Quasilocalized states of self stress in packing-derived networks

States of self stress (SSS) are assignments of forces on the edges of a network that satisfy mechanical equilibrium in the absence of external forces. In this work we show that a particular class of quasilocalized SSS in packing-derived networks, first introduced in [D. M. Sussman, C. P. Goodrich, and A. J. Liu, Soft Matter 12, 3982 (2016)], are characterized by a lengthscale $\ell_c$ that scales as $1/\sqrt{z_c-z}$ where $z$ is the mean connectivity of the network, and $z_c\!\equiv\!4$ is the Maxwell threshold in two dimensions, at odds with previous claims. Our results verify the previously proposed analogy between quasilocalized SSS and the mechanical response to a local dipolar force in random networks of relaxed Hookean springs. We show that the normalization factor that distinguishes between quasilocalized SSS and the response to a local dipole constitutes a measure of the mechanical coupling of the forced spring to the elastic network in which it is embedded. We further demonstrate that the lengthscale that characterizes quasilocalized SSS does not depend on its associated degree of mechanical coupling, but instead only on the network connectivity.Comment: 8 pages, 4 figure

Fathers of hospitalized schizophrenic patients

Thesis (M.S.)--Boston Universit

One-Dimensional Transport of Ultracold Bosons

Advances in cooling and trapping of atoms have enabled unprecedented experimental control of many-body quantum systems. This led to the observation of numerous quantum phenomena, important for fundamental science, indispensable for high-precision simulations of condensed-matter systems and promising for technological applications. However, transport measurements in neutral quantum gases are still in their infancy in contrast to the central role they play in electronics. In these lectures, after reviewing nascent experiments on quantum fermionic transport, I will focus on our theoretical prediction sand the possibility of experimental observations of qualitatively new phenomena in transport of ultracold bosons which do not have a direct counterpart in quantum electronic transport in condensed matter systems. The description of this transport is based on the Luttinger liquid (LL) theory. So in the first part of the lectures I will introduce main concepts of the LL based on the functional bosonisation approach.Comment: Lecture notes for 13th International School on Theoretical Physics "Symmetry and Structural Properties of Condensed Matter", Sep 2018, Rzesz\'ow, Polan