Strength Of Local Interactions Research Articles

Optimal distributed multi-parameter estimation in noisy environments

We consider the task of multiple parameter estimation in the presence of strong correlated noise with a network of distributed sensors. The signals and the noises have different spatial dependence but are encoded with the same local generators. We study how to find and improve noise-insensitive strategies. We show that sequentially probing with GHZ states from the decoherence-free subspace that we identify is asymptotically optimal up to a factor of at most 4 in the limit of many repetitions. The implementation of such strategies only requires local read-out and ‘passive’ resources—an initially entangled state of the sensors and tunable local interaction strength.

Rationalizing doping and electronic correlations in LaFe2As2

We compute the electronic properties of the normal state of uncollapsed $\mathrm{La}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$, taking into account local dynamical correlations by means of slave-spin mean-field$+$density-functional theory. Assuming the same local interaction strength used to model the whole electron- and hole-doped $\mathrm{Ba}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$ family, our calculations reproduce the experimental Sommerfeld specific heat coefficient, which is twice the value predicted by uncorrelated band theory. We find that $\mathrm{La}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$ has a reduced bare bandwidth and this solves the apparent paradox of its sizable correlations despite its nominal valence ${\mathrm{d}}^{6.5}$, which would imply extreme overdoping and uncorrelated behavior in $\mathrm{Ba}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$. Our results yield a consistent picture of the whole 122 family and point at the importance of the correlation strength, rather than sheer doping, in the interpretation of the phase diagram of iron-based superconductors

Undecidability of the Spectral Gap

Abstract We construct families of translationally invariant, nearest-neighbour Hamiltonians on a 2D square lattice of d-level quantum systems (d constant), for which determining whether the system is gapped or gapless is an undecidable problem. This is true even with the promise that each Hamiltonian is either gapped or gapless in the strongest sense: it is promised to either have continuous spectrum above the ground state in the thermodynamic limit, or its spectral gap is lower-bounded by a constant. Moreover, this constant can be taken equal to the operator norm of the local operator that generates the Hamiltonian (the local interaction strength). The result still holds true if one restricts to arbitrarily small quantum perturbations of classical Hamiltonians. The proof combines a robustness analysis of Robinson’s aperiodic tiling, together with tools from quantum information theory: the quantum phase estimation algorithm and the history state technique mapping Quantum Turing Machines to Hamiltonians.

Scattering length in holographic confining theories

The low-energy effective theory description of a confining theory, such as QCD, is constructed including local interactions between hadrons organized in a derivative expansion. This kind of approach also applies more generically to theories with a mass gap, once the relevant low energy degrees of freedom are identified. The strength of local interactions in the effective theory is determined by the low momentum expansion of scattering amplitudes, with the scattering length capturing the leading order. We compute the main contribution to the scattering length between two spin-zero particles in strongly coupled theories using the gauge/gravity duality. We study two different theories with a mass gap: a massive deformation of ${\cal N}=4$ super Yang-Mills theory (${\cal N}=1^*$) and a non-supersymmetric five-dimensional theory compactified on a circle. These cases have a different realization of the mass gap in the dual gravity description: the former is the well-known GPPZ singular solution and the latter a smooth $AdS_6$ soliton geometry. Despite disparate gravity duals, we find that the scattering lengths have strikingly similar functional dependences on the masses of the particles and on the conformal dimension of the operators that create them. This evinces universal behavior in the effective description of gapped strongly coupled theories beyond what is expected from symmetry considerations alone.

Flow Equation Approach to Periodically Driven Quantum Systems

We present a theoretical method to generate a highly accurate {\em time-independent} Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which renormalization group-like flow equations are derived to produce the effective Hamiltonian. Our tractable method has a range of validity reaching into frequency regimes that are usually inaccessible via high frequency $\omega$ expansions in the parameter $h/\omega$, where $h$ is the upper limit for the strength of local interactions. We demonstrate our approach on both interacting and non-interacting many-body Hamiltonians where it offers an improvement over the more well-known Magnus expansion and other high frequency expansions. For the interacting models, we compare our approximate results to those found via exact diagonalization. While the approximation generally performs better globally than other high frequency approximations, the improvement is especially pronounced in the regime of lower frequencies and strong external driving. This regime is of special interest because of its proximity to the resonant regime where the effect of a periodic drive is the most dramatic. Our results open a new route towards identifying novel non-equilibrium regimes and behaviors in driven quantum many-particle systems.

