Entanglement Entropy and Full Counting Statistics for 2d2d-Rotating Trapped Fermions

We consider $N$ non-interacting fermions in a $2d$ harmonic potential of trapping frequency $\omega$ and in a rotating frame at angular frequency $\Omega$, with $0<\omega - \Omega\ll \omega$. At zero temperature, the fermions are in the non-degenerate lowest Landau level and their positions are in one to one correspondence with the eigenvalues of an $N\times N$ complex Ginibre matrix. For large $N$, the fermion density is uniform over the disk of radius $\sqrt{N}$ centered at the origin and vanishes outside this disk. We compute exactly, for any finite $N$, the R\'enyi entanglement entropy of order $q$, $S_q(N,r)$, as well as the cumulants of order $p$, $\langle{N_r^{p}}\rangle_c$, of the number of fermions $N_r$ in a disk of radius $r$ centered at the origin. For $N \gg 1$, in the (extended) bulk, i.e., for $0 < r/\sqrt{N} < 1$, we show that $S_q(N,r)$ is proportional to the number variance ${\rm Var}\,(N_r)$, despite the non-Gaussian fluctuations of $N_r$. This relation breaks down at the edge of the fermion density, for $r \approx \sqrt{N}$, where we show analytically that $S_q(N,r)$ and ${\rm Var}\,(N_r)$ have a different $r$-dependence.Comment: 6 pages + 7 pages (Supplementary material), 2 Figure

Polarization of the nuclear surface in deformed nuclei

The density profiles of around 750 nuclei are analyzed using the Skyrme energy density functional theory. Among them, more than 350 nuclei are found to be deformed. In addition to rather standard properties of the density, we report a non-trivial behavior of the nuclear diffuseness as the system becomes more and more deformed. Besides the geometric effects expected in rigid body, the diffuseness acquires a rather complex behavior leading to a reduction of the diffuseness along the main axis of deformation simultaneously with an increase of the diffuseness along the other axis. The possible isospin dependence of this polarization is studied. This effect, that is systematically seen in medium- and heavy-nuclei, can affect the nuclear dynamical properties. A quantitative example is given with the fusion barrier in the $^{40}$Ca+ $^{238}$U reaction.Comment: 8 pages, 13 figure

A study of the impact of weathering upon the minmal force required to fracture bone

Thesis (M.S.)--Boston UniversityThis project examined the effects of weathering processes on the minimal force required to fracture long bones exposed in a coastal microhabitat located in Southeastern Massachusetts, U.S.A. The experimental remains consisted of isolated white-tailed deer (Odocoileus virginianus) long bones as a proxy for human and other large vertebrate remains. The sample contained both raw (unprocessed) and boiled (processed) bones, to mimic forensic and archaeological settings, respectively. This study was conducted over a period of nine months, during which stages of weathering and breaking force of bone were recorded to establish if there is a correlation between weathering processes and the minimal force required to fracture bone. The bones were removed from the microhabitat at monthly intervals and fractured using a bone-breaking apparatus that measures force. It was hypothesized that the weathering processes in this microenvironment will weaken the bone and therefore have an impact on different fracture attributes. Studying certain fracture attributes, such as force required to fracture and fracture morphology, will provide more information regarding the impact of weathering upon bone biomechanics and subsequently may be of assistance in determining the postmortem interval. Examining fracture characteristics of the exposed bones will offer a comparison between perimortem and postmortem breakage patterns in exposed bones. Additionally, the weathering data collected were micro- habitat specific. This study confirmed the hypothesis and concluded that the main effect of exposure time to weathering elements on the minimum force required to fracture long bones was significant and influenced several of the fracture characteristics defined by Wheatley (2008). The length of exposure had an effect on texture of the fracture surface, the fracture angle produced, and the number of fragments produced. Additionally, although the results were not statistically significant, analysis of the shape of broken ends and the presence of fracture lines displayed a trend relative to the length of exposure. The type of fractures produced did not show a statistically significant relationship to the length of exposure time. Although a portion of the animal bone sample was processed and juvenile, neither processing nor age was found to significantly affect the force required to fracture bone nor did these factors impact the type of fracture characteristics produced in this study

Non-Markovian dynamics with fermions

Employing the quadratic fermionic Hamiltonians for the collective and internal subsystems with a linear coupling, we studied the role of fermionic statistics on the dynamics of the collective motion. The transport coefficients are discussed as well as the associated fluctuation-dissipation relation. Due to different nature of the particles, the path to equilibrium is slightly affected. However, in the weak coupling regime, the time-scale for approaching equilibrium is found to be globally unchanged. The Pauli-blocking effect can modify the usual picture in open quantum system. In some limits, contrary to boson, this effect can strongly hinder the influence of the bath by blocking the interacting channels.Comment: 13 pages, 6 figures. Submitted to PR

Extremes of 2d2d Coulomb gas: universal intermediate deviation regime

In this paper, we study the extreme statistics in the complex Ginibre ensemble of $N \times N$ random matrices with complex Gaussian entries, but with no other symmetries. All the $N$ eigenvalues are complex random variables and their joint distribution can be interpreted as a $2d$ Coulomb gas with a logarithmic repulsion between any pair of particles and in presence of a confining harmonic potential $v(r) \propto r^2$. We study the statistics of the eigenvalue with the largest modulus $r_{\max}$ in the complex plane. The typical and large fluctuations of $r_{\max}$ around its mean had been studied before, and they match smoothly to the right of the mean. However, it remained a puzzle to understand why the large and typical fluctuations to the left of the mean did not match. In this paper, we show that there is indeed an intermediate fluctuation regime that interpolates smoothly between the large and the typical fluctuations to the left of the mean. Moreover, we compute explicitly this "intermediate deviation function" (IDF) and show that it is universal, i.e. independent of the confining potential $v(r)$ as long as it is spherically symmetric and increases faster than $\ln r^2$ for large $r$ with an unbounded support. If the confining potential $v(r)$ has a finite support, i.e. becomes infinite beyond a finite radius, we show via explicit computation that the corresponding IDF is different. Interestingly, in the borderline case where the confining potential grows very slowly as $v(r) \sim \ln r^2$ for $r \gg 1$ with an unbounded support, the intermediate regime disappears and there is a smooth matching between the central part and the left large deviation regime.Comment: 36 pages, 7 figure