747 research outputs found
Classical Diffusion of a quantum particle in a noisy environment
We study the spreading of a quantum-mechanical wavepacket in a
one-dimensional tight-binding model with a noisy potential, and analyze the
emergence of classical diffusion from the quantum dynamics due to decoherence.
We consider a finite correlation time of the noisy environment, and treat the
system by utilizing the separation of fast (dephasing) and slow (diffusion)
processes. We show that classical diffusive behavior emerges at long times, and
we calculate analytically the dependence of the classical diffusion coefficient
on the noise magnitude and correlation time. This method provides a general
solution to this problem for arbitrary conditions of the noisy environment. The
results are relevant to a large variety of physical systems, from electronic
transport in solid state physics, to light transmission in optical devices,
diffusion of excitons, and quantum computation
A method for dense packing discovery
The problem of packing a system of particles as densely as possible is
foundational in the field of discrete geometry and is a powerful model in the
material and biological sciences. As packing problems retreat from the reach of
solution by analytic constructions, the importance of an efficient numerical
method for conducting \textit{de novo} (from-scratch) searches for dense
packings becomes crucial. In this paper, we use the \textit{divide and concur}
framework to develop a general search method for the solution of periodic
constraint problems, and we apply it to the discovery of dense periodic
packings. An important feature of the method is the integration of the unit
cell parameters with the other packing variables in the definition of the
configuration space. The method we present led to improvements in the
densest-known tetrahedron packing which are reported in [arXiv:0910.5226].
Here, we use the method to reproduce the densest known lattice sphere packings
and the best known lattice kissing arrangements in up to 14 and 11 dimensions
respectively (the first such numerical evidence for their optimality in some of
these dimensions). For non-spherical particles, we report a new dense packing
of regular four-dimensional simplices with density
and with a similar structure to the densest known tetrahedron packing.Comment: 15 pages, 5 figure
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