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We present a comparative analysis of the plethora of nonextensive and/or nonadditive entropies which go beyond the standard Boltzmann–Gibbs formulation. After defining the basic notions of additivity, extensivity, and composability, we discuss the properties of these entropies and their mutual relations, if they exist. The results are presented in two informative tables that are of strong interest to the gravity and cosmology community in the context of the recently intensively explored horizon entropies for black hole and cosmological models. Gravitational systems admit long-range interactions, which usually lead to a break of the standard additivity rule for thermodynamic systems composed of subsystems in Boltzmann–Gibbs thermodynamics. The features of additivity, extensivity, and composability are listed systematically. A brief discussion on the validity of the notion of equilibrium temperature for nonextensive systems is also presented. [ABSTRACT FROM AUTHOR]

Abstract In a world made of atoms, computer simulations of molecular systems such as proteins in water play an enormous role in science. Software packages for molecular simulation have been developed for decades. They all discretize Hamilton’s equations of motion and treat long-range potentials through cutoffs or discretization of reciprocal space. This introduces severe approximations and artifacts that must be controlled algorithmically. Here, we bring to fruition a paradigm for molecular simulation that relies on modern concepts in statistics to explore the thermodynamic equilibrium with an exact and efficient non-reversible Markov process. It is free of all discretizations, approximations, and cutoffs. We explicitly demonstrate that this approach reaches a break-even point with traditional molecular simulation performed at high precision, but without any of its approximations. We stress the potential of our paradigm for crucial applications in biophysics and other fields, and as a practical approach to molecular simulation. We set out a strategy to reach our goal of rigorous molecular simulation.

In recent years, the heat kernel has proven to be a valuable tool for graph characterization and graph-based object clustering. It serves as the fundamental solution to the heat diffusion equation associated with the discrete graph Laplacian, describing how information flows across graph edges over time by exponentiating the Laplacian eigensystem. This paper focuses on the novel concept of the generalized heat kernel of a network, recently introduced by Kalala Mutombo et al. These authors build upon the k-path Laplacian operator for graphs, pioneered by Estrada et al., to incorporate long-range interactions (LRI) into information transmission across nodes and edges of a network/graph. LRI are handled through the use of Mellin and Laplace transforms. This paper makes a notable contribution by highlighting the practical application of the generalized heat kernel. We achieve this by demonstrating the effectiveness of the generalised heat kernel invariants in object clustering with real data using principal component analysis (PCA). Moreover, we investigate how incorporating long-range interactions (LRI) impacts object characterization and clustering, revealing superior results compared to conventional diffusion methods. Through experimentation, we show that object clustering remains achievable even with small values of the Mellin and Laplace parameters, contrasting with the requirement of an infinite value in the absence of LRI. • Application of graph generalised heat kernel invariants in object clustering via PCA. • Long-range interactions enhance graph-based object clustering. • Object clustering achieved with small Mellin/Laplace parameters. [ABSTRACT FROM AUTHOR]

In a world made of atoms, computer simulations of molecular systems such as proteins in water play an enormous role in science. Software packages for molecular simulation have been developed for decades. They all discretize Hamilton's equations of motion and treat long-range potentials through cutoffs or discretization of reciprocal space. This introduces severe approximations and artifacts that must be controlled algorithmically. Here, we bring to fruition a paradigm for molecular simulation that relies on modern concepts in statistics to explore the thermodynamic equilibrium with an exact and efficient non-reversible Markov process. It is free of all discretizations, approximations, and cutoffs. We explicitly demonstrate that this approach reaches a break-even point with traditional molecular simulation performed at high precision, but without any of its approximations. We stress the potential of our paradigm for crucial applications in biophysics and other fields, and as a practical approach to molecular simulation. We set out a strategy to reach our goal of rigorous molecular simulation. [ABSTRACT FROM AUTHOR]

