper dependence on the number of particles. Here we show that the scalings discussed in the literature are mainly due either to small size effects or the use of unsuitable variables to describe the dynamics. The scaling obtained from both simulations and theoretical considerations is proportional to the square of the number of particles, and a general form for the kinetic equation valid for the homogeneous regime is obtained. Numerical evidence is given for the Hamiltonian mean field and ring models, and a kinetic equation valid for the homogeneous state is obtained for the former system.

In this letter we discuss the validity of the ergodicity hypothesis in theories of violent relaxation in long-range interacting systems. We base our reasoning on the Hamiltonian Mean Field model and show that the life-time of quasi-stationary states resulting from the violent relaxation does not allow the system to reach a complete mixed state. We also discuss the applicability of a generalization of the central limit theorem. In this context, we show that no attractor exists in distribution space for the sum of velocities of a particle other than the Gaussian distribution. The long-range nature of the interaction leads in fact to a new instance of sluggish convergence to a Gaussian distribution.

Although the Vlasov equation is used as a good approximation for a sufficiently large N , Braun and Hepp have showed that the time evolution of the one particle distribution function of a N particle classical Hamiltonian system with long range interactions satisfies the Vlasov equation in the limit of infinite N . Here we rederive this result using a different approach allowing a discussion of the role of inter-particle correlations on the system dynamics. Otherwise for finite N collisional corrections must be introduced. This has allowed the a quite comprehensive study of the Quasi Stationary States (QSS) but many aspects of the physical interpretations of these states remain unclear. In this paper a proper definition of timescale for long time evolution is discussed and several numerical results are presented, for different values of N . Previous reports indicates that the lifetimes of the QSS scale as N 1.7 or even the system properties scales with exp(N ). However, preliminary results presented here shows indicates that time scale goes as N 2 for a different type of initial condition. We also discuss how the form of the inter-particle potential determines the convergence of the N -particle dynamics to the Vlasov equation. The results are obtained in the context of following models: the Hamiltonian Mean Field, the Self Gravitating Ring Model, and a 2-D Systems of Gravitating Particles. We have also provided information of the validity of the Vlasov equation for finite N , i. e. how the dynamics converges to the mean-field (Vlasov) description as N increases and how inter-particle correlations arise.

We discuss the nature of nonequilibrium phase transitions in the Hamiltonian mean-field model using detailed numerical simulations of the Vlasov equation and molecular dynamics. Starting from fixed magnetization water bag initial distributions and varying the energy, the states obtained after a violent relaxation undergo a phase transition from magnetized to nonmagnetized states when going from lower to higher energies. The phase transitions are either first order or are composed of a cascade of phase reentrances. This result is at variance with most previous results in the literature mainly based on the Lynden-Bell theory of violent relaxation. The latter is a rough approximation and, consequently, is not suited for an accurate description of nonequilibrium phase transition in long-range interacting systems.

International audienceAbstract A two-dimensional class of mean-field models that may serve as a minimal model to study the properties of long-range systems in two space dimensions is considered. The statistical equilibrium mechanics is derived in the microcanonical ensemble using Monte Carlo simulations for different combinations of the coupling constants in the potential leading to fully repulsive, fully attractive and mixed attractive?repulsive potential along the Cartesian axis and diagonals. Then, having in mind potential realizations of long-range systems using cold atoms, the linear theory of this two-dimensional mean-field Hamiltonian models is derived in the low temperature limit

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The advent of lasers created entirely new possibilities for the study of the interaction of intense fields with solids. These strong fields can reduce energy gaps [l, 21, distort optical absorption edges [3], shift critical temperatures of magnetic solids [4, 51, change phonon and magnon damping coefficients [6 to 81, etc. Another new and interesting intense field effect we bring about in this note is that of the changes induced by an intense high-frequency radiation field in the binding energy of a bound electron in a solid, e.g. an impurity in a semiconductor.The system we are interested in is a substitutional impurity in a semiconductor. In such circumstances either a shallow or deep level appears. In order to avoid problems with the description of the wave function for deep levels we will restrict our analyses only to shallow traps.The problem of the description of a shallow level impurity whose electron is loosely bound to the charged impurity ion, can be simplified to that of a hydrogenic atom in a dielectric medium where the mass of the bound electron is the effective mass of the free electron in the associated band. The result of the full quantum mechanical treatment gives the following equation of motion for the impurity electron [9]:[ 2m* h2 ( 3 1 F(r) represents an envelope function, which modulates the rapidly varying part of the total wave function, in this case a Bloch function. The impurity potential is reduced in the solid by a factor of dielectric constant c. The complete wave function, in general, is written in the form In other words, the Bloch function unK(r) to be taken into account is that of the nearest band where the impurity sits. The solution of (1) gives the allowed energy levels of the bound electron as where En is the energy of the levels measured relative to the band edge, m* is the electron effective mass, E the dielectric constant, and R, the Rydberg constant.') P.O. Box 04629, 70910-900 Brasilia-DF, Brazil.