13,583 research outputs found

### A new coherent states approach to semiclassics which gives Scott's correction

We introduce new coherent states and use them to prove semi-classical
estimates for Schr\"odinger operators with regular potentials. This can be
further applied to the Thomas-Fermi potential yielding a new proof of the Scott
correction for molecules.Comment: A misprint in the definition of new coherent states correcte

### Singlets and reflection symmetric spin systems

We rigorously establish some exact properties of reflection symmetric spin
systems with antiferromagnetic crossing bonds: At least one ground state has
total spin zero and a positive semidefinite coefficient matrix. The crossing
bonds obey an ice rule. This augments some previous results which were limited
to bipartite spin systems and is of particular interest for frustrated spin
systems.Comment: 11 pages, LaTeX 2

### The 200 MeV Pi+ induced single-nucleon removal from 24Mg

Nuclear gamma-rays in coincidence with outgoing pions or protons following single nucleon removal from Mg-24 by 200 MeV pions (+) were detected with Ge(Li) detectors. Differential cross sections are reported for gamma-rays from the first excited mirror states of Na-23 and Mg-23 in coincidence with positive pions or protons detected in particle telescopes at 30, 60, 90, 120, and 150 deg; angle-integrated absolute cross sections and cross section ratios are calculated. These results are compared with the predictions of a Pauli-blocked plane-wave impulse approximation (PWIA) and the intranuclear cascade (INC) and nucleon charge exchange (NCX) reaction models. The PWIA and the INC calculations generally agree with the angular dependence of the experimental results but not the absolute magnitude. The NCX calculation does not reproduce the observed cross section charge ratios

### Bose-Einstein Condensation and Spontaneous Symmetry Breaking

After recalling briefly the connection between spontaneous symmetry breaking
and off-diagonal long range order for models of magnets a general proof of
spontaneous breaking of gauge symmetry as a consequence of Bose-Einstein
Condensation is presented. The proof is based on a rigorous validation of
Bogoliubov's $c$-number substitution for the ${\bf k}={\bf 0}$ mode operator
$a_{\bf 0}$.Comment: Contribution to the proceedings of the 21st Max Born Symposium,
Wroclaw, Poland, June 26--28, 2006. (References added. To be published in
Reports on Mathematical Physics.

### Proof of Bose-Einstein Condensation for Dilute Trapped Gases

The ground state of bosonic atoms in a trap has been shown experimentally to
display Bose-Einstein condensation (BEC). We prove this fact theoretically for
bosons with two-body repulsive interaction potentials in the dilute limit,
starting from the basic Schroedinger equation; the condensation is 100% into
the state that minimizes the Gross-Pitaevskii energy functional. This is the
first rigorous proof of BEC in a physically realistic, continuum model.Comment: Revised version with some simplifications and clarifications. To
appear in Phys. Rev. Let

### 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

### A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-Dimensional Bose Gas

We consider the ground state properties of an inhomogeneous two-dimensional
Bose gas with a repulsive, short range pair interaction and an external
confining potential. In the limit when the particle number $N$ is large but
$\bar\rho a^2$ is small, where $\bar\rho$ is the average particle density and
$a$ the scattering length, the ground state energy and density are rigorously
shown to be given to leading order by a Gross-Pitaevskii (GP) energy functional
with a coupling constant $g\sim 1/|\ln(\bar\rho a^2)|$. In contrast to the 3D
case the coupling constant depends on $N$ through the mean density. The GP
energy per particle depends only on $Ng$. In 2D this parameter is typically so
large that the gradient term in the GP energy functional is negligible and the
simpler description by a Thomas-Fermi type functional is adequate.Comment: 14 pages, no figures, latex 2e. References, some clarifications and
an appendix added. To appear in Commun. Math. Phy

### Free Energy of a Dilute Bose Gas: Lower Bound

A lower bound is derived on the free energy (per unit volume) of a
homogeneous Bose gas at density $\rho$ and temperature $T$. In the dilute
regime, i.e., when $a^3\rho \ll 1$, where $a$ denotes the scattering length of
the pair-interaction potential, our bound differs to leading order from the
expression for non-interacting particles by the term $4\pi a (2\rho^2 -
[\rho-\rho_c]_+^2)$. Here, $\rho_c(T)$ denotes the critical density for
Bose-Einstein condensation (for the non-interacting gas), and $[ ]_+$ denotes
the positive part. Our bound is uniform in the temperature up to temperatures
of the order of the critical temperature, i.e., $T \sim \rho^{2/3}$ or smaller.
One of the key ingredients in the proof is the use of coherent states to extend
the method introduced in [arXiv:math-ph/0601051] for estimating correlations to
temperatures below the critical one.Comment: LaTeX2e, 53 page

### Stability of Matter in Magnetic Fields

In the presence of arbitrarily large magnetic fields, matter composed of
electrons and nuclei was known to be unstable if $\alpha$ or $Z$ is too large.
Here we prove that matter {\it is stable\/} if $\alpha<0.06$ and
$Z\alpha^2<0.04$.Comment: 10 pages, LaTe

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