2,693 research outputs found
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
, 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 . 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 -electron system in a
confining potential ( is a coupling constant) and a homogeneous
magnetic field is studied in the high density limit , with 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 varies as : A 2D Thomas-Fermi (TF) theory applies
in the case ; if the correct limit theory
is a modified -dependent TF model, and the case is described
by a ``classical'' continuum electrostatic theory. For homogeneous potentials
this last model describes also the weak coupling limit for arbitrary
. 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 for all values of using diagonalizations of 12-site (20-site)
chain segm ents. For dimerized chains the dimerization order parameter as a
function of the onsite repulsion interaction has a maximum at nonzero
values of , if the electron-phonon coupling is lower than a critical
value . The critical value is found with high accuracy to be
. For smaller values of the position of the maximum of is
approximately , and rapidly tends to zero as approaches 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
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