We study the effect of a strong, oscillating driving field on the dynamics of ultracold bosons held in an optical lattice. Modeling the system as a Bose-Hubbard model, we show how the driving field can be used to produce and maintain a coherent atomic current by controlling the phase of the intersite tunneling processes. We investigate both the stroboscopic and time-averaged behavior using Floq...

First we develop the theory of reduced instability in order to analyze stability of bifurcating solutions via the Liapunov{Schmidt reduction. Next, this theory is generalized to cover sideband instabilities using a Floquet ansatz. The method is applied to roll patterns in the Swift{Hohenberg equation which serves as a model for pattern formation. We analyze the stability problem of small rolls ...

Avoided crossings are common in the quasienergy spectra of strongly driven nonlinear quantum wells. In this paper we examine the sinusoidally driven particle in a square potential well to show that avoided crossings can alter the structure of Floquet states in this system. Two types of avoided crossings are identi ed: one type leads only to temporary changes (as a function of driving eld streng...

A recently proposed theoretical framework for the description of electronic quantum friction constant-velocity nuclear projectiles traversing periodic crystals is here implemented using a local basis representation. The theory requires change reference frame to that projectile, and set transformation target functions gliding presented, which time-periodic but does not displace in space with res...

This paper deals with the linear system x′ = A(t)x with A(t) being a 2× 2 matrix. The anti-diagonal components of A(t) are assumed to be periodic, but the diagonal components are not necessarily periodic. Our concern is to establish sufficient conditions for the zero solution to be attractive. Floquet theory is of no use in solving our problem, because not all components are periodic. Another a...

We provide an elementary approach to integrable systems associated with hyperelliptic curves of infinite genus. In particular, we explore the extent to which the classical Burchnall-Chaundy theory generalizes in the infinite genus limit, and systematically study the effect of Darboux transformations for the KdV hierarchy on such infinite genus curves. Our approach applies to complex-valued peri...

Quantum mechanics predicts that certain stationary potentials can sustain bound states with an energy buried in the continuous spectrum of scattered states, the so-called bound states in the continuum (BIC). Originally regarded as mathematical curiosities, BIC have found an increasing interest in recent years, particularly in quantum and classical transport of matter and optical waves in mesosc...