Single‐atom catalysis involves loading the active metal onto the carrier's surface as a single‐atom. This atom is primarily bonded to the carrier surface through hetero‐atom bonding. It is important to note that the coordination environment of the metal atoms may not be the same when each dispersed active metal atom has an identical coordination environment on the carrier's surface. The utilization of single‐atom catalysts (SACs) doesn't strictly imply that a solitary metal atom with zero valency functions as the active core. Singular atoms can also engage in distant interactions with other atoms or clusters of atoms on the substrate, like electron transfer, and frequently demonstrate specific charges. The main reason for the high activity of the catalyst is the remote (i.e., long‐range) interaction of the active atom with the surrounding coordination atoms. For this reason, the study of the mechanism of long‐range interactions between multiple single‐atom sites and between single‐atom sites and atomic cluster sites has become an important and urgent task in the design and regulation of single‐atom catalyst performance. [ABSTRACT FROM AUTHOR]

Unitarity sets upper limits on partial-wave elastic and inelastic cross-sections, which are often violated by perturbative computations. We discuss the dynamics underlying these limits in the non-relativistic regime, namely long-range interactions, and show how the resummation of the 2-particle-irreducible diagrams arising from squaring inelastic processes unitarizes both elastic and inelastic cross-sections. We provide a simple prescription to obtain the unitarized cross-sections from those that do not include resummation of the squared inelastic processes. Our results are model-independent, apply to all partial waves, and affect elastic and inelastic cross-sections, with extensive implications for new physics scenarios, such as dark-matter freeze-out, indirect detection and self-interactions.

Abstract Background Insulator-binding proteins (IBPs) play a critical role in genome architecture by forming and maintaining contact domains. While the involvement of several IBPs in organising chromatin architecture in Drosophila has been described, the specific contribution of the Suppressor of Hairy wings (Su(Hw)) insulator-binding protein to genome topology remains unclear. Results In this study, we provide evidence for the existence of long-range interactions between chromatin bound Su(Hw) and Combgap, which was first characterised as Polycomb response elements binding protein. Loss of Su(Hw) binding to chromatin results in the disappearance of Su(Hw)-Combgap long-range interactions and in a decrease in spatial self-interactions among a subset of Su(Hw)-bound genome sites. Our findings suggest that Su(Hw)-Combgap long-range interactions are associated with active chromatin rather than Polycomb-directed repression. Furthermore, we observe that the majority of transcription start sites that are down-regulated upon loss of Su(Hw) binding to chromatin are located within 2 kb of Combgap peaks and exhibit Su(Hw)-dependent changes in Combgap and transcriptional regulators’ binding. Conclusions This study demonstrates that Su(Hw) insulator binding protein can form long-range interactions with Combgap, Polycomb response elements binding protein, and that these interactions are associated with active chromatin factors rather than with Polycomb dependent repression.

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum–optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations. [ABSTRACT FROM AUTHOR]

Some physical systems, although different by their microscopic nature, in the vicinity of critical points can have similar thermodynamic and structural properties governed by universal power laws. Such systems are grouped into the so-called universality classes. The latter are determined by such global characteristics as the type of interaction, space dimensionality, symmetry, and the number of components of the order parameter. Therefore, it is interesting to investigate how the mutual influence of these characteristics can affect the critical features of the system. The goal of our research is to analyze the changes in the critical behavior of a many-particle magnetic system under the influence of two competing factors: long-range interaction and weak structural disorder. Using the example of an n-vector model in a d-dimensional space, we will investigate ferromagnetic ordering in a structurally disordered magnet with the long-range interaction decaying with the distance x as J(x)~x-d-σ, with the control parameter σ. The analysis is carried out using the field-theoretical renormalization group methods, which makes it possible to identify the universality classes of the system under consideration, their change with global parameters, and to determine the universal characteristics of critical behavior (critical exponents and marginal dimensions). It will be shown that there exists such a region of parameters (d,n,σ), where the long-range interaction and structural disorder lead to a synergistic effect and the appearance of a new, “random long-range” universality class. We obtain the renormalization group functions in the three-loop approximation, and calculate the correlation length critical exponent ν(ϵ',n) as a perturbation theory series in ϵ′ = 2σ − d. Quantitative estimates are obtained using asymptotic series resummation methods. [ABSTRACT FROM AUTHOR]

In the last years, state-to-state molecular dynamics simulations of some basic elementary processes, occurring at the gas–surface interface in a wide range of temperatures and collision energies, have been performed by adopting new potential energy surfaces. In this contribution, our attention is mostly addressed to the role of long-range forces, determining the physisorption of gaseous molecules on the surface. Such forces, formulated in terms of the improved Lennard–Jones interaction potential model, control the formation of precursor or pre-reactive state that