相关论文: Quantum resonances and analysis of the survival am…

Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…

Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two…

Non-linear parametric resonances occur frequently in nature. Here we summarize how they can be studied by means of perturbative methods. We show in particular how resonances can affect the motion of a test particle orbiting in the vicinity…

We study the quantum remnant of a scalar field protected by the uncertainty principle. The quantum remnant that survived the later stage of evolution of the universe may provide dark energy and dark matter depending on the potential. Though…

Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…

This paper considers the question of global in time existence and asymptotic behavior of small-data solutions of nonlinear dispersive equations with a real potential $V$. The main concern is treating nonlinearities whose degree is low…

In this article we investigate no-resonance conditions for quantum many body chaotic systems and random matrix models. No-resonance conditions are properties of the spectrum of a model, usually employed as a theoretical tool in the analysis…

We consider the one-dimensional nonlinear Schr\"odinger equation with Dirichlet boundary conditions in the fully resonant case (absence of the zero-mass term). We investigate conservation of small amplitude periodic-solutions for a large…

The inexactness of the time-dependent Schr\"odinger equation of a charged particle in an external electromagnetic field is discussed in terms of the damping effect of the radiation. A possible improvement is to add a nonlinear term…

Non-Markovian effects in quantum evolution appear when the system is strongly coupled to the environment and interacts with it for long periods of time. To include memory effects in the master equations, one usually incorporates time-local…

An important class of resonance problems involves the study of perturbations of systems having embedded eigenvalues in their continuous spectrum. Problems with this mathematical structure arise in the study of many physical systems, e.g.…

Nonlinear modifications of quantum mechanics generically lead to nonlocal effects which violate relativistic causality. We study these effects using the functional Schrodinger equation for quantum fields and identify a type of nonlocality…

We revisit the time-adiabatic theorem of quantum mechanics and show that it can be extended to weakly nonlinear situations, that is to nonlinear Schroedinger equations in which either the nonlinear coupling constant or, equivalently, the…

We consider the dynamics of quantum systems which possess stationary states as well as slowly decaying, metastable states arising from the perturbation of bound states. We give a decomposition of the propagator into a sum of a stationary…

With a choice of boundary conditions for solutions of the Schr\"odinger equation, state vectors and density operators even for closed systems evolve asymmetrically in time. For open systems, standard quantum mechanics consequently predicts…

Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…

In this article we prove that for a large class of operators, including Schroedinger operators, with hyperbolic classical flows, the smallness of dimension of the trapped set implies that there is a gap between the resonances and the real…

We consider a nonlinear semi-classical Schrodinger equation for which it is known that quadratic oscillations lead to focusing at one point, described by a nonlinear scattering operator. If the initial data is an energy bounded sequence, we…

The linearity of quantum mechanics leads, under the assumption that the wave function offers a complete description of reality, to grotesque situations famously known as Schroedinger's cat. Ways out are either adding elements of reality or…

We investigate quantum persistence by analyzing amplitude and phase fluctuations of the wave function governed by the time-dependent free-particle Schr\"odinger equation. The quantum system is initialized with local random uncorrelated…