Search results for "nonlinear"
showing 10 items of 3684 documents
Quantum Nekhoroshev Theorem for Quasi-Periodic Floquet Hamiltonians
1998
A quantum version of Nekhoroshev estimates for Floquet Hamiltonians associated to quasi-periodic time dependent perturbations is developped. If the unperturbed energy operator has a discrete spectrum and under finite Diophantine conditions, an effective Floquet Hamiltonian with pure point spectrum is constructed. For analytic perturbations, the effective time evolution remains close to the original Floquet evolution up to exponentially long times. We also treat the case of differentiable perturbations.
Diffusive energy growth in classical and quantum driven oscillators
1991
We study the long-time stability of oscillators driven by time-dependent forces originating from dynamical systems with varying degrees of randomness. The asymptotic energy growth is related to ergodic properties of the dynamical system: when the autocorrelation of the force decays sufficiently fast one typically obtains linear diffusive growth of the energy. For a system with good mixing properties we obtain a stronger result in the form of a central limit theorem. If the autocorrelation decays slowly or does not decay, the behavior can depend on subtle properties of the particular model. We study this dependence in detail for a family of quasiperiodic forces. The solution involves the ana…
Control of hysteretic instability in rotating machinery by elastic suspension systems subject to dry and viscous friction
2010
Abstract Most of the undesired whirling motions of rotating machines can be efficiently reduced by supporting journal boxes elastically and controlling their movement by viscous dampers or by dry friction surfaces normal to the shaft axis, which rub against the frame. In the case of dry dampers, resonance ranges of the floating support configuration can be easily cut off by planning a motionless adhesive state of the friction surfaces. On the contrary, the dry friction contact must change automatically into sliding conditions when the fixed support resonances are to be feared. Moreover, the whirl amplitude can be restrained throughout the speed range by a proper choice of the suspension-to-…
Floquet spectrum for two-level systems in quasiperiodic time-dependent fields
1992
We study the time evolution ofN-level quantum systems under quasiperiodic time-dependent perturbations. The problem is formulated in terms of the spectral properties of a quasienergy operator defined in an enlarged Hilbert space, or equivalently of a generalized Floquet operator. We discuss criteria for the appearance of pure point as well as continuous spectrum, corresponding respectively to stable quasiperiodic dynamics and to unstable chaotic behavior. We discuss two types of mechanisms that lead to instability. The first one is due to near resonances, while the second one is of topological nature and can be present for arbitrary ratios between the frequencies of the perturbation. We tre…
Floquet theory: exponential perturbative treatment
2001
We develop a Magnus expansion well suited for Floquet theory of linear ordinary differential equations with periodic coefficients. We build up a recursive scheme to obtain the terms in the new expansion and give an explicit sufficient condition for its convergence. The method and formulae are applied to an illustrative example from quantum mechanics.
Numerical investigation of optical heartbeats with external driving forces
2010
The role of harmonic and random external forces in a phenomenological nonlinear model of optical heartbeats is investigated. External forces trigger damped oscillations at the natural frequency of the system and higher harmonics. The numerical results are compared with experimental ones.
Asymptotic regime in N random interacting species
2005
The asymptotic regime of a complex ecosystem with \emph{N}random interacting species and in the presence of an external multiplicative noise is analyzed. We find the role of the external noise on the long time probability distribution of the i-th density species, the extinction of species and the local field acting on the i-th population. We analyze in detail the transient dynamics of this field and the cavity field, which is the field acting on the $i^{th}$ species when this is absent. We find that the presence or the absence of some population give different asymptotic distributions of these fields.
Resonant activation in piecewise linear asymmetric potentials
2011
7 páginas, 8 figuras.-- PACS number(s): 05.40.−a, 05.45.−a, 02.50.Ey
Anomalous wave structure in magnetized materials described by non-convex equations of state
2014
Agraïments: Institute for Pure and Applied Mathematics (UCLA) 2012 program on "Computational Methods in High Energy Density Plasmas. We analyze the anomalous wave structure appearing in flow dynamics under the influence of magnetic field in materials described by non-ideal equations of state. We consider the system of magnetohydrodynamics equations closed by a general equation of state (EOS) and propose a complete spectral decomposition of the fluxes that allows us to derive an expression of the nonlinearity factor as the mathematical tool to determine the nature of the wave phenomena. We prove that the possible formation of non-classical wave structure is determined by both the thermodynam…
Efficient protocol for qubit initialization with a tunable environment
2017
We propose an efficient qubit initialization protocol based on a dissipative environment that can be dynamically adjusted. Here the qubit is coupled to a thermal bath through a tunable harmonic oscillator. On-demand initialization is achieved by sweeping the oscillator rapidly into resonance with the qubit. This resonant coupling with the engineered environment induces fast relaxation to the ground state of the system, and a consecutive rapid sweep back to off resonance guarantees weak excess dissipation during quantum computations. We solve the corresponding quantum dynamics using a Markovian master equation for the reduced density operator of the qubit-bath system. This allows us to optim…