566 research outputs found
Condensate deformation and quantum depletion of Bose-Einstein condensates in external potentials
The one-body density matrix of weakly interacting, condensed bosons in
external potentials is calculated using inhomogeneous Bogoliubov theory. We
determine the condensate deformation caused by weak external potentials on the
mean-field level. The momentum distribution of quantum fluctuations around the
deformed ground state is obtained analytically, and finally the resulting
quantum depletion is calculated. The depletion due to the external potential,
or potential depletion for short, is a small correction to the homogeneous
depletion, validating our inhomogeneous Bogoliubov theory. Analytical results
are derived for weak lattices and spatially correlated random potentials, with
simple, universal results in the Thomas-Fermi limit of very smooth potentials.Comment: 17 pages, 4 figures. v2: published version, minor change
Equation of state of an interacting Bose gas at finite temperature: a Path Integral Monte Carlo study
By using exact Path Integral Monte Carlo methods we calculate the equation of
state of an interacting Bose gas as a function of temperature both below and
above the superfluid transition. The universal character of the equation of
state for dilute systems and low temperatures is investigated by modeling the
interatomic interactions using different repulsive potentials corresponding to
the same s-wave scattering length. The results obtained for the energy and the
pressure are compared to the virial expansion for temperatures larger than the
critical temperature. At very low temperatures we find agreement with the
ground-state energy calculated using the diffusion Monte Carlo method.Comment: 7 pages, 6 figure
Machine Learning Scoring Functions for Drug Discoveries from Experimental and Computer-Generated Protein-Ligand Structures: Towards Per-Target Scoring Functions
In recent years, machine learning has been proposed as a promising strategy
to build accurate scoring functions for computational docking finalized to
numerically empowered drug discovery. However, the latest studies have
suggested that over-optimistic results had been reported due to the
correlations present in the experimental databases used for training and
testing. Here, we investigate the performance of an artificial neural network
in binding affinity predictions, comparing results obtained using both
experimental protein-ligand structures as well as larger sets of
computer-generated structures created using commercial software. Interestingly,
similar performances are obtained on both databases. We find a noticeable
performance suppression when moving from random horizontal tests to vertical
tests performed on target proteins not included in the training data. The
possibility to train the network on relatively easily created
computer-generated databases leads us to explore per-target scoring functions,
trained and tested ad-hoc on complexes including only one target protein.
Encouraging results are obtained, depending on the type of protein being
addressed.Comment: 22 pages, 8 figure
Bose-Einstein Condensate in Weak 3d Isotropic Speckle Disorder
The effect of a weak three-dimensional (3d) isotropic laser speckle disorder
on various thermodynamic properties of a dilute Bose gas is considered at zero
temperature. First, we summarize the derivation of the autocorrelation function
of laser speckles in 1d and 2d following the seminal work of Goodman. The goal
of this discussion is to show that a Gaussian approximation of this function,
proposed in some recent papers, is inconsistent with the general background of
laser speckle theory. Then we propose a possible experimental realization for
an isotropic 3d laser speckle potential and derive its corresponding
autocorrelation function. Using a Fourier transform of that function, we
calculate both condensate depletion and sound velocity of a Bose-Einstein
condensate as disorder ensemble averages of such a weak laser speckle potential
within a perturbative solution of the Gross-Pitaevskii equation. By doing so,
we reproduce the expression of the normalfluid density obtained earlier within
the treatment of Landau. This physically transparent derivation shows that
condensate particles, which are scattered by disorder, form a gas of
quasiparticles which is responsible for the normalfluid component
Dilute Bose gas with correlated disorder: A Path Integral Monte Carlo study
We investigate the thermodynamic properties of a dilute Bose gas in a
correlated random potential using exact path integral Monte Carlo methods. The
study is carried out in continuous space and disorder is produced in the
simulations by a 3D speckle pattern with tunable intensity and correlation
length. We calculate the shift of the superfluid transition temperature due to
disorder and we highlight the role of quantum localization by comparing the
critical chemical potential with the classical percolation threshold. The
equation of state of the gas is determined in the regime of strong disorder,
where superfluidity is suppressed and the normal phase exists down to very low
temperatures. We find a dependence of the energy in agreement with the
expected behavior in the Bose glass phase. We also discuss the major role
played by the disorder correlation length and we make contact with a
Hartree-Fock mean-field approach that holds valid if the correlation length is
very large. The density profiles are analyzed as a function of temperature and
interaction strength. Effects of localization and the depletion of the order
parameter are emphasized in the comparison between local condensate and total
density. At very low temperature we find that the energy and the particle
distribution of the gas are very well described by the T=0 Gross-Pitaevskii
theory even in the regime of very strong disorder.Comment: 27 pages, 20 figure
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Validation issues: a view from the trenches
Most papers on model evaluation or assessment dealing with verification and validation discuss means and mechanisms by which outside parties can perform peer review to provide verification and establish the validity of models. Little attention is paid to activities performed by the user-modeling team itself to improve the ability of the model to provide information useful in the decision-making process, and to provide confidence that the information is meaningful. This paper presents a number of case histories describing the authors' experience with this type of model improvement activity, called internal validation. They have been convinced that internal validation schemes should be incorporated in the project description and that they be used in part to answer questions of formulation. They further recommend that modelers incorporate sufficient funding in their project plans to carry out this function
Dynamical spin-flip susceptibility for a strongly interacting ultracold Fermi gas
The Stoner model predicts that a two-component Fermi gas at increasing
repulsive interactions undergoes a ferromagnetic transition. Using the
random-phase approximation we study the dynamical properties of the interacting
Fermi gas. For an atomic Fermi gas under harmonic confinement we show that the
transverse (spin-flip) dynamical susceptibility displays a clear signature of
the ferromagnetic phase in a magnon peak emerging from the Stoner particle-hole
continuum. The dynamical spin susceptibilities could be experimentally explored
via spin-dependent Bragg spectroscopy.Comment: 4 pages, 3 figure
Metastability in spin polarised Fermi gases and quasiparticle decays
We investigate the metastability associated with the first order transition from normal to superfluid phases in the phase diagram of two-component polarised Fermi gases.We begin by detailing the dominant decay processes of single quasiparticles.Having determined the momentum thresholds of each process and calculated their rates, we apply this understanding to a Fermi sea of polarons by linking its metastability to the stability of individual polarons, and predicting a region of metastability for the normal partially polarised phase. In the limit of a single impurity, this region extends from the interaction strength at which a polarised phase of molecules becomes the groundstate, to the one at which the single quasiparticle groundstate changes character from polaronic to molecular. Our argument in terms of a Fermi sea of polarons naturally suggests their use as an experimental probe. We propose experiments to observe the threshold of the predicted region of metastability, the interaction strength at which the quasiparticle groundstate changes character, and the decay rate of polarons
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