Macroscopic Observables Research Articles

Turbulent transport in 2D collisionless guide field reconnection

Transport in hot and dilute, i.e., collisionless, astrophysical and space, plasmas is called “anomalous.” This transport is due to the interaction between the particles and the self-generated turbulence by their collective interactions. The anomalous transport has very different and not well known properties compared to the transport due to binary collisions, dominant in colder and denser plasmas. Because of its relevance for astrophysical and space plasmas, we explore the excitation of turbulence in current sheets prone to component- or guide-field reconnection, a process not well understood yet. This configuration is typical for stellar coronae, and it is created in the laboratory for which a 2.5D geometry applies. In our analysis, in addition to the immediate vicinity of the X-line, we also include regions outside and near the separatrices. We analyze the anomalous transport properties by using 2.5D Particle-in-Cell code simulations. We split off the mean slow variation (in contrast to the fast turbulent fluctuations) of the macroscopic observables and determine the main transport terms of the generalized Ohm's law. We verify our findings by comparing with the independently determined slowing-down rate of the macroscopic currents (due to a net momentum transfer from particles to waves) and with the transport terms obtained by the first order correlations of the turbulent fluctuations. We find that the turbulence is most intense in the “low density” separatrix region of guide-field reconnection. It is excited by streaming instabilities, is mainly electrostatic and “patchy” in space, and so is the associated anomalous transport. Parts of the energy exchange between turbulence and particles are reversible and quasi-periodic. The remaining irreversible anomalous resistivity can be parametrized by an effective collision rate ranging from the local ion-cyclotron to the lower-hybrid frequency. The contributions to the parallel and the perpendicular (to the magnetic field) components of the slowly varying DC-electric fields, balanced by the turbulence, are similar. This anomalous electric field is, however, smaller than the contributions of the off-diagonal pressure and electron inertia terms of Ohm's law. This result can now be verified by in-situ measurements of the turbulence, in and around the magnetic reconnection regions of the Earth's magnetosphere by the multi-spacecraft mission MMS and in laboratory experiments like MRX and VINETA-II.

Theoretical Study of Anomalous Forces Externally Induced by Superconductors

In this work we present a theoretical explanation for the possible anomalous forces induced by superconducting disks and toroids, based on the hypothesis of a preexisting state of generalized quantum entanglement that can produce momentum variation exchanged between Cooper pairs and outer particles. Considering the immense amount of particles involved in the phenomenon as coherent Cooper pairs, and indications of previous studies, we use classical quantities as macroscopic observables in our calculations. We here analyzed the behavior of such superconductors and compared the experimental results early obtained in the literature with our theoretical proposal. We found that the theoretical calculations agreed with very good accuracy for two different experiments and devices. The present work really highlights the possibility of superconducting materials to be applied to induce outer forces in the environment and in external objects, as explained by our theoretical model.

Predictive coarse-graining

We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a probabilistic coarse-to-fine map. This corresponds to a directed probabilistic model where the coarse variables play the role of latent generators of the fine scale (all-atom) data. From an information-theoretic perspective, the framework proposed provides an improvement upon the relative entropy method [1] and is capable of quantifying the uncertainty due to the information loss that unavoidably takes place during the coarse-graining process. Furthermore, it can be readily extended to a fully Bayesian model where various sources of uncertainties are reflected in the posterior of the model parameters. The latter can be used to produce not only point estimates of fine-scale reconstructions or macroscopic observables, but more importantly, predictive posterior distributions on these quantities. Predictive posterior distributions reflect the confidence of the model as a function of the amount of data and the level of coarse-graining. The issues of model complexity and model selection are seamlessly addressed by employing a hierarchical prior that favors the discovery of sparse solutions, revealing the most prominent features in the coarse-grained model. A flexible and parallelizable Monte Carlo – Expectation–Maximization (MC-EM) scheme is proposed for carrying out inference and learning tasks. A comparative assessment of the proposed methodology is presented for a lattice spin system and the SPC/E water model.

The relation between stretched-exponential relaxation and the vibrational density of states in glassy disordered systems

Amorphous solids or glasses are known to exhibit stretched-exponential decay over broad time intervals in several of their macroscopic observables: intermediate scattering function, dielectric relaxation modulus, time-dependent elastic modulus, etc. This behaviour is prominent especially near the glass transition. In this Letter we show, on the example of dielectric relaxation, that stretched-exponential relaxation is intimately related to the peculiar lattice dynamics of glasses. By reformulating the Lorentz model of dielectric matter in a more general form, we express the dielectric response as a function of the vibrational density of states (DOS) for a random assembly of spherical particles interacting harmonically with their nearest-neighbours. Surprisingly we find that near the glass transition for this system (which coincides with the Maxwell rigidity transition in this model), the dielectric relaxation is perfectly consistent with stretched-exponential behaviour with Kohlrausch exponents 0.56<β<0.65, which is the range where exponents are measured in most experimental systems. Crucially, the root cause of stretched-exponential relaxation can be traced back to soft modes (boson-peak) in the DOS.

