123 research outputs found
Towards AC-induced optimum control of dynamical localization
It is shown that optimum control of dynamical localization (quantum
suppression of classical diffusion) in the context of ultracold atoms in
periodically shaken optical lattices subjected to time-periodic forces having
equidistant zeros depends on the \textit{impulse} transmitted by the external
force over half-period rather than on the force amplitude. This result provides
a useful principle for optimally controlling dynamical localization in general
periodic systems, which is capable of experimental realization.Comment: 7 pages, 6 figure
Short periodic orbits theory for partially open quantum maps
We extend the semiclassical theory of short periodic orbits [Phys. Rev. E
{\bf 80}, 035202(R) (2009)] to partially open quantum maps. They correspond to
classical maps where the trajectories are partially bounced back due to a
finite reflectivity . These maps are representative of a class that has many
experimental applications. The open scar functions are conveniently redefined,
providing a suitable tool for the investigation of these kind of systems. Our
theory is applied to the paradigmatic partially open tribaker map. We find that
the set of periodic orbits that belong to the classical repeller of the open
map () are able to support the set of long-lived resonances of the
partially open quantum map in a perturbative regime. By including the most
relevant trajectories outside of this set, the validity of the approximation is
extended to a broad range of values. Finally, we identify the details of
the transition from qualitatively open to qualitatively closed behaviour,
providing an explanation in terms of short periodic orbits.Comment: 6 pages, 4 figure
Anticipating food price crises by reservoir computing
Anticipating price crises in the market of agri-commodities is critical to guarantee both the sustainability of the food system and to ensure food security. However, this is not an easy task, since the problem implies analyzing small and very volatile time series, which are highly influenced by external factors. In this paper, we show that suitable reservoir computing algorithms can be developed that outperform traditional approaches, by reducing the Mean Absolute Error and, more importantly, increasing the Market Direction Accuracy. For this purpose, the applicability of five variants of such method to forecast this market is explored, and their performance evaluated by comparing the results with those obtained with the standard LSTM and SARIMA benchmarks. We conclude that decomposing the time series and modeling each component with a separate RC is essential to successfully anticipate price trends, and that this method works even in the complex changing temporal scenario of the Covid-19 pandemic, when part of the data were collectedThe project that gave rise to these results received the support of a fellowship from ‘‘la Caixa’’ Foundation (ID 100010434). The fellowship code is LCF/BQ/DR20/11790028. This work has also been partially supported by the Spanish Ministry of Science, Innovation and Universities, Gobierno de España, under Contract No. PID2021-122711NB-C21; and by DG of Research and Technological Innovation of the Community of Madrid (Spain) under Contract No. IND2022/TIC-2371
To Each According to its Degree: The Meritocracy and Topocracy of Embedded Markets
A system is said to be meritocratic if the compensation and power available to individuals is determined by their abilities and merits. A system is topocratic if the compensation and power available to an individual is determined primarily by her position in a network. Here we introduce a model that is perfectly meritocratic for fully connected networks but that becomes topocratic for sparse networks-like the ones in society. In the model, individuals produce and sell content, but also distribute the content produced by others when they belong to the shortest path connecting a buyer and a seller. The production and distribution of content defines two channels of compensation: a meritocratic channel, where individuals are compensated for the content they produce, and a topocratic channel, where individual compensation is based on the number of shortest paths that go through them in the network. We solve the model analytically and show that the distribution of payoffs is meritocratic only if the average degree of the nodes is larger than a root of the total number of nodes. We conclude that, in the light of this model, the sparsity and structure of networks represents a fundamental constraint to the meritocracy of societies.MIT Media Lab Consortiu
Reaction rate calculation with time-dependent invariant manifolds
The identification of trajectories that contribute to the reaction rate is
the crucial dynamical ingredient in any classical chemical reactivity
calculation. This problem often requires a full scale numerical simulation of
the dynamics, in particular if the reactive system is exposed to the influence
of a heat bath. As an efficient alternative, we propose here to compute
invariant surfaces in the phase space of the reactive system that separate
reactive from nonreactive trajectories. The location of these invariant
manifolds depends both on time and on the realization of the driving force
exerted by the bath. These manifolds allow the identification of reactive
trajectories simply from their initial conditions, without the need of any
further simulation. In this paper, we show how these invariant manifolds can be
calculated, and used in a formally exact reaction rate calculation based on
perturbation theory for any multidimensional potential coupled to a noisy
environment
The scar mechanism revisited
Unstable periodic orbits are known to originate scars on some eigenfunctions
of classically chaotic systems through recurrences causing that some part of an
initial distribution of quantum probability in its vicinity returns
periodically close to the initial point. In the energy domain, these
recurrences are seen to accumulate quantum density along the orbit by a
constructive interference mechanism when the appropriate quantization (on the
action of the scarring orbit) is fulfilled. Other quantized phase space
circuits, such as those defined by homoclinic tori, are also important in the
coherent transport of quantum density in chaotic systems. The relationship of
this secondary quantum transport mechanism with the standard mechanism for
scarring is here discussed and analyzed.Comment: 6 pages, 6 figure
Lagrangian descriptors for open maps
We adapt the concept of Lagrangian descriptors, which have been recently
introduced as efficient indicators of phase space structures in chaotic
systems, to unveil the key features of open maps. We apply them to the open
tribaker map, a paradigmatic example not only in classical but also in quantum
chaos. Our definition allows to identify in a very simple way the inner
structure of the chaotic repeller, which is the fundamental invariant set that
governs the dynamics of this system. The homoclinic tangles of periodic orbits
(POs) that belong to this set are clearly found. This could also have important
consequences for chaotic scattering and in the development of the semiclassical
theory of short POs for open systems.Comment: 7 pages, 10 figure
The role of short periodic orbits in quantum maps with continuous openings
We apply a recently developed semiclassical theory of short periodic orbits
to the continuously open quantum tribaker map. In this paradigmatic system the
trajectories are partially bounced back according to continuous reflectivity
functions. This is relevant in many situations that include optical
microresonators and more complicated boundary conditions. In a perturbative
regime, the shortest periodic orbits belonging to the classical repeller of the
open map - a cantor set given by a region of exactly zero reflectivity - prove
to be extremely robust in supporting a set of long-lived resonances of the
continuously open quantum maps. Moreover, for step like functions a significant
reduction in the number needed is obtained, similarly to the completely open
situation. This happens despite a strong change in the spectral properties when
compared to the discontinuous reflectivity case.Comment: 6 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1604.0181
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