The structure of interactions in most animal and human societies can be best represented by complex hierarchical networks. In order to maintain close-to-optimal function both stability and adaptability are necessary. Here we investigate the stability of hierarchical networks that emerge from the simulations of an organization type with an efficiency function reminiscent of the Hamiltonian of spin glasses. Using this quantitative approach we find a number of expected (from everyday observations) and highly non-trivial results for the obtained locally optimal networks, including, for example: (i) stability increases with growing efficiency and level of hierarchy; (ii) the same perturbation results in a larger change for more efficient states; (iii) networks with a lower level of hierarchy become more efficient after perturbation; (iv) due to the huge number of possible optimal states only a small fraction of them exhibit resilience and, finally, (v) 'attacks' targeting the nodes selectively (regarding their position in the hierarchy) can result in paradoxical outcomes.
We analyze the ground state of a two-dimensional quantum system of a few strongly confined dipolar bosons. Dipoles arrange in different stable structures that depend on the tilting polarization angle and the anisotropy of the confining trap. To this end, we use the exact diffusion Monte Carlo method and the quantum results are compared with classical ones obtained by stochastic optimization using simulated annealing. We establish the stability domains for the different patterns and estimate the transition boundaries delimiting them. Our results show significant differences between the classical and quantum regimes which are mainly due to the quantum kinetic energy.
The temperature dependence of the dielectric response of ordinary ferroelectric materials exhibits a frequency-independent anomalous peak as a manifestation of the ferroelectric to paraelectric phase transition. A second anomaly in the permittivity has been reported in different ferroelectric perovskite-type systems at low temperatures, often at cryogenic temperatures. This anomaly manifests as a frequency-dependent local maximum, which exhibits similar characteristics to that observed in relaxor ferroelectrics around their phase transition. The origin of this unexpected behavior is still controversial. In order to clarify this phenomenon, a model-free route solution is developed in this work. Our findings reveal the same critical linear pattern/glass-like freezing behavior previously observed for glass-forming systems. Contrary to current thought, our results suggest that a critical-like dynamic parameterization could provide a more appropriate solution than the conventional Vogel–Fulcher–Tammann equation. The implemented methodology may open a new pathway for analyzing relaxation phenomena in other functional materials like relaxor ferroics.
Mobile impurity atoms immersed in Bose–Einstein condensates provide a new platform for exploring Bose polarons. Recent experimental advances in the field of ultracold atoms make it possible to realize such systems with highly tunable microscopic parameters and to explore equilibrium and dynamical properties of polarons using a rich toolbox of atomic physics. In this paper we present a detailed theoretical analysis of Bose polarons in one-dimensional systems of ultracold atoms. By combining a non-perturbative renormalization group approach with numerically exact diffusion Monte Carlo calculations we obtain not only detailed numerical results over a broad range of parameters but also qualitative understanding of different regimes of the system. We find that an accurate description of Bose polarons requires the inclusion of two-phonon scattering terms which go beyond the commonly used Fröhlich model. Furthermore we show that when the Bose gas is in the strongly interacting regime, one needs to include interactions between the phonon modes. We use several theoretical approaches to calculate the polaron energy and its effective mass. The former can be measured using radio-frequency spectroscopy and the latter can be studied experimentally using impurity oscillations in a harmonic trapping potential. We compare our theoretical results for the effective mass to the experiments by Catani et al (2012 Phys. Rev. A 85 023623). In the weak-to-intermediate coupling regimes we obtain excellent quantitative agreement between theory and experiment, without any free fitting parameter. We supplement our analysis by full dynamical simulations of polaron oscillations in a shallow trapping potential. We also use our renormalization group approach to analyze the full phase diagram and identify regions that support repulsive and attractive polarons, as well as multi-particle bound states.