CT-X: An efficient continuous-time quantum Monte Carlo impurity solver in the Kondo regime

In the present paper, we present an efficient continuous-time quantum Monte Carlo impurity solver termed CT-X with high acceptance rate at low temperature for multi-orbital quantum impurity models with general interaction. In this hybridization expansion impurity solver, the imaginary time evolution operator for the high energy multiplets, which decays very rapidly with the imaginary time, is approximated by a probability normalized δ-function. As the result, the virtual charge fluctuations of fn→fn±1 are well included on the same footing without applying Schrieffer–Wolff transformation (SWT) explicitly. CT-X is proven to be equivalent to SWT on the leading order of W/U, where W is half the conduction band width and U is the local interaction strength. As benchmarks, our algorithm perfectly reproduces the results for both Coqblin–Schriffeer model and Kondo lattice model obtained by CT-J method developed by Otsuki et al.. Furthermore, it allows capturing low energy physics of heavy-fermion materials directly without fitting the exchange coupling J in the Kondo model. Finally, we reformulate the dynamical mean-field theory loops using only the quasi-particle part of the f-electron Green’s function measured in CT-X. Our benchmark calculations on CeIrIn5 at low temperature demonstrate a very reasonable low-energy f-electron density of states, which is in good agreement with the recent ARPES experiment.

Phase transition, structure and color-transition behaviors of monocarboxylic diacetylene and polydiacetylene assemblies: The opposite effects of alkyl chain length

This contribution demonstrates the structural-property relationship of diacetylene(DA) and polydiacetylene(PDA) assemblies in solid state and aqueous suspension. We explore two series of 7 monocarboxylic DA monomers and the resulting PDAs, constituting systematic variation of alkyl chain length at the tail and carboxylic head group position. The shortening of DA alkyl tail causes a reduction of its melting temperature. The shortening of alkyl segment adjacent to the carboxylic head group, in contrary, causes the opposite effect. The DA monomer constituting the shortest alkyl segment exhibits the highest melting temperature. Infrared spectroscopy is utilized to probe the strength of local interactions within these DA assemblies. X-ray diffraction reveals the variation of segmental orientation within the lamella bilayer structure of these DAs and PDAs depending on the alkyl chain length. The change of alkyl length also affects morphology and particle size. The color-transition behaviors of these PDAs investigated upon exposure to heat, ethanol and NaOH show discrepancies. The thermochromic transition temperature of PDAs is consistent with the melting temperature of their DA precursors. Interestingly, perturbation of the systems by adding ethanol or NaOH results in rather different trends, attributed to different local interactions of these stimuli at the interfacial region.

Rigorous symmetry adaptation of multiorbital rotationally invariant slave-boson theory with application to Hund's rules physics

The theory of correlated electron systems on a lattice proves notoriously complicated because of the exponential growth of Hilbert space. Mean-field approaches provide valuable insight when the self-energy has a dominant local structure. Additionally, the extraction of effective low-energy theories from the generalized many-body representation is highly desirable. In this respect, the rotational-invariant slave boson (RISB) approach in its mean-field formulation enables versatile access to correlated lattice problems. However in its original form, due to numerical complexity, the RISB approach is limited to about three correlated orbitals per lattice site. We thus present a thorough symmetry-adapted advancement of RISB theory, suited to efficiently deal with multi-orbital Hubbard Hamiltonians for complete atomic-shell manifolds. It is utilized to study the intriguing problem of Hund's physics for three- and especially five-orbital manifolds on the correlated lattice, including crystal-field terms as well as spin-orbit interaction. The well-known Janus-face phenomenology, i.e. strenghtening of correlations at smaller-to-intermediate Hubbard $U$ accompanied by a shift of the Mott transition to a larger $U$ value, has a stronger signature and more involved multiplet resolution for five-orbital problems. Spin-orbit interaction effectively reduces the critical local interaction strength and weakens the Janus-face behavior. Application to the realistic challenge of Fe chalcogenides underlines the subtle interplay of the orbital degrees of freedom in these materials

Negative density dependence mediates biodiversity-productivity relationships across scales.

