14,954 research outputs found
Interacting Hofstadter spectrum of atoms in an artificial gauge field
Motivated by experimental advances in the synthesis of gauge potentials for
ultracold atoms, we consider the superfluid phase of interacting bosons on a
square lattice in the presence of a magnetic field. We show that superfluid
order implies spatial symmetry breaking, and predict clear signatures of
many-body effects in time-of-flight measurements. By developing a Bogoliubov
expansion based on the exact Hofstadter spectrum, we find the dispersion of the
quasiparticle modes within the superfluid phase, and describe the consequences
for Bragg spectroscopy measurements. The theory also provides an estimate of
the critical interaction strength at the transition to the Mott insulator
phase.Comment: 4+ pages, 2 figures; v2: published versio
Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder
We study the Anderson localization of Bogoliubov quasiparticles (elementary
many-body excitations) in a weakly interacting Bose gas of chemical potential
subjected to a disordered potential . We introduce a general mapping
(valid for weak inhomogeneous potentials in any dimension) of the Bogoliubov-de
Gennes equations onto a single-particle Schr\"odinger-like equation with an
effective potential. For disordered potentials, the Schr\"odinger-like equation
accounts for the scattering and localization properties of the Bogoliubov
quasiparticles. We derive analytically the localization lengths for correlated
disordered potentials in the one-dimensional geometry. Our approach relies on a
perturbative expansion in , which we develop up to third order, and we
discuss the impact of the various perturbation orders. Our predictions are
shown to be in very good agreement with direct numerical calculations. We
identify different localization regimes: For low energy, the effective
disordered potential exhibits a strong screening by the quasicondensate density
background, and localization is suppressed. For high-energy excitations, the
effective disordered potential reduces to the bare disordered potential, and
the localization properties of quasiparticles are the same as for free
particles. The maximum of localization is found at intermediate energy when the
quasicondensate healing length is of the order of the disorder correlation
length. Possible extensions of our work to higher dimensions are also
discussed.Comment: Published versio
Quantum temporal correlations and entanglement via adiabatic control of vector solitons
It is shown that optical pulses with a mean position accuracy beyond the
standard quantum limit can be produced by adiabatically expanding an optical
vector soliton followed by classical dispersion management. The proposed scheme
is also capable of entangling positions of optical pulses and can potentially
be used for general continuous-variable quantum information processing.Comment: 5 pages, 1 figure, v2: accepted by Physical Review Letters, v3: minor
editing and shortening, v4: included the submitted erratu
Transfer Entropy as a Log-likelihood Ratio
Transfer entropy, an information-theoretic measure of time-directed
information transfer between joint processes, has steadily gained popularity in
the analysis of complex stochastic dynamics in diverse fields, including the
neurosciences, ecology, climatology and econometrics. We show that for a broad
class of predictive models, the log-likelihood ratio test statistic for the
null hypothesis of zero transfer entropy is a consistent estimator for the
transfer entropy itself. For finite Markov chains, furthermore, no explicit
model is required. In the general case, an asymptotic chi-squared distribution
is established for the transfer entropy estimator. The result generalises the
equivalence in the Gaussian case of transfer entropy and Granger causality, a
statistical notion of causal influence based on prediction via vector
autoregression, and establishes a fundamental connection between directed
information transfer and causality in the Wiener-Granger sense
Sampling bias in systems with structural heterogeneity and limited internal diffusion
Complex systems research is becomingly increasingly data-driven, particularly
in the social and biological domains. Many of the systems from which sample
data are collected feature structural heterogeneity at the mesoscopic scale
(i.e. communities) and limited inter-community diffusion. Here we show that the
interplay between these two features can yield a significant bias in the global
characteristics inferred from the data. We present a general framework to
quantify this bias, and derive an explicit corrective factor for a wide class
of systems. Applying our analysis to a recent high-profile survey of conflict
mortality in Iraq suggests a significant overestimate of deaths
Which group velocity of light in a dispersive medium?