Turbulent-laminar patterns are ubiquitous near transition in wall-bounded shear flows. Despite recent progress in describing their dynamics in analogy to non-equilibrium phase transitions, there is no theory explaining their emergence. Dynamical-system approaches suggest that invariant solutions to the Navier–Stokes equations, such as traveling waves and relative periodic orbits in pipe flow, act as building blocks of the disordered dynamics. While recent studies have shown how transient chaos arises from such solutions, the ensuing dynamics lacks the strong fluctuations in size, shape and speed of the turbulent spots observed in experiments. We here show that chaotic spots with distinct dynamical and kinematic properties merge in phase space and give rise to the enhanced spatio-temporal patterns observed in pipe flow. This paves the way for a dynamical-system foundation to the phenomenology of turbulent-laminar patterns in wall-bounded extended shear flows.
A one-dimensional world is very unusual as there is an interplay between quantum statistics and geometry, and a strong short-range repulsion between atoms mimics Fermi exclusion principle, fermionizing the system. Instead, a system with a large number of components with a single atom in each, on the opposite acquires many bosonic properties. We study the ground-state properties of a multicomponent repulsive Fermi gas trapped in a harmonic trap by a fixed-node diffusion Monte Carlo method. The interaction between all components is considered to be the same. We investigate how the energetic properties (energy, contact) and correlation functions (density profile and momentum distribution) evolve as the number of components is changed. It is shown that the system fermionizes in the limit of strong interactions. Analytical expressions are derived in the limit of weak interactions within the local density approximation for an arbitrary number of components and for one plus one particle using an exact solution.
The ground-state properties of one-dimensional electron-spin-polarized hydrogen H-1, deuterium H-2, and tritium 3 Hare obtained by means of quantum Monte Carlo methods. The equations of state of the three isotopes are calculated for a wide range of linear densities. The pair correlation function and the static structure factor are obtained and interpreted within the framework of the Luttinger liquid theory. We report the density dependence of the Luttinger parameter and use it to identify different physical regimes: Bogoliubov Bose gas, super-Tonks-Girardeau gas, and quasi-crystal regimes for bosons; repulsive, attractive Fermi gas, and quasi-crystal regimes for fermions. We find that the tritium isotope is the one with the richest behavior. Our results show unambiguously the relevant role of the isotope mass in the properties of this quantum system.
We analyze the effects of noise on the permutation entropy of dynamical systems. We take as numerical examples the logistic map and the Rössler system. Upon varying the noise strength we find a transition from an almost-deterministic regime, where the permutation entropy grows slower than linearly with the pattern dimension, to a noise-dominated regime, where the permutation entropy grows faster than linearly with the pattern dimension. We perform the same analysis on experimental time-series by considering the stochastic spiking output of a semiconductor laser with optical feedback, and find that the permutation entropy always increases faster than linearly. Nevertheless, the analysis allows to detect regularities of the underlying dynamics and model simulations are in a good agreement with the empirical data. By comparing the results of these three different examples, we discuss the possibility of determining from a time series whether the underlying dynamics is dominated by noise or not.
Masoller, C.; Hong, Y.; Ayad, S.; Gustave, F.; Barland, S.; Pons, A. J.; Gómez Jiménez, Sergio; Arenas, A. New journal of physics Vol. 17, num. 2 DOI: 10.1088/1367-2630/17/2/023068 Data de publicació: 2015-02-24 Article en revista
We characterize the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time series we construct a network in which every node weight represents the probability of an ordinal pattern (OP) to appear in the symbolic sequence and each edge's weight represents the probability of transitions between two consecutive OPs. Several network-based diagnostics are then proposed to characterize the dynamics of different systems: logistic, tent, and circle maps. We show that these diagnostics are able to capture changes produced in the dynamics as a control parameter is varied. We also apply our new measures to empirical data from semiconductor lasers and show that they are able to anticipate the polarization switchings, thus providing early warning signals of abrupt transitions.
