2,353 research outputs found
Nondiffracting Accelerating Waves: Weber waves and parabolic momentum
Diffraction is one of the universal phenomena of physics, and a way to
overcome it has always represented a challenge for physicists. In order to
control diffraction, the study of structured waves has become decisive. Here,
we present a specific class of nondiffracting spatially accelerating solutions
of the Maxwell equations: the Weber waves. These nonparaxial waves propagate
along parabolic trajectories while approximately preserving their shape. They
are expressed in an analytic closed form and naturally separate in forward and
backward propagation. We show that the Weber waves are self-healing, can form
periodic breather waves and have a well-defined conserved quantity: the
parabolic momentum. We find that our Weber waves for moderate to large values
of the parabolic momenta can be described by a modulated Airy function. Because
the Weber waves are exact time-harmonic solutions of the wave equation, they
have implications for many linear wave systems in nature, ranging from
acoustic, electromagnetic and elastic waves to surface waves in fluids and
membranes.Comment: 10 pages, 4 figures, v2: minor typos correcte
Solution to the Landau-Zener problem via Susskind-Glogower operators
We show that, by means of a right-unitary transformation, the fully quantized
Landau-Zener Hamiltonian in the weak-coupling regime may be solved by using
known solutions from the standard Landau-Zener problem. In the strong-coupling
regime, where the rotating wave approximation is not valid, we show that the
quantized Landau-Zener Hamiltonian may be diagonalized in the atomic basis by
means of a unitary transformation; hence allowing numerical solutions for the
few photons regime via truncation.Comment: 6 pages, 5 figure
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