4,129 research outputs found
Recent developments in Quantum Monte-Carlo simulations with applications for cold gases
This is a review of recent developments in Monte Carlo methods in the field
of ultra cold gases. For bosonic atoms in an optical lattice we discuss path
integral Monte Carlo simulations with worm updates and show the excellent
agreement with cold atom experiments. We also review recent progress in
simulating bosonic systems with long-range interactions, disordered bosons,
mixtures of bosons, and spinful bosonic systems. For repulsive fermionic
systems determinantal methods at half filling are sign free, but in general no
sign-free method exists. We review the developments in diagrammatic Monte Carlo
for the Fermi polaron problem and the Hubbard model, and show the connection
with dynamical mean-field theory. We end the review with diffusion Monte Carlo
for the Stoner problem in cold gases.Comment: 68 pages, 22 figures, review article; replaced with published versio
A review of Monte Carlo simulations for the Bose-Hubbard model with diagonal disorder
We review the physics of the Bose-Hubbard model with disorder in the chemical
potential focusing on recently published analytical arguments in combination
with quantum Monte Carlo simulations. Apart from the superfluid and Mott
insulator phases that can occur in this system without disorder, disorder
allows for an additional phase, called the Bose glass phase. The topology of
the phase diagram is subject to strong theorems proving that the Bose Glass
phase must intervene between the superfluid and the Mott insulator and implying
a Griffiths transition between the Mott insulator and the Bose glass. The full
phase diagrams in 3d and 2d are discussed, and we zoom in on the insensitivity
of the transition line between the superfluid and the Bose glass in the close
vicinity of the tip of the Mott insulator lobe. We briefly comment on the
established and remaining questions in the 1d case, and give a short overview
of numerical work on related models.Comment: 30 pages, 8 figure
A Petrov type I and generically asymmetric rotating dust family
The general line element corresponding to the family of algebraically
general, gravito-electric, expanding, rotating dust models with one
functionally independent zero-order Riemann invariant is constructed. The
isometry group is at most one-dimensional but generically trivial. It is shown
that the asymmetric solutions with constant ratio of energy density and
vorticity amplitude provide first examples of Petrov type I space-times for
which the Karlhede classification requires the computation of the third
covariant derivative of the Riemann tensor.Comment: 7 pages, irrotational limit case added, several minor errors
correcte
Anti-Newtonian universes do not exist
In a paper by Maartens, Lesame and Ellis (Class. Quant. Grav. 15, 1005) it
was shown that irrotational dust solutions with vanishing electric part of the
Weyl tensor are subject to severe integrability conditions and it was
conjectured that the only such solutions are FLRW spacetimes. In their analysis
the possibility of a cosmological constant Lambda was omitted. The conjecture
is proved, irrespective as to whether Lambda is zero or not, and qualitative
differences with the case of vanishing magnetic Weyl curvature are pointed out.Comment: 16 page
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