Ground State Asymptotics of a Dilute, Rotating Gas

We investigate the ground state properties of a gas of interacting particles confined in an external potential in three dimensions and subject to rotation around an axis of symmetry. We consider the so-called Gross-Pitaevskii (GP) limit of a dilute gas. Analyzing both the absolute and the bosonic ground state of the system we show, in particular, their different behavior for a certain range of parameters. This parameter range is determined by the question whether the rotational symmetry in the minimizer of the GP functional is broken or not. For the absolute ground state, we prove that in the GP limit a modified GP functional depending on density matrices correctly describes the energy and reduced density matrices, independent of symmetry breaking. For the bosonic ground state this holds true if and only if the symmetry is unbroken.Comment: LaTeX2e, 37 page

Gradient corrections for semiclassical theories of atoms in strong magnetic fields

This paper is divided into two parts. In the first one the von Weizs\"acker term is introduced to the Magnetic TF theory and the resulting MTFW functional is mathematically analyzed. In particular, it is shown that the von Weizs\"acker term produces the Scott correction up to magnetic fields of order $B \ll Z^2$, in accordance with a result of V. Ivrii on the quantum mechanical ground state energy. The second part is dedicated to gradient corrections for semiclassical theories of atoms restricted to electrons in the lowest Landau band. We consider modifications of the Thomas-Fermi theory for strong magnetic fields (STF), i.e. for $B \ll Z^3$. The main modification consists in replacing the integration over the variables perpendicular to the field by an expansion in angular momentum eigenfunctions in the lowest Landau band. This leads to a functional (DSTF) depending on a sequence of one-dimensional densities. For a one-dimensional Fermi gas the analogue of a Weizs\"acker correction has a negative sign and we discuss the corresponding modification of the DSTF functional.Comment: Latex2e, 36 page

Extensions of Lieb's concavity theorem

The operator function (A,B)\to\tr f(A,B)(K^*)K, defined on pairs of bounded self-adjoint operators in the domain of a function f of two real variables, is convex for every Hilbert Schmidt operator K, if and only if f is operator convex. As a special case we obtain a new proof of Lieb's concavity theorem for the function (A,B)\to\tr A^pK^*B^{q}K, where p and q are non-negative numbers with sum p+q\le 1. In addition, we prove concavity of the operator function (A,B)\to \tr(A(A+\mu_1)^{-1}K^* B(B+\mu_2)^{-1}K) on its natural domain D_2(\mu_1,\mu_2), cf. Definition 4.1Comment: The format of one reference is changed such that CiteBase can identify i

The Ground States of Large Quantum Dots in Magnetic Fields

The quantum mechanical ground state of a 2D $N$-electron system in a confining potential $V(x)=Kv(x)$ ($K$ is a coupling constant) and a homogeneous magnetic field $B$ is studied in the high density limit $N\to\infty$, $K\to \infty$ with $K/N$ fixed. It is proved that the ground state energy and electronic density can be computed {\it exactly} in this limit by minimizing simple functionals of the density. There are three such functionals depending on the way $B/N$ varies as $N\to\infty$: A 2D Thomas-Fermi (TF) theory applies in the case $B/N\to 0$; if $B/N\to{\rm const.}\neq 0$ the correct limit theory is a modified $B$-dependent TF model, and the case $B/N\to\infty$ is described by a ``classical'' continuum electrostatic theory. For homogeneous potentials this last model describes also the weak coupling limit $K/N\to 0$ for arbitrary $B$. Important steps in the proof are the derivation of a new Lieb-Thirring inequality for the sum of eigenvalues of single particle Hamiltonians in 2D with magnetic fields, and an estimation of the exchange-correlation energy. For this last estimate we study a model of classical point charges with electrostatic interactions that provides a lower bound for the true quantum mechanical energy.Comment: 57 pages, Plain tex, 5 figures in separate uufil

The Role of Blowing Snow in the Activation of Bromine Over First-year Antarctic Sea Ice

It is well known that during polar springtime halide sea salt ions, in particular Br-, are photochemically activated into reactive halogen species (e.g., Br and BrO), where they break down tropospheric ozone. This research investigated the role of blowing snow in transporting salts from the sea ice/snow surface into reactive bromine species in the air. At two different locations over first-year ice in the Ross Sea, Antarctica, collection baskets captured blowing snow at different heights. In addition, sea ice cores and surface snow samples were collected throughout the month-long campaign. Over this time, sea ice and surface snow Br- / Cl- mass ratios remained constant and equivalent to seawater, and only in lofted snow did bromide become depleted relative to chloride. This suggests that replenishment of bromide in the snowpack occurs faster than bromine activation in mid-strength wind conditions (approximately 10 m s−1) or that blowing snow represents only a small portion of the surface snowpack. Additionally, lofted snow was found to be depleted in sulfate and enriched in nitrate relative to surface snow

Semiclassics in the lowest Landau band

This paper deals with the comparison between the strong Thomas-Fermi theory and the quantum mechanical ground state energy of a large atom confined to lowest Landau band wave functions. Using the tools of microlocal semiclassical spectral asymptotics we derive precise error estimates. The approach presented in this paper suggests the definition of a modified strong Thomas-Fermi functional, where the main modification consists in replacing the integration over the variables perpendicular to the magnetic field by an expansion in angular momentum eigenfunctions. The resulting DSTF theory is studied in detail in the second part of the paper.Comment: Latex2e, 31 page

Incremental expansions for Hubbard-Peierls systems

The ground state energies of infinite half-filled Hubbard-Peierls chains are investigated combining incremental expansion with exact diagonalization of finite chain segments. The ground state energy of equidistant infinite Hubbard (Heisenberg) chains is calculated with a relative error of less than $3 \cdot 10^{-3}$ for all values of $U$ using diagonalizations of 12-site (20-site) chain segm ents. For dimerized chains the dimerization order parameter $d$ as a function of the onsite repulsion interaction $U$ has a maximum at nonzero values of $U$, if the electron-phonon coupling $g$ is lower than a critical value $g_c$. The critical value $g_c$ is found with high accuracy to be $g_c=0.69$. For smaller values of $g$ the position of the maximum of $d(U)$ is approximately $3t$, and rapidly tends to zero as $g$ approaches $g_c$ from below. We show how our method can be applied to calculate breathers for the problem of phonon dynamics in Hubbard-Peierls systems.Comment: 4 Pages, 3 Figures, REVTE

A Stronger Subadditivity of Entropy

The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[\rho]= - Tr (\rho \ln \rho) of a density matrix \rho_{123} on the product of three Hilbert spaces satisfies S[\rho_{123}] - S[\rho_{23}] \leq S[\rho_{12}]- S[\rho_2]. We strengthen this to S[\rho_{123}] - S[\rho_{12}] \leq \sum_\alpha n^\alpha (S[\rho_{23}^\alpha ] - S[\rho_2^\alpha ]), where the n^\alpha are weights and the \rho_{23}^\alpha are partitions of \rho_{23}. Correspondingly, there is a strengthening of the theorem that the map A -> Tr \exp[L + \ln A] is concave. As applications we prove some monotonicity and convexity properties of the Wehrl entropy and entropy inequalities for quantum gases.Comment: LaTeX2e, 24 page