Regional species diversity generally increases with primary productivity whereas local diversity-productivity relationships are highly variable. This scale-dependence of the biodiversity-productivity relationship highlights the importance of understanding the mechanisms that govern variation in species composition among local communities, which isknown as β-diversity. Hypotheses to explain changes in β-diversity with productivity invoke multiple mechanisms operating at local and regional scales, but the relative importance of these mechanisms is unknown. Here we show that changes in the strength of local density-dependent interactions within and among tree species explain changes in β-diversity across a subcontinental-productivity gradient. Stronger conspecific relative to heterospecific negative density dependence in more productive regions was associated with higher local diversity, weaker habitat partitioning (less species sorting), and homogenization of community composition among sites (lower β-diversity). Regional processes associated with changes in species pools had limited effects on β-diversity. Our study suggests that systematic shifts in the strength of local interactions within and among species might generally contribute to some of the most prominent but poorly understood gradients in global biodiversity.

Atomic force spectroscopy and density-functional study of graphene corrugation on Ru(0001)

Graphene, a thinnest material in the world, can form moire structures on different substrates, including graphite, h-BN, or metal surfaces. In such systems the structure of graphene, i. e. its corrugation, as well as its electronic and elastic properties are defined by the combination of the system geometry and local interaction strength at the interface. The corrugation in such structures on metals is heavily extracted from diffraction or local probe microscopy experiments and can be obtained only via comparison with theoretical data, which usually simulate the experimental findings. Here we show that graphene corrugation on metals can be measured directly employing atomic force spectroscopy and obtained value coincides with state-of-the-art theoretical results. We also address the elastic reaction of the formed graphene nanodoms on the indentation process by the scanning tip that is important for the modeling and fabrication of graphene-based nanoresonators on the nanoscale.

Optimal Synchronizability of Bearings

Bearings are mechanical dissipative systems that, when perturbed, relax toward a synchronized (bearing) state. Here we find that bearings can be perceived as physical realizations of complex networks of oscillators with asymmetrically weighted couplings. Accordingly, these networks can exhibit optimal synchronization properties through fine-tuning of the local interaction strength as a function of node degree [Motter, Zhou, and Kurths, Phys. Rev. E 71, 016116 (2005)]. We show that, in analogy, the synchronizability of bearings can be maximized by counterbalancing the number of contacts and the inertia of their constituting rotor disks through the mass-radius relation, m~r(α), with an optimal exponent α=α(×) which converges to unity for a large number of rotors. Under this condition, and regardless of the presence of a long-tailed distribution of disk radii composing the mechanical system, the average participation per disk is maximized and the energy dissipation rate is homogeneously distributed among elementary rotors.

Orbital and magnetic order in the two-orbital Hubbard model

We examine the orbital and magnetic order of the two-orbital Hubbard model within dynamical mean-field theory. The model describes the low-energy physics of a partially filled ${e}_{g}$ band as can be found in some transition metal compounds. The model shows antiferromagnetic as well as ferromagnetic phases. For stabilizing ferromagnetism we find that Hund's coupling is particularly important. Quarter filling represents a very special situation in the phase diagram, where the coupling of spin, charge, and orbital degrees of freedom are involved. Exactly at quarter filling we find a metal insulator transition (MIT) between two almost fully polarized ferromagnetic states. This MIT can be tuned by changing the local interaction strength and seems to be a first order transition at zero temperature. Apart from these ferromagnetic states we were also able to stabilize antiferromagnetic and charge ordered phases at quarter filling, depending on the interaction parameters.