The interaction between a light pulse, traveling in air, and a generic
linear, non-absorbing and dispersive structure is analyzed. It is shown that
energy conservation imposes a constraint between the group velocities of the
transmitted and reflected light pulses. It follows that the two fields
propagate with group velocities depending on the dispersive properties of the
environment (air) and on the transmission properties of the optical structure,
and are one faster and the other slower than the incident field. In other
words, the group velocity of a light pulse in a dispersive medium is
reminiscent of previous interactions. One example is discussed in detail.Comment: To be submitted on PR
Quantum rotor theory of spinor condensates in tight traps
In this work, we theoretically construct exact mappings of many-particle
bosonic systems onto quantum rotor models. In particular, we analyze the rotor
representation of spinor Bose-Einstein condensates. In a previous work it was
shown that there is an exact mapping of a spin-one condensate of fixed particle
number with quadratic Zeeman interaction onto a quantum rotor model. Since the
rotor model has an unbounded spectrum from above, it has many more eigenstates
than the original bosonic model. Here we show that for each subset of states
with fixed spin F_z, the physical rotor eigenstates are always those with
lowest energy. We classify three distinct physical limits of the rotor model:
the Rabi, Josephson, and Fock regimes. The last regime corresponds to a
fragmented condensate and is thus not captured by the Bogoliubov theory. We
next consider the semiclassical limit of the rotor problem and make connections
with the quantum wave functions through use of the Husimi distribution
function. Finally, we describe how to extend the analysis to higher-spin
systems and derive a rotor model for the spin-two condensate. Theoretical
details of the rotor mapping are also provided here.Comment: 10 pages, 2 figure
Building an Argument for the Use of Science Fiction in HCI Education
Science fiction literature, comics, cartoons and, in particular, audio-visual
materials, such as science fiction movies and shows, can be a valuable addition
in Human-computer interaction (HCI) Education. In this paper, we present an
overview of research relative to future directions in HCI Education, distinct
crossings of science fiction in HCI and Computer Science teaching and the
Framework for 21st Century Learning. Next, we provide examples where science
fiction can add to the future of HCI Education. In particular, we argue herein
first that science fiction, as tangible and intangible cultural artifact, can
serve as a trigger for creativity and innovation and thus, support us in
exploring the design space. Second, science fiction, as a means to analyze
yet-to-come HCI technologies, can assist us in developing an open-minded and
reflective dialogue about technological futures, thus creating a singular base
for critical thinking and problem solving. Provided that one is cognizant of
its potential and limitations, we reason that science fiction can be a
meaningful extension of selected aspects of HCI curricula and research.Comment: 6 pages, 1 table, IHSI 2019 accepted submissio
Contracts in Practice
Contracts are a form of lightweight formal specification embedded in the
program text. Being executable parts of the code, they encourage programmers to
devote proper attention to specifications, and help maintain consistency
between specification and implementation as the program evolves. The present
study investigates how contracts are used in the practice of software
development. Based on an extensive empirical analysis of 21 contract-equipped
Eiffel, C#, and Java projects totaling more than 260 million lines of code over
7700 revisions, it explores, among other questions: 1) which kinds of contract
elements (preconditions, postconditions, class invariants) are used more often;
2) how contracts evolve over time; 3) the relationship between implementation
changes and contract changes; and 4) the role of inheritance in the process. It
has found, among other results, that: the percentage of program elements that
include contracts is above 33% for most projects and tends to be stable over
time; there is no strong preference for a certain type of contract element;
contracts are quite stable compared to implementations; and inheritance does
not significantly affect qualitative trends of contract usage
Generalized Hermite-Gauss decomposition of the two-photon state produced by spontaneous parametric down-conversion
We provide a general decomposition of the two-photon state produced by
spontaneous parametric down-conversion in Hermite-Gaussian modes, in the case
that the pump beam is described by a Hermite-Gaussian beam of any order. We
show that the spatial correlations depend explicitly on the order of the pump
beam, as well as other experimental parameters. We use the decomposition to
demonstrate a few interesting cases. Our results are applicable to the
engineering of two-photon spatial entanglement, in particular for non-Gaussian
states.Comment: 14 page draft, 5 figure
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