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Bloch oscillations and Landau-Zener tunneling are ubiquitous phenomena which are sustained by a band-gap spectrum of a periodic Hamiltonian and can be observed in dynamics of a quantum particle or a wavepacket in a periodic potential under…
The generalised Boltzmann equation which treats the combined localised and delocalised nature of transport present in certain materials is extended to accommodate time-dependent fields. In particular, AC fields are shown to be a means to…
A vortex in a superfluid gas inside an optical lattice can behave as a massive particle moving in a periodic potential and exhibiting quantum properties. In this Letter we discuss these properties and show that the excitation of vortex…
Light transport in periodic waveguides coupled to a two-level atom is investigated. By using optical Bloch equations and a photonic modal formalism, we derive semi-analytical expressions for the scattering matrix of one atom trapped in a…
We consider the quantization of a general spatially homogeneous space-time belonging to an arbitrary but fixed Class A Bianchi type. Exploiting the information furnished by the quantum version of the momentum constraints, we use as…
We study the homogenization of a stochastic Schr\"odinger equation with a large periodic potential in solid state physics. Denoting by $\varepsilon$ the period, the potential is scaled as $\varepsilon^{-2}$. Under a generic assumption on…
Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is…
The effect of the electrodynamic forces on a charged particle in a propagating plane electromagnetic wave is investigated. First it is pointed out that for constant fields fulfilling the radiation condition there will be an acceleration in…
We consider the evolution of a quantum particle hopping on a cubic lattice in any dimension and subject to a potential consisting of a periodic part and a random part that fluctuates stochastically in time. If the random potential evolves…
The Bloch equation is the fundamental dynamical model applicable to arbitrary two-level systems. Analytical solutions to date are incomplete for a number of reasons that motivate further investigation. The solution obtained here for the…
The paper contains mathematical justification of basic facts concerning the Brownian motor theory. The homogenization theorems are proved for the Brownian motion in periodic tubes with a constant drift. The study is based on an application…
There are considered some corollaries of certain hypotheses on the observation process of microphenomena. We show that an enlargement of the phase space and of its motion group and an account for the diffusion motions of microsystems in the…
We demonstrate that nonlinearity may play a constructive role in supporting Bloch oscillations in a model which is discrete, in one dimension and continuous in the orthogonal one. The model can be experimentally realized in several fields…
As is well known, there exist some Lorentz breaking scenarios which explain the smallness of the cosmological constant in the present era. An important aspect to analyze is the propagation of gravitational waves and the screening or…
We give simple conditions implying the well-posedness of the Cauchy problem for the propagation of classical scalar fields in general (n+2)-dimensional static and spherically symmetric spacetimes. They are related to properties of the…
The acceleration theorem for Bloch electrons in a homogenous external field is usually presented using quasiclassical arguments. In quantum mechanical versions the Heisenberg equations of motion for an operator $\hat {\vec k}(t)$ are…
We study the large-scale dynamics of charged particles in a rapidly oscillating field and formulate its classical and quantum effective theory description. The high-order perturbative results for the effective action are presented.…
We present a dynamical framework for modeling the motion of point-like charged particles, with or without mass, in general external electromagnetic fields. A key feature of this formulation is the treatment of time coordinate as a dynamical…
Band theory for partially coherent light is introduced by using the formalism of second-order classical coherence theory under paraxial approximation. It is demonstrated that the cross-spectral density function, describing correlations…
A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…