Innovation and growth through local and global interaction

This paper investigates the research and development activity of heterogeneous and rationally bounded firms. The latter conduct this activity through in-house research and by collecting information originating in other firms’ spillovers. Thus, research and development activity owes both to independent searching and to interaction diffusing information. We study the conditions under which this idiosyncratic effort yields effects that have either local, system-wise negligible impacts or cumulate to generate significant aggregate ones. In the latter case, global effects feed back upon the incentive to innovate and therefore on the strength of local interaction as well as on autonomous research efforts. It is these dynamic forces that we model. We compare cases in which significant aggregate effects do emerge with cases in which they do not and study their outcome on innovation-directed investment and on long-term growth.

A mutation designed to alter crystal packing permits structural analysis of a tight‐binding fluorescein–scFv complex

The structure of the scFv fragment FITC-E2, obtained from a naive phage antibody scFv library derived from human donors, was determined at 2.1 A resolution in the free form and at 3.0 A in the complexed form. The wild-type (wt) scFv binds fluorescein with a K(D) of 0.75 nM. The free scFv readily crystallizes by compacting its 18 amino acid-long CDR-H3, partially occluding the binding site and further blocking access by binding to the "bottom" of a neighboring scFv molecule with a cluster of exposed aromatic residues within CDR-H3. Only upon mutating one of the residues involved in this dominant crystal contact, an exposed tryptophan in the middle of CDR-H3, crystals of the complex could be obtained. A series of alanine mutants within the putative antigen binding site, covering a range of binding affinities, were used to relate macroscopic thermodynamic and kinetic binding parameters to single-molecule disruption forces measured by AFM. The effects of the mutations on the binding properties, particularly on the fraction of binding-competent molecules within the population, cannot be fully explained by changes in the strength of local interactions. The significant conformational change of CDR-H3 between the free and the liganded form illustrates the plasticity of the binding site. An accompanying study in this issue by Curcio and colleagues presents the molecular dynamics simulation of the forced unbinding experiments and explores possible effects of the mutations on the unbinding pathway of the hapten.

Interaction strength and extinction risk in a metacommunity

Species interactions and connectivity are both central to explaining the stability of ecological communities and the problem of species extinction. Yet, the role of species interactions for the stability of spatially subdivided communities still eludes ecologists. Ecological models currently address the problem of stability by exploring the role of interaction strength in well mixed habitats, or of connectivity in subdivided communities. Here I propose a unification of interaction strength and connectivity as mechanisms explaining regional community stability. I introduce a metacommunity model based on succession dynamics in coastal ecosystems, incorporating limited dispersal and facilitative interactions. I report a sharp transition in regional stability and extinction probability at intermediate interaction strength, shown to correspond to a phase transition that generates scale-invariant distribution and high regional stability. In contrast with previous studies, stability results from intermediate interaction strength only in subdivided communities, and is associated with large-scale (scale-invariant) synchrony. These results can be generalized to other systems exhibiting phase transitions to show how local interaction strength can be used to resolve the link between regional community stability and pattern formation.

Slow relaxation in the Ising model on a small-world network with strong long-range interactions

We consider the Ising model on a small-world network, where the long-range interaction strength J2 is in general different from the local interaction strength J1, and examine its relaxation behaviors as well as phase transitions. As J(2)/J(1) is raised from zero, the critical temperature also increases, manifesting contributions of long-range interactions to ordering. However, it becomes saturated eventually at large values of J(2)/J(1) and the system is found to display very slow relaxation, revealing that ordering dynamics is inhibited rather than facilitated by strong long-range interactions. To circumvent this problem, we propose a modified updating algorithm in Monte Carlo simulations, assisting the system to reach equilibrium quickly.

Regional and local impact on species diversity - from pattern to processes.

