2,841 research outputs found
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
An equivalence relation of boundary/initial conditions, and the infinite limit properties
The 'n-equivalences' of boundary conditions of lattice models are introduced
and it is derived that the models with n-equivalent boundary conditions result
in the identical free energy. It is shown that the free energy of the
six-vertex model is classified through the density of left/down arrows on the
boundary. The free energy becomes identical to that obtained by Lieb and
Sutherland with the periodic boundary condition, if the density of the arrows
is equal to 1/2. The relation to the structure of the transfer matrix and a
relation to stochastic processes are noted.Comment: 6 pages with a figure, no change but the omitted figure is adde
On the flux phase conjecture at half-filling: an improved proof
We present a simplification of Lieb's proof of the flux phase conjecture for
interacting fermion systems -- such as the Hubbard model --, at half filling on
a general class of graphs. The main ingredient is a procedure which transforms
a class of fermionic Hamiltonians into reflection positive form. The method can
also be applied to other problems, which we briefly illustrate with two
examples concerning the model and an extended Falicov-Kimball model.Comment: 23 pages, Latex, uses epsf.sty to include 3 eps figures, to appear in
J. Stat. Phys., Dec. 199
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
Polarization of interacting bosons with spin
We demonstrate rigorously that in the absence of explicit spin-dependent
forces one of the ground states of interacting bosons with spin is always fully
polarized -- however complicated the many-body interaction potential might be.
Depending on the particle spin, the polarized ground state will generally be
degenerate with other states, but one can specify the exact degeneracy. For T>0
the magnetization and susceptibility necessarily exceed that of a pure
paramagnet. These results are relevant to recent experiments exploring the
relation between triplet superconductivity and ferromagnetism, and the
Bose-Einstein condensation of atoms with spin. They eliminate the possibility,
raised in some theoretical speculations, that the ground state or positive
temperature state might be antiferromagnetic.Comment: v4: as published in PR
Decay of Correlations in Fermi Systems at Non-zero Temperature
The locality of correlation functions is considered for Fermi systems at
non-zero temperature. We show that for all short-range, lattice Hamiltonians,
the correlation function of any two fermionic operators decays exponentially
with a correlation length which is of order the inverse temperature for small
temperature. We discuss applications to numerical simulation of quantum systems
at non-zero temperature.Comment: 3 pages, 0 figure
Effect of electronic interactions on the persistent current in one-dimensional disordered rings
The persistent current is here studied in one-dimensional disordered rings
that contain interacting electrons. We used the density matrix renormalization
group algorithms in order to compute the stiffness, a measure that gives the
magnitude of the persistent currents as a function of the boundary conditions
for different sets of both interaction and disorder characteristics. In
contrast to its non-interacting value, an increase in the stiffness parameter
was observed for systems at and off half-filling for weak interactions and
non-zero disorders. Within the strong interaction limit, the decrease in
stiffness depends on the filling and an analytical approach is developed to
recover the observed behaviors. This is required in order to understand its
mechanisms. Finally, the study of the localization length confirms the
enhancement of the persistent current for moderate interactions when disorders
are present at half-filling. Our results reveal two different regimes, one for
weak and one for strong interactions at and off half-filling.Comment: 16 pages, 21 figures; minor changes (blanks missing, sentences
starting with a mathematical symbol
A One-Dimensional Model for Many-Electron Atoms in Extremely Strong Magnetic Fields: Maximum Negative Ionization
We consider a one-dimensional model for many-electron atoms in strong
magnetic fields in which the Coulomb potential and interactions are replaced by
one-dimensional regularizations associated with the lowest Landau level. For
this model we show that the maximum number of electrons is bounded above by
2Z+1 + c sqrt{B}.
We follow Lieb's strategy in which convexity plays a critical role. For the
case of two electrons and fractional nuclear charge, we also discuss the
critical value at which the nuclear charge becomes too weak to bind two
electrons.Comment: 23 pages, 5 figures. J. Phys. A: Math and General (in press) 199
The ground state of a general electron-phonon Hamiltonian is a spin singlet
The many-body ground state of a very general class of electron-phonon
Hamiltonians is proven to contain a spin singlet (for an even number of
electrons on a finite lattice). The phonons interact with the electronic system
in two different ways---there is an interaction with the local electronic
charge and there is a functional dependence of the electronic hopping
Hamiltonian on the phonon coordinates. The phonon potential energy may include
anharmonic terms, and the electron-phonon couplings and the hopping matrix
elements may be nonlinear functions of the phonon coordinates. If the hopping
Hamiltonian is assumed to have no phonon coordinate dependence, then the ground
state is also shown to be unique, implying that there are no ground-state level
crossings, and that the ground-state energy is an analytic function of the
parameters in the Hamiltonian. In particular, in a finite system any
self-trapping transition is a smooth crossover not accompanied by a
nonanalytical change in the ground state. The spin-singlet theorem applies to
the Su-Schrieffer-Heeger model and both the spin-singlet and uniqueness
theorems apply to the Holstein and attractive Hubbard models as special cases.
These results hold in all dimensions --- even on a general graph without
periodic lattice structure.Comment: 25 pages, no figures, plainte
Ground State Energy of the Low Density Bose Gas
Now that the properties of low temperature Bose gases at low density, ,
can be examined experimentally it is appropriate to revisit some of the
formulas deduced by many authors 4-5 decades ago. One of these is that the
leading term in the energy/particle is , where is
the scattering length. Owing to the delicate and peculiar nature of bosonic
correlations, four decades of research have failed to establish this plausible
formula rigorously. The only known lower bound for the energy was found by
Dyson in 1957, but it was 14 times too small. The correct bound is proved here.Comment: 4 pages, Revtex, reference 12 change
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