27,203 research outputs found
Ermakov approach for the one-dimensional Helmholtz Hamiltonian
For the one-dimensional Helmholtz equation we write the corresponding
time-dependent Helmholtz Hamiltonian in order to study it as an Ermakov problem
and derive geometrical angles and phases in this contextComment: 6 pages, LaTe
The quantum Rabi model in a superfluid Bose-Einstein condensate
We propose a quantum simulation of the quantum Rabi model in an atomic
quantum dot, which is a single atom in a tight optical trap coupled to the
quasiparticle modes of a superfluid Bose-Einstein condensate. This widely
tunable setup allows to simulate the ultrastrong coupling regime of
light-matter interaction in a system which enjoys an amenable characteristic
timescale, paving the way for an experimental analysis of the transition
between the Jaynes-Cummings and the quantum Rabi dynamics using cold-atom
systems. Our scheme can be naturally extended to simulate multi-qubit quantum
Rabi models. In particular, we discuss the appearance of effective two-qubit
interactions due to phononic exchange, among other features.Comment: Improved version and references adde
On the differential geometry of curves in Minkowski space
We discuss some aspects of the differential geometry of curves in Minkowski
space. We establish the Serret-Frenet equations in Minkowski space and use them
to give a very simple proof of the fundamental theorem of curves in Minkowski
space. We also state and prove two other theorems which represent Minkowskian
versions of a very known theorem of the differential geometry of curves in
tridimensional Euclidean space. We discuss the general solution for torsionless
paths in Minkowki space. We then apply the four-dimensional Serret-Frenet
equations to describe the motion of a charged test particle in a constant and
uniform electromagnetic field and show how the curvature and the torsions of
the four-dimensional path of the particle contain information on the
electromagnetic field acting on the particle.Comment: 10 pages. Typeset using REVTE
A retarded coupling approach to intermolecular interactions
A wide range of physical phenomena such as optical binding and resonance energy transfer involve electronic coupling between adjacent molecules. A quantum electrodynamical description of these intermolecular interactions reveals the presence of retardation effects. The clarity of the procedure associated with the construction of the quantum amplitudes and the precision of the ensuing results for observable energies and rates are widely acknowledged. However, the length and complexity of the derivations involved in such quantum electrodynamical descriptions increase rapidly with the order of the process under study. Whether through the use of time-ordering approaches, or the more expedient state-sequence method, time-consuming calculations cannot usually be bypassed. A simple and succinct method is now presented, which provides for a direct and still entirely rigorous determination of the quantum electrodynamical amplitudes for processes of arbitrarily high order. Using the approach, new results for optical binding in two- and three-particle systems are secured and discussed
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