Critical exponents and scaling invariance in the absence of a critical point.

The paramagnetic-to-ferromagnetic phase transition is classified as a critical phenomenon due to the power-law behaviour shown by thermodynamic observables when the Curie point is approached. Here we report the observation of such a behaviour over extraordinarily many decades of suitable scaling variables in ultrathin Fe films, for certain ranges of temperature T and applied field B. This despite the fact that the underlying critical point is practically unreachable because protected by a phase with a modulated domain structure, induced by the dipole–dipole interaction. The modulated structure has a well-defined spatial period and is realized in a portion of the (T, B) plane that extends above the putative critical temperature, where thermodynamic quantities do not display any singularity. Our results imply that scaling behaviour of macroscopic observables is compatible with an avoided critical point.

Systematic and Automated Development of Quantum Mechanically Derived Force Fields: The Challenging Case of Halogenated Hydrocarbons.

A robust and automated protocol for the derivation of sound force field parameters, suitable for condensed-phase classical simulations, is here tested and validated on several halogenated hydrocarbons, a class of compounds for which standard force fields have often been reported to deliver rather inaccurate performances. The major strength of the proposed protocol is that all of the parameters are derived only from first principles because all of the information required is retrieved from quantum mechanical data, purposely computed for the investigated molecule. This a priori parametrization is carried out separately for the intra- and intermolecular contributions to the force fields, respectively exploiting the Joyce and Picky programs, previously developed in our group. To avoid high computational costs, all quantum mechanical calculations were performed exploiting the density functional theory. Because the choice of the functional is known to be crucial for the description of the intermolecular interactions, a specific procedure is proposed, which allows for a reliable benchmark of different functionals against higher-level data. The intramolecular and intermolecular contribution are eventually joined together, and the resulting quantum mechanically derived force field is thereafter employed in lengthy molecular dynamics simulations to compute several thermodynamic properties that characterize the resulting bulk phase. The accuracy of the proposed parametrization protocol is finally validated by comparing the computed macroscopic observables with the available experimental counterparts. It is found that, on average, the proposed approach is capable of yielding a consistent description of the investigated set, often outperforming the literature standard force fields, or at least delivering results of similar accuracy.

Learning the mechanisms of chemical disequilibria.

When at equilibrium, large-scale systems obey thermodynamics because they have microscopic configurations that are typical. "Typical" states are a fraction of those possible with the majority of the probability. A more precise definition of typical states underlies the transmission, coding, and compression of information. However, this definition does not apply to natural systems that are transiently away from equilibrium. Here, we introduce a variational measure of typicality and apply it to atomistic simulations of a model for hydrogen oxidation. While a gaseous mixture of hydrogen and oxygen combusts, reactant molecules transform through a variety of ephemeral species en route to the product, water. Out of the exponentially growing number of possible sequences of chemical species, we find that greater than 95% of the probability concentrates in less than 1% of the possible sequences. Overall, these results extend the notion of typicality across the nonequilibrium regime and suggest that typical sequences are a route to learning mechanisms from experimental measurements. They also open up the possibility of constructing ensembles for computing the macroscopic observables of systems out of equilibrium.

Consistency of the structure of Legendre transform in thermodynamics with the Kolmogorov–Nagumo average

We show the robustness of the structure of Legendre transform in thermodynamics against the replacement of the standard linear average with the Kolmogorov–Nagumo nonlinear average to evaluate the expectation values of the macroscopic physical observables. The consequence of this statement is twofold: 1) the relationships between the expectation values and the corresponding Lagrange multipliers still hold in the present formalism; 2) the universality of the Gibbs equation as well as other thermodynamic relations are unaffected by the structure of the average used in the theory.

Quantum capacitance of an HgTe quantum well as an indicator of the topological phase

Varying the quantum-well width in an HgTe/CdTe heterostructure allows to realize normal and inverted semiconducting band structures, making it a prototypical system to study two-dimensional (2D) topological-insulator behavior. We have calculated the zero-temperature thermodynamic density of states $D_\mathrm{T}$ for the electron-doped situation in both regimes, treating interactions within the Hartree-Fock approximation. A distinctively different behavior for the density dependence of $D_\mathrm{T}$ is revealed in the inverted and normal cases, making it possible to detect the system's topological order through measurement of macroscopic observables such as the quantum capacitance or electronic compressibility. Our results establish the 2D electron system in HgTe quantum wells as unique in terms of its collective electronic properties.