The impact of regional factors (such as speciation or dispersal) on the species richness in local communities (S L) has received increasing attention. A prominent method to infer the impact of regional factors is the comparison of species richness in local assemblages (S L) with the total number of species in the region (S R). Linear relations between S R and S L have been interpreted as an indication of strong regional influence and weak influence of interactions within local communities. We propose that two aspects bias the outcome of such comparisons: (1) the spatial scale of local and regional sampling, and (2) the body size of the organisms. The impact of the local area reflects the scales of ecological interactions, whereas the ratio between local and regional area reflects the inherent moment of autocorrelation. A proposed impact of body size on the relation is based on the high dispersal and high abundance of small organisms. We predict strongest linearity between S R and S L for large organisms, for large local areas (less important ecological interactions) and for sampling designs where the local habitat area covers a high proportion of the regional area (more important autocorrelation). We conducted a meta-analysis on 63 relations obtained from the literature. As predicted, the linearity of the relationship between S L and S R increased with the proportion of local to regional sampling area. In contrast, neither the body size of the organisms nor the local area itself was significantly related to the relation between S L and SR. This indicated that ecological interactions played a minor role in the shape of local to regional richness plots, which instead was mainly influenced by the sampling design. We found that the studies published so far were highly biased towards larger organisms and towards high similarity between the local and regional area. The proposed prevalence of linear relationships may thus be an artefact and plots of S L to S R are not a suitable tool with which to infer the strength of local interactions.

Local interactions and the optimization of protein folding.

The role of local interactions in protein folding has recently been the subject of some controversy. Here we investigate an extension of Zwanzig's simple and general model of folding in which local and nonlocal interactions are represented by functions of single and multiple conformational degrees of freedom, respectively. The kinetics and thermodynamics of folding are studied for a series of energy functions in which the energy of the native structure is fixed, but the relative contributions of local and nonlocal interactions to this energy are varied over a broad range. For funnel shaped energy landscapes, we find that 1) the rate of folding increases, but the stability of the folded state decreases, as the contribution of local interactions to the energy of the native structure increases, and 2) the amount of native structure in the unfolded state and the transition state vary considerably with the local interaction strength. Simple exponential kinetics and a well-defined free energy barrier separating folded and unfolded states are observed when nonlocal interactions make an appreciable contribution to the energy of the native structure; in such cases a transition state theory type approximation yields reasonably accurate estimates of the folding rate. Bumps in the folding funnel near the native state, which could result from desolvation effects, side chain freezing, or the breaking of nonnative contacts, significantly alter the dependence of the folding rate on the local interaction strength: the rate of folding decreases when the local interaction strength is increased beyond a certain point. A survey of the distribution of strong contacts in the protein structure database suggests that evolutionary optimization has involved both kinetics and thermodynamics: strong contacts are enriched at both very short and very long sequence separations.

Colloidal Flocculation in Near-Critical Binary Mixtures

Colloids suspended in a binary host close to its critical point of demixing are considered theoretically. The colloids do not interact directly, but couple to the host degrees of freedom by preferring one of the two binary components and by decreasing the local interaction strength in the host system. Both couplings lead to flocculation, i.e., reversible aggregation of colloids, as the host critical point is approached. The flocculation is more pronounced in binary mixtures which are poor in the binary component preferred by the colloids, in accord with experimental observations.

Thermodynamic properties of chain liquid mixtures with strong, local interactions

AbstractThis paper addresses the effect in chain liquids on thermodynamic behavior of a large charge in the strength of local interactions on mixing. We classified real systems according to the ability of the Flory equation of state (FES) theory to prodict the excess volume. The FES theory enables reliable estimates provided the mixture is nearly athermal and the pure components obey the Flory equation of state. These requirements arise from Flory's approximations for the lattice part of the configuration integral, ZL, and the cell part, ZC, respectively. We revised ZL without adding adjustable parameters by the quasichemical perturbation method to account for local ordering in the mixture because of a large change in the strength of binary interactions on mixing. The modification improves the predictions of the thermodynamic functions for systems where Flory's ZL is inadequate.