1,089 research outputs found
Localization of eigenstates in a modified Tomonaga-Luttinger model
We study the localization in the Hilbert space of a modified
Tomonaga-Luttinger model. For the standard version of this model, the states
are found to be extended in the basis of Slater determinants, representing the
eigenstates of the non-interacting system. The linear dispersion which leads to
the fact that these eigenstates are extended in the modified model is replaced
by one with random level spacings modeling the complicated one-particle spectra
of realistic models. The localization properties of the eigenstates are
studied. The interactions are simplified and an effective one-dimensional Lloyd
model is obtained. The effects of many-body energy correlations are studied
numerically. The eigenstates of the system are found to be localized in Fock
space for any strength of the interactions, but the localization is not
exponential.Comment: 19 pages, 7 figure
Virtual Frame Technique: Ultrafast Imaging with Any Camera
Many phenomena of interest in nature and industry occur rapidly and are
difficult and cost-prohibitive to visualize properly without specialized
cameras. Here we describe in detail the Virtual Frame Technique (VFT), a
simple, useful, and accessible form of compressed sensing that increases the
frame acquisition rate of any camera by several orders of magnitude by
leveraging its dynamic range. VFT is a powerful tool for capturing rapid
phenomenon where the dynamics facilitate a transition between two states, and
are thus binary. The advantages of VFT are demonstrated by examining such
dynamics in five physical processes at unprecedented rates and spatial
resolution: fracture of an elastic solid, wetting of a solid surface, rapid
fingerprint reading, peeling of adhesive tape, and impact of an elastic
hemisphere on a hard surface. We show that the performance of the VFT exceeds
that of any commercial high speed camera not only in rate of imaging but also
in field of view, achieving a 65MHz frame rate at 4MPx resolution. Finally, we
discuss the performance of the VFT with several commercially available
conventional and high-speed cameras. In principle, modern cell phones can
achieve imaging rates of over a million frames per second using the VFT.Comment: 7 Pages, 4 Figures, 1 Supplementary Vide
A model for the fragmentation kinetics of crumpled thin sheets
As a confined thin sheet crumples, it spontaneously segments into flat facets
delimited by a network of ridges. Despite the apparent disorder of this
process, statistical properties of crumpled sheets exhibit striking
reproducibility. Experiments have shown that the total crease length accrues
logarithmically when repeatedly compacting and unfolding a sheet of paper.
Here, we offer insight to this unexpected result by exploring the
correspondence between crumpling and fragmentation processes. We identify a
physical model for the evolution of facet area and ridge length distributions
of crumpled sheets, and propose a mechanism for re-fragmentation driven by
geometric frustration. This mechanism establishes a feedback loop in which the
facet size distribution informs the subsequent rate of fragmentation under
repeated confinement, thereby producing a new size distribution. We then
demonstrate the capacity of this model to reproduce the characteristic
logarithmic scaling of total crease length, thereby supplying a missing
physical basis for the observed phenomenon.Comment: 11 pages, 7 figures (+ Supplemental Materials: 15 pages, 9 figures);
introduced a simpler approximation to model, key results unchanged; added
references, expanded supplementary information, corrected Fig. 2 and revised
Figs. 4 and 7 for clearer presentation of result
- …