Garcia, M.; Julia, B.; Astrakharchik, G.; Busch, T.; Boronat, J.; Polls, A. New journal of physics Vol. 16, p. 1-18 DOI: 10.1088/1367-2630/16/10/103004 Data de publicació: 2014-10-07 Article en revista
We present the complete phase diagram for one-dimensional binary mixtures of bosonic ultracold atomic gases in a harmonic trap. We obtain exact results with direct numerical diagonalization for a small number of atoms, which permits us to quantify quantum many-body correlations. The quantum Monte Carlo method is used to calculate energies and density profiles for larger system sizes. We study the system properties for a wide range of interaction parameters. For the extreme values of these parameters, different correlation limits can be identified, where the correlations are either weak or strong. We investigate in detail how the correlations evolve between the limits. For balanced mixtures in the number of atoms in each species, the transition between the different limits involves sophisticated changes in the one-and two-body correlations. Particularly, we quantify the entanglement between the two components by means of the von Neumann entropy. We show that the limits equally exist when the number of atoms is increased for balanced mixtures. Also, the changes in the correlations along the transitions among these limits are qualitatively similar. We also show that, for imbalanced mixtures, the same limits with similar transitions exist. Finally, for strongly imbalanced systems, only two limits survive, i.e., a miscible limit and a phase-separated one, resembling those expected with a mean-field approach.
Rubido, N.; Marti, A.; Bianco-Martinez, E.; Grebogi, C.; Baptista, M.; Masoller, C. New journal of physics Vol. 16, p. 093010- DOI: 10.1088/1367-2630/16/9/093010 Data de publicació: 2014-09 Article en revista
The inference of an underlying network topology from local observations of a complex system composed of interacting units is usually attempted by using statistical similarity measures, such as cross-correlation (CC) and mutual information (MI). The possible existence of a direct link between different units is, however, hindered within the time-series measurements. Here we show that, for the class of systems studied, when an abrupt change in the ordered set of CC or MI values exists, it is possible to infer, without errors, the underlying network topology from the time-series measurements, even in the presence of observational noise, non-identical units, and coupling heterogeneity. We find that a necessary condition for the discontinuity to occur is that the dynamics of the coupled units is partially coherent, i.e., neither complete disorder nor globally synchronous patterns are present. We critically compare the inference methods based on CC and MI, in terms of how effective, robust, and reliable they are, and conclude that, in general, MI outperforms CC in robustness and reliability. Our findings could be relevant for the construction and interpretation of functional networks, such as those constructed from brain or climate data.
We show, by means of numerical and analytical methods, that media with a repulsive nonlinearity which grows from the center to the periphery support a remarkable variety of previously unknown complex stationary and dynamical three-dimensional (3D) solitary-wave states. Peanut-shaped modulation profiles give rise to vertically symmetric and antisymmetric vortex states, and novel stationary hybrid states, built of top and bottom vortices with opposite topological charges, as well as robust dynamical hybrids, which feature stable precession of a vortex on top of a zero-vorticity soliton. The analysis reveals stability regions for symmetric, antisymmetric, and hybrid states. In addition, bead-shaped modulation profiles give rise to the first example of exact analytical solutions for stable 3D vortex solitons. The predicted states may be realized in media with a controllable cubic nonlinearity, such as Bose-Einstein condensates.
Coupling frequently enhances noise-induced coherence and synchronization in interacting nonlinear systems, but it does so separately. In principle collective stochastic coherence and synchronizability are incompatible phenomena, since strongly synchronized elements behave identically and thus their response to noise is indistinguishable to that of a single element. Therefore one can expect systems that synchronize well to have a poor collective response to noise. Here we show that, in spite of this apparent conflict, a certain coupling architecture is able to reconcile the two properties. Specifically, our results reveal that weighted scale-free networks of diffusively coupled excitable elements exhibit both high synchronizability of their subthreshold dynamics and a good collective response to noise of their pulsed dynamics. This is established by comparing the behavior of this system to that of random, regular, and unweighted scale-free networks. We attribute the optimal response of weighted scale-free networks to a balance between degree heterogeneity, which ensures a good collective response to noise, and the coupling-strength weighting procedure, which overcomes the paradox of heterogeneity that would otherwise impair synchronization.