Dissipative entanglement of quantum spin fluctuations

We consider two non-interacting infinite quantum spin chains immersed in a common thermal environment and undergoing a local dissipative dynamics of Lindblad type. We study the time evolution of collective mesoscopic quantum spin fluctuations that, unlike macroscopic mean-field observables, retain a quantum character in the thermodynamical limit. We show that the microscopic dissipative dynamics is able to entangle these mesoscopic degrees of freedom, through a purely mixing mechanism. Further, the behaviour of the dissipatively generated quantum correlations between the two chains is studied as a function of temperature and dissipation strength.

Asymptotic behavior of macroscopic observables in generic spin systems

This work clarifies a fundamental relationship between spectral gap and ground state properties, where the spectral gap means the energy difference between the ground state and the first excited state. In short-range interacting systems, the well-known exponential clustering theorem has been derived for the ground states: the bipartite correlations decay exponentially beyond a finite localization length, which is smaller than the inverse of the spectral gap. However, in more general systems including long-range interacting systems, the problem of how to characterize universal ground state structures by reference to the spectral gap is an ongoing challenge. Recently, for such systems, another fundamental constraint dubbed local reversibility has been proved for arbitrarily gapped ground states; as a consequence, it also results in the exponential concentration of the probability distribution of macroscopic observables. In this paper, we extend this kind of asymptotic behavior to more general setups.

Shear viscosity over entropy density ratio with extended quasiparticles

We consider an effective field theory description of beyond-quasi-particle excitations aiming to associate the transport properties of the system with the spectral density of states. Tuning various properties of the many-particle correlations, we investigate how the robust microscopic features are translated into the macroscopic observables like shear viscosity and entropy density. The liquid-gas crossover is analysed using several examples. A thermal constraint on the fluidity measure, the ratio of shear viscosity to entropy density, is discussed.

A General Approximation for the Dynamics of Quantitative Traits.

Selection, mutation, and random drift affect the dynamics of allele frequencies and consequently of quantitative traits. While the macroscopic dynamics of quantitative traits can be measured, the underlying allele frequencies are typically unobserved. Can we understand how the macroscopic observables evolve without following these microscopic processes? This problem has been studied previously by analogy with statistical mechanics: the allele frequency distribution at each time point is approximated by the stationary form, which maximizes entropy. We explore the limitations of this method when mutation is small (4Nμ < 1) so that populations are typically close to fixation, and we extend the theory in this regime to account for changes in mutation strength. We consider a single diallelic locus either under directional selection or with overdominance and then generalize to multiple unlinked biallelic loci with unequal effects. We find that the maximum-entropy approximation is remarkably accurate, even when mutation and selection change rapidly.

In-Silico Electrophysiology: On the Activation of Voltage-Gated Ion Channels using Molecular Dynamics Simulations

The working cycle of voltage gated ion channels involves the complex conformational change of modular protein units called voltage sensor domains (VSDs). For over forty years, these rearrangements have been recorded as “gating” currents, intensities and kinetics of which are unique signatures of VGC function. Here we show, for the potassium VGC Kv1.2, that the atomistic description of VSD activation obtained by molecular dynamics simulations and free energy calculations is consistent with the phenomenological models adopted so far to account for the macroscopic observables measured by electrophysiology. The properties of the computed single channel current traces, as well as “whole-cell” gating currents under several voltage clamped protocols are in agreement with experiments. Hence, by providing a connection between microscopic and macroscopic dynamics, our results pave the way for a deeper understanding of the molecular level factors affecting VSD activation, such as lipid composition, amino acid mutations, and binding of endogenous ligands.

Anomalous Effects from Dipole-Environment Quantum Entanglement

In this work, we analyze anomalous effects observed in the operation of two different technological devices: a magnetic core and a parallel plate (symmetrical or asymmetrical) capacitor. From experimental measurements on both devices, we detected small raised anomalous forces that cannot be explained by known interactions in the traditional theories. So, we verify that magnetic cores also exhibits an effect similar to BB effect in capacitors. As the variations of device inertia have not been completely understood by means of current theories, we here propose a theoretical framework in which the anomalous effects can consistently be explained by a preexisting state of quantum entanglement between the external environment and either magnetic dipoles of magnetic cores or electric dipoles of capacitors, so that the effects would be manifested by the application of a strong magnetic field on the former or an intense electric field on the latter. The values of the macroscopic observables calculated in such a theoretical framework revealed good agreement with the experimental measurements performed in both cases, so that the non-locality hypothesis based on the generalized quantum correlation between dipoles and environment is consistent as explanation for the anomalous effects observed. The control and enhancement of the effect can allow the future viability of a new technology based on electric propulsion of rockets and aircrafts.

