22 research outputs found
Quantum Monte Carlo estimation of complex-time correlations for the study of the ground-state dynamic structure function
We present a method based on the Path Integral Monte Carlo formalism for the
calculation of ground-state time correlation functions in quantum systems. The
key point of the method is the consideration of time as a complex variable
whose phase acts as an adjustable parameter. By using high-order
approximations for the quantum propagator, it is possible to obtain Monte Carlo
data all the way from purely imaginary time to values near the limit
of real time. As a consequence, it is possible to infer accurately the spectral
functions using simple inversion algorithms. We test this approach in the
calculation of the dynamic structure function of two
one-dimensional model systems, harmonic and quartic oscillators, for which
can be exactly calculated. We notice a clear improvement in the
calculation of the dynamic response with respect to the common approach based
on the inverse Laplace transform of the imaginary-time correlation function.Comment: Accepted for publication on "Jornal of Chemical Physics
Optical lattices as a tool to study defect-induced superfluidity
We study the superfluid response, the energetic and structural properties of
a one-dimensional ultracold Bose gas in an optical lattice of arbitrary
strength. We use the Bose-Fermi mapping in the limit of infinitely large
repulsive interaction and the diffusion Monte Carlo method in the case of
finite interaction. For slightly incommensurate fillings we find a superfluid
behavior which is discussed in terms of vacancies and interstitials. It is
shown that both the excitation spectrum and static structure factor are
different for the cases of microscopic and macroscopic fractions of defects.
This system provides a extremely well-controlled model for studying
defect-induced superfluidity.Comment: 14 pages, 13 figures, published versio
Weighted Contrastive Divergence
Learning algorithms for energy based Boltzmann architectures that rely on
gradient descent are in general computationally prohibitive, typically due to
the exponential number of terms involved in computing the partition function.
In this way one has to resort to approximation schemes for the evaluation of
the gradient. This is the case of Restricted Boltzmann Machines (RBM) and its
learning algorithm Contrastive Divergence (CD). It is well-known that CD has a
number of shortcomings, and its approximation to the gradient has several
drawbacks. Overcoming these defects has been the basis of much research and new
algorithms have been devised, such as persistent CD. In this manuscript we
propose a new algorithm that we call Weighted CD (WCD), built from small
modifications of the negative phase in standard CD. However small these
modifications may be, experimental work reported in this paper suggest that WCD
provides a significant improvement over standard CD and persistent CD at a
small additional computational cost
Two-dimensional repulsive Fermi polarons with short and long-range interactions
We study the repulsive polaron problem in a two-component two-dimensional
system of fermionic atoms. We use two different interaction models: a
short-range (hard-disk) potential and a dipolar potential. In our approach, all
the atoms have the same mass and we consider the system to be composed of a
uniform bath of a single species and a single atomic impurity. We use the
diffusion Monte Carlo method to evaluate polaron properties such as its
chemical potential and pair distribution functions, together with a discussion
on the deficit of volume induced by the impurity. We also evaluate observables
that allow us to determine the validity of the quasi-particle picture: the
quasi-particle residue and the effective mass of the polaron. Employing two
different potentials allows us to identify the universality regime, where the
properties depend only on the gas parameter fixed by the bath density
and the two-dimensional scattering length
Self-bound Bose mixtures
Recent experiments confirmed that fluctuations beyond the mean-field
approximation can lead to self-bound liquid droplets of ultra-dilute binary
Bose mixtures. We proceed beyond the beyond-mean-field approximation, and study
liquid Bose mixtures using the variational hypernetted-chain Euler Lagrange
method, which accounts for correlations non-perturbatively. Focusing on the
case of a mixture of uniform density, as realized inside large saturated
droplets, we study the conditions for stability against evaporation of one of
the components (both chemical potentials need to be negative) and against
liquid-gas phase separation (spinodal instability), the latter being
accompanied by a vanishing speed of sound. Dilute Bose mixtures are stable only
in a narrow range near an optimal ratio and near the total
energy minimum. Deviations from a universal dependence on the s-wave scattering
lengths are significant despite the low density.Comment: 5 pages, 5 figure
High-Momentum Response of Liquid 3He
A final-state-effects formalism suitable to analyze the high-momentum response of Fermi liquids is presented and used to study the dynamic structure function of liquid 3He. The theory, developed as a natural extension of the Gersch-Rodriguez formalism, incorporates the Fermi statistics explicitly through a new additive term which depends on the semidiagonal two-body density matrix. The use of a realistic momentum distribution, calculated using the diffusion Monte Carlo method, and the inclusion of this additive correction allows for good agreement with available deep-inelastic neutron scattering data