We analyze in detail the discrete-time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic increase in the variance of the quantum walker's position with time is a direct consequence of the coherence of the quantum evolution. If the evolution is decoherent, as in the classical case, the variance is shown to increase linearly with time, as expected. Furthermore we show that this system has an evolution operator analogous to that of a resonant quantum kicked rotor. As this rotator may be described through a quantum computational algorithm, one may employ this algorithm to describe the time evolution of the quantum walker.
The separation of the Schrödinger equation into a Markovian and an interference term provides a new insight in the quantum dynamics of classically chaotic systems. The competition between these two terms determines the localized or diffusive character of the dynamics. In the case of the Kicked Rotor, we show how the constrained maximization of the entropy implies exponential localization.
Key words: kicked rotor; markovian process; dynamical localizationIn the last few decades the field of Quantum Chaos has drawn the attention of researchers in several areas of science. Many interesting phenomena were studied in systems such as atom traps and microwave cavities. Furthermore, the recent advances in technology that allow to construct and almost perfectly preserve quantum states, has opened the field of quantum computation, where chaotic effects and their control play an essential role (1).In this work we develop a different and general approach to the subject of dynamical localization (DL) and the related issue of quantum diffusion. This approach leads to an improved understanding of why DL takes place in some systems while in others quantum diffusion continues for ever. The path we follow consists in rewriting the Schrödinger equation in a form in which the part responsible for DL is separated from the part responsible for quantum 1 also at: Facultad de Ciencias, Universidad de la República.
We investigate how the time dependence of the Hamiltonian determines the occurrence of dynamical localization (DL) in driven quantum systems with two incommensurate frequencies. If both frequencies are associated to impulsive terms, DL is permanently destroyed. In this case, we show that the evolution is similar to a decoherent case. On the other hand, if both frequencies are associated to smooth driving functions, DL persists although on a time scale longer than in the periodic case. When the driving function consists of a series of pulses of duration sigma, we show that the localization time increases as sigma(-2) as the impulsive limit, sigma-->0, is approached. In the intermediate case, in which only one of the frequencies is associated to an impulsive term in the Hamiltonian, a transition from a localized to a delocalized dynamics takes place at a certain critical value of the strength parameter. We provide an estimate for this critical value, based on analytical considerations. We show how, in all cases, the frequency spectrum of the dynamical response can be used to understand the global features of the motion. All results are numerically checked.
-The dynamics of the Loccnz model of general circulation of the atmosphere is investigated.The attractors found ace characterized by calculating their Fourier spectra, Lyapunov exponents and dimensions.In addition, the self similarity of the attractors is studied with the aid of a Poincare map. A series of ~r~~~di~~~e~lsional maps derived from the Poincare section illustrates the structural changes of the attractors as a function of parameters variations.
We study the formation of helical vortex filaments in a tube. The helical flow is assumed to be potential except in a very slender core. The boundary conditions are satisfied by introducing a helical image vortex. By assuming an axisymmetric flow upstream and imposing conservation laws, we obtain a set of conditions that must be satisfied by the helical flow downstream. We obtain that, when a generalized swirl parameter Ω reaches a critical value Ωc a bifurcation occurs and for Ω>Ωc there are two solutions for the helical filamentary vortex. Such a bifurcation can be produced by increasing the swirl level of the inlet flow or the radius of the outlet tube, in agreement with experiments. We have discussed the influence of the core size and the Reynolds number on Ωc and with these results we have explained some experimental observations.
Abstract. Using methods of non-equilibrium thermodynamics that extend and generalize the MHD energy principle of Bernstein et al. (1958, Proc. Roy. Soc. A, 244, 17) we develop a formalism in order to analyze the stability properties of prominence models considered as dissipative states i.e. states far form thermodynamic equilibrium. As an example, the criterion is applied to the Kippenhahn-Schlüter model (hereafter K-S) considering the addition of dissipative terms in the coupled system of equations: the balance of energy equation and the equation of motion. We show from this application, that periods corresponding to typical oscillations of the chromosphere and photosphere (3 and 5 min respectively), that were reported as observations of the prominence structure, can be explained as internal modes of the prominence itself. This is an alternative explanation to the one that supposes that the source of these perturbations are the cold foot chromospheric and photospheric basis.
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