Witnessing entanglement by proxy

Entanglement is a ubiquitous feature of low temperature systems and believed to be highly relevant for the dynamics of condensed matter properties and quantum computation even at higher temperatures. The experimental certification of this paradigmatic quantum effect in macroscopic high temperature systems is constrained by the limited access to the quantum state of the system. In this paper we show how macroscopic observables beyond the mean energy of the system can be exploited as proxy witnesses for entanglement detection. Using linear and semi-definite relaxations we show that all previous approaches to this problem can be outperformed by our proxies, i.e. entanglement can be certified at higher temperatures without access to any local observable. For an efficient computation of proxy witnesses one can resort to a generalised grand canonical ensemble, enabling entanglement certification even in complex systems with macroscopic particle numbers.

Leadership emergence in a data-driven model of zebrafish shoals with speed modulation

Models of collective animal motion can greatly aid in the design and interpretation of behavioural experiments that seek to unravel, isolate, and manipulate the determinants of leader-follower relationships. Here, we develop an initial model of zebrafish social behaviour, which accounts for both speed and angular velocity regulatory interactions among conspecifics. Using this model, we analyse the macroscopic observables of small shoals influenced by an “informed” agent, showing that leaders which actively modulate their speed with respect to their neighbours can entrain and stabilise collective dynamics of the naive shoal.

Entangling two transportable neutral atoms via local spin exchange.

To advance quantum information science, physical systems are sought that meet the stringent requirements for creating and preserving quantum entanglement. In atomic physics, robust two-qubit entanglement is typically achieved by strong, long-range interactions in the form of either Coulomb interactions between ions or dipolar interactions between Rydberg atoms. Although such interactions allow fast quantum gates, the interacting atoms must overcome the associated coupling to the environment and cross-talk among qubits. Local interactions, such as those requiring substantial wavefunction overlap, can alleviate these detrimental effects; however, such interactions present a new challenge: to distribute entanglement, qubits must be transported, merged for interaction, and then isolated for storage and subsequent operations. Here we show how, using a mobile optical tweezer, it is possible to prepare and locally entangle two ultracold neutral atoms, and then separate them while preserving their entanglement. Ground-state neutral atom experiments have measured dynamics consistent with spin entanglement, and have detected entanglement with macroscopic observables; we are now able to demonstrate position-resolved two-particle coherence via application of a local gradient and parity measurements. This new entanglement-verification protocol could be applied to arbitrary spin-entangled states of spatially separated atoms. The local entangling operation is achieved via spin-exchange interactions, and quantum tunnelling is used to combine and separate atoms. These techniques provide a framework for dynamically entangling remote qubits via local operations within a large-scale quantum register.

Vienna Soil-Organic-Matter Modeler—Generating condensed-phase models of humic substances

Humic substances are ubiquitous in the environment and have manifold functions. While their composition is well known, information on the chemical structure and three-dimensional conformation is scarce. Here we describe the Vienna Soil-Organic-Matter Modeler, which is an online tool to generate condensed phase computer models of humic substances (http://somm.boku.ac.at). Many different models can be created that reflect the diversity in composition and conformations of the constituting molecules. To exemplify the modeler, 18 different models are generated based on two experimentally determined compositions, to explicitly study the effect of varying e.g. the amount of water molecules in the models or the pH. Molecular dynamics simulations were performed on the models, which were subsequently analyzed in terms of structure, interactions and dynamics, linking macroscopic observables to the microscopic composition of the systems. We are convinced that this new tool opens the way for a wide range of in silico studies on soil organic matter.

Shape, orientation and magnitude of the curl quantum flux, the coherence and the statistical correlations in energy transport at nonequilibrium steady state

We provide a quantitative description of the nonequilibriumness based on the model of coupled oscillators interacting with multiple energy sources. This can be applied to the study of vibrational energy transport in molecules. The curl quantum flux quantifying the nonequilibriumness and time-irreversibility is quantified in the coherent representation and we find the geometric description of the shape and polarization of the flux which provides the connection between the microscopic description of quantum nonequilibriumness and the macroscopic observables, i.e., correlation function. We use the Wilson loop integral to quantify the magnitude of curl flux, which is shown to be correlated to the correlation function as well. Coherence contribution is explicitly demonstrated to be non-trivial and to considerably promote the heat transport quantified by heat current and efficiency. This comes from the fact that coherence effect is microscopically reflected by the geometric description of the flux. To uncover the effect of vibron–phonon coupling between the vibrational modes of molecular stretching (vibron) and the molecular chain (phonon), we further explore the influences of localization, which leads to the coherent and incoherent regimes that are characterized by the current–current correlations.