323 research outputs found
Beyond Gross-Pitaevskii:local density vs. correlated basis approach for trapped bosons
We study the ground state of a system of Bose hard-spheres trapped in an
isotropic harmonic potential to investigate the effect of the interatomic
correlations and the accuracy of the Gross-Pitaevskii equation. We compare a
local density approximation, based on the energy functional derived from the
low density expansion of the energy of the uniform hard sphere gas, and a
correlated wave function approach which explicitly introduces the correlations
induced by the potential. Both higher order terms in the low density expansion,
beyond Gross-Pitaevskii, and explicit dynamical correlations have effects of
the order of percent when the number of trapped particles becomes similar to
that attained in recent experiments.Comment: Revtex, 2 figure
Collapse of ringlike structures in 2DEGs under tilted magnetic fields
In the quantum Hall regime, the longitudinal resistivity plotted
as a density--magnetic-field () diagram displays ringlike structures
due to the crossings of two sets of spin split Landau levels from different
subbands [e.g., Zhang \textit{et al.}, Phys. Rev. Lett. \textbf{95}, 216801
(2005)]. For tilted magnetic fields, some of these ringlike structures "shrink"
as the tilt angle is increased and fully collapse at . Here we theoretically investigate the topology of these structures
via a non-interacting model for the 2DEG. We account for the inter Landau-level
coupling induced by the tilted magnetic field via perturbation theory. This
coupling results in anti-crossings of Landau levels with parallel spins. With
the new energy spectrum, we calculate the corresponding diagram of
the density of states (DOS) near the Fermi level. We argue that the DOS
displays the same topology as in the diagram. For the
ring with filling factor , we find that the anti-crossings make it
shrink for increasing tilt angles and collapse at a large enough angle. Using
effective parameters to fit the data, we find a collapsing
angle . Despite this factor-of-two discrepancy with
the experimental data, our model captures the essential mechanism underlying
the ring collapse.Comment: 3 pages, 2 figures; Proceedings of the PASPS V Conference Held in
August 2008 in Foz do Igua\c{c}u, Brazi
Beyond Gross-Pitaevskii:local density vs. correlated basis approach for trapped bosons
We study the ground state of a system of Bose hard-spheres trapped in an
isotropic harmonic potential to investigate the effect of the interatomic
correlations and the accuracy of the Gross-Pitaevskii equation. We compare a
local density approximation, based on the energy functional derived from the
low density expansion of the energy of the uniform hard sphere gas, and a
correlated wave function approach which explicitly introduces the correlations
induced by the potential. Both higher order terms in the low density expansion,
beyond Gross-Pitaevskii, and explicit dynamical correlations have effects of
the order of percent when the number of trapped particles becomes similar to
that attained in recent experiments.Comment: Revtex, 2 figure
Pure Stationary States of Open Quantum Systems
Using Liouville space and superoperator formalism we consider pure stationary
states of open and dissipative quantum systems. We discuss stationary states of
open quantum systems, which coincide with stationary states of closed quantum
systems. Open quantum systems with pure stationary states of linear oscillator
are suggested. We consider stationary states for the Lindblad equation. We
discuss bifurcations of pure stationary states for open quantum systems which
are quantum analogs of classical dynamical bifurcations.Comment: 7p., REVTeX
The Time-Energy Uncertainty Relation
The time energy uncertainty relation has been a controversial issue since the
advent of quantum theory, with respect to appropriate formalisation, validity
and possible meanings. A comprehensive account of the development of this
subject up to the 1980s is provided by a combination of the reviews of Jammer
(1974), Bauer and Mello (1978), and Busch (1990). More recent reviews are
concerned with different specific aspects of the subject. The purpose of this
chapter is to show that different types of time energy uncertainty relation can
indeed be deduced in specific contexts, but that there is no unique universal
relation that could stand on equal footing with the position-momentum
uncertainty relation. To this end, we will survey the various formulations of a
time energy uncertainty relation, with a brief assessment of their validity,
and along the way we will indicate some new developments that emerged since the
1990s.Comment: 33 pages, Latex. This expanded version (prepared for the 2nd edition
of "Time in quantum mechanics") contains minor corrections, new examples and
pointers to some additional relevant literatur
The Mathematical Universe
I explore physics implications of the External Reality Hypothesis (ERH) that
there exists an external physical reality completely independent of us humans.
I argue that with a sufficiently broad definition of mathematics, it implies
the Mathematical Universe Hypothesis (MUH) that our physical world is an
abstract mathematical structure. I discuss various implications of the ERH and
MUH, ranging from standard physics topics like symmetries, irreducible
representations, units, free parameters, randomness and initial conditions to
broader issues like consciousness, parallel universes and Godel incompleteness.
I hypothesize that only computable and decidable (in Godel's sense) structures
exist, which alleviates the cosmological measure problem and help explain why
our physical laws appear so simple. I also comment on the intimate relation
between mathematical structures, computations, simulations and physical
systems.Comment: Replaced to match accepted Found. Phys. version, 31 pages, 5 figs;
more details at http://space.mit.edu/home/tegmark/toe.htm
Dark soliton states of Bose-Einstein condensates in anisotropic traps
Dark soliton states of Bose-Einstein condensates in harmonic traps are
studied both analytically and computationally by the direct solution of the
Gross-Pitaevskii equation in three dimensions. The ground and self-consistent
excited states are found numerically by relaxation in imaginary time. The
energy of a stationary soliton in a harmonic trap is shown to be independent of
density and geometry for large numbers of atoms. Large amplitude field
modulation at a frequency resonant with the energy of a dark soliton is found
to give rise to a state with multiple vortices. The Bogoliubov excitation
spectrum of the soliton state contains complex frequencies, which disappear for
sufficiently small numbers of atoms or large transverse confinement. The
relationship between these complex modes and the snake instability is
investigated numerically by propagation in real time.Comment: 11 pages, 8 embedded figures (two in color
Entropic Corrections to Coulomb's Law
Two well-known quantum corrections to the area law have been introduced in
the literatures, namely, logarithmic and power-law corrections. Logarithmic
corrections, arises from loop quantum gravity due to thermal equilibrium
fluctuations and quantum fluctuations, while, power-law correction appears in
dealing with the entanglement of quantum fields in and out the horizon.
Inspired by Verlinde's argument on the entropic force, and assuming the quantum
corrected relation for the entropy, we propose the entropic origin for the
Coulomb's law in this note. Also we investigate the Uehling potential as a
radiative correction to Coulomb potential in 1-loop order and show that for
some value of distance the entropic corrections of the Coulomb's law is
compatible with the vacuum-polarization correction in QED. So, we derive
modified Coulomb's law as well as the entropy corrected Poisson's equation
which governing the evolution of the scalar potential . Our study further
supports the unification of gravity and electromagnetic interactions based on
the holographic principle.Comment: 17 pages, 5 figures, accepted in IJT
Engineering serendipity: high-throughput discovery of materials that resist bacterial attachment
Controlling the colonisation of materials by microorganisms is important in a wide range of industries and clinical settings. To date, the underlying mechanisms that govern the interactions of bacteria with material surfaces remain poorly understood, limiting the ab initio design and engineering of biomaterials to control bacterial attachment. Combinatorial approaches involving high-throughput screening have emerged as key tools for identifying materials to control bacterial attachment. The hundreds of different materials assessed using these methods can be carried out with the aid of computational modelling. This approach can develop an understanding of the rules used to predict bacterial attachment to surfaces of non-toxic synthetic materials. Here we outline our view on the state of this field and the challenges and opportunities in this area for the coming years
- …