44,595 research outputs found
Statistical properties of the spectrum the extended Bose-Hubbard model
Motivated by the role that spectral properties play for the dynamical
evolution of a quantum many-body system, we investigate the level spacing
statistic of the extended Bose-Hubbard model. In particular, we focus on the
distribution of the ratio of adjacent level spacings, useful at large
interaction, to distinguish between chaotic and non-chaotic regimes. After
revisiting the bare Bose-Hubbard model, we study the effect of two different
perturbations: next-nearest neighbor hopping and nearest-neighbor interaction.
The system size dependence is investigated together with the effect of the
proximity to integrable points or lines. Lastly, we discuss the consequences of
a cutoff in the number of onsite bosons onto the level statistics.Comment: 18 pages, 15 figure
Fundamental structures of dynamic social networks
Social systems are in a constant state of flux with dynamics spanning from
minute-by-minute changes to patterns present on the timescale of years.
Accurate models of social dynamics are important for understanding spreading of
influence or diseases, formation of friendships, and the productivity of teams.
While there has been much progress on understanding complex networks over the
past decade, little is known about the regularities governing the
micro-dynamics of social networks. Here we explore the dynamic social network
of a densely-connected population of approximately 1000 individuals and their
interactions in the network of real-world person-to-person proximity measured
via Bluetooth, as well as their telecommunication networks, online social media
contacts, geo-location, and demographic data. These high-resolution data allow
us to observe social groups directly, rendering community detection
unnecessary. Starting from 5-minute time slices we uncover dynamic social
structures expressed on multiple timescales. On the hourly timescale, we find
that gatherings are fluid, with members coming and going, but organized via a
stable core of individuals. Each core represents a social context. Cores
exhibit a pattern of recurring meetings across weeks and months, each with
varying degrees of regularity. Taken together, these findings provide a
powerful simplification of the social network, where cores represent
fundamental structures expressed with strong temporal and spatial regularity.
Using this framework, we explore the complex interplay between social and
geospatial behavior, documenting how the formation of cores are preceded by
coordination behavior in the communication networks, and demonstrating that
social behavior can be predicted with high precision.Comment: Main Manuscript: 16 pages, 4 figures. Supplementary Information: 39
pages, 34 figure
Entropy of the Nordic electricity market: anomalous scaling, spikes, and mean-reversion
The electricity market is a very peculiar market due to the large variety of
phenomena that can affect the spot price. However, this market still shows many
typical features of other speculative (commodity) markets like, for instance,
data clustering and mean reversion. We apply the diffusion entropy analysis
(DEA) to the Nordic spot electricity market (Nord Pool). We study the waiting
time statistics between consecutive spot price spikes and find it to show
anomalous scaling characterized by a decaying power-law. The exponent observed
in data follows a quite robust relationship with the one implied by the DEA
analysis. We also in terms of the DEA revisit topics like clustering,
mean-reversion and periodicities. We finally propose a GARCH inspired model but
for the price itself. Models in the context of stochastic volatility processes
appear under this scope to have a feasible description.Comment: 16 pages, 7 figure
Probing many-body localization with neural networks
We show that a simple artificial neural network trained on entanglement
spectra of individual states of a many-body quantum system can be used to
determine the transition between a many-body localized and a thermalizing
regime. Specifically, we study the Heisenberg spin-1/2 chain in a random
external field. We employ a multilayer perceptron with a single hidden layer,
which is trained on labeled entanglement spectra pertaining to the fully
localized and fully thermal regimes. We then apply this network to classify
spectra belonging to states in the transition region. For training, we use a
cost function that contains, in addition to the usual error and regularization
parts, a term that favors a confident classification of the transition region
states. The resulting phase diagram is in good agreement with the one obtained
by more conventional methods and can be computed for small systems. In
particular, the neural network outperforms conventional methods in classifying
individual eigenstates pertaining to a single disorder realization. It allows
us to map out the structure of these eigenstates across the transition with
spatial resolution. Furthermore, we analyze the network operation using the
dreaming technique to show that the neural network correctly learns by itself
the power-law structure of the entanglement spectra in the many-body localized
regime.Comment: 12 pages, 10 figure
Persistence and Stochastic Periodicity in the Intensity Dynamics of a Fiber Laser During the Transition to Optical Turbulence
Many natural systems display transitions among different dynamical regimes,
which are difficult to identify when the data is noisy and high dimensional. A
technologically relevant example is a fiber laser, which can display complex
dynamical behaviors that involve nonlinear interactions of millions of cavity
modes. Here we study the laminar-turbulence transition that occurs when the
laser pump power is increased. By applying various data analysis tools to
empirical intensity time series we characterize their persistence and
demonstrate that at the transition temporal correlations can be precisely
represented by a surprisingly simple model.Comment: 10 pages, 13 figure
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