Colangelo, G.; Sewell, R.; Behbood, N.; Ciurana, F.; Triginer, J.; Mitchell, M.W. New journal of physics Vol. 15, p. 103007-1-103007-26 DOI: 10.1088/1367-2630/15/10/103007 Data de publicació: 2013-10 Article en revista
We extend the covariance matrix description of atom-light quantum interfaces, originally developed for real and effective spin-1/2 atoms, to include 'spin alignment' degrees of freedom. This allows accurate modelling of optically probed spin-1 ensembles in arbitrary magnetic fields. We also include technical noise terms that are very common in experimental situations. These include magnetic field noise, variable atom number and the effect of magnetic field inhomogeneities. We demonstrate the validity of our extended model by comparing numerical simulations to a free-induction decay measurement of polarized 87Rb atoms in the f = 1 ground state. We qualitatively and quantitatively reproduce experimental results with no free parameters. The model can be easily extended to larger spin systems, and adapted to more complicated experimental situations.
We extend the covariance matrix description of atom–light quantum interfaces, originally developed for real and effective spin-1/2 atoms, to include ‘spin alignment’ degrees of freedom. This allows accurate modelling of
optically probed spin-1 ensembles in arbitrary magnetic fields. We also include
technical noise terms that are very common in experimental situations. These include magnetic field noise, variable atom number and the effect of magnetic field inhomogeneities. We demonstrate the validity of our extended model by comparing numerical simulations to a free–induction decay measurement of polarized 87Rb atoms in the f = 1 ground state. We qualitatively and
quantitatively reproduce experimental results with no free parameters. The model can be easily extended to larger spin systems, and adapted to more complicated experimental situations.
Here, we enhance the capabilities of the atomic force microscope (AFM) to show that force profiles can be reconstructed without restriction by monitoring the wave profile of the cantilever during a single oscillation cycle. Two approaches are provided to reconstruct the force profile in both the steady and transient states in what we call single-cycle measurements. The robustness of the formalism is tested numerically to recover complex but relevant interactions. With single-cycle measurements, we add high temporal resolution (possibly microsecond range) to the spatial resolution of AFM. The access to simultaneous high throughput and high sensitivity further opens the door to a variety of feedback options for imaging.
Here, we enhance the capabilities of the atomic force microscope (AFM) to show that force profiles can be reconstructed without restriction by monitoring the wave profile of the cantilever during a single oscillation cycle.
Two approaches are provided to reconstruct the force profile in both the steady
and transient states in what we call single-cycle measurements. The robustness of
the formalism is tested numerically to recover complex but relevant interactions.
With single-cycle measurements, we add high temporal resolution (possibly microsecond range) to the spatial resolution of AFM. The access to simultaneous high throughput and high sensitivity further opens the door to a variety of feedback options for imaging
The true role of entanglement in two-photon virtual-state spectroscopy (Saleh et al 1998 Phys. Rev. Lett. 80 3483), a two-photon absorption spectroscopic technique that can retrieve information about the energy level structure of an atom or a molecule, is controversial. The consideration of closely related techniques, such as multidimensional pump–probe spectroscopy (Roslyak et al 2009 Phys. Rev. A 79, 063409), suggests that spectroscopic information might also be retrieved by using uncorrelated pairs of photons. Here we show that this is not the case. In the two-photon absorption process, the ability to obtain information about the energy level structure of a medium depends on the spectral shape of existing temporal (frequency) correlations between the absorbed photons. In fact, it is a combination of both the presence of frequency correlations (entanglement) and their specific spectral shape that makes the realization of two-photon virtual-state spectroscopy possible. This result helps in selecting the type of two-photon source that needs to be used in order to experimentally perform the two-photon virtual-state spectroscopy technique.
A formalism to extract and quantify unknown quantities such as
sample deformation, the viscosity of the sample and surface energy hysteresis
in amplitude modulation atomic force microscopy is presented. Recovering
the unknowns only requires the cantilever to be accurately calibrated and the
dissipative processes occurring during sample deformation to be well modeled.
The theory is validated by comparison with numerical simulations and shown
to be able to provide, in principle, values of sample deformation with picometer
We show that the sensitivity and robustness of a label-free optical imaging technique based on stimulated Raman scattering (SRS) can be enhanced by using resonant optical transitions in a Raman adiabatic passage scheme. Our approach is based on the consideration that any enhancement of the flow of energy between two light beams involved in the SRS process is related to an increase in atomic population transfer between the energy levels of interest. One can thus profit from techniques developed in quantum optics to maximize such atomic population transfer for enhancing the sensitivity and robustness of optical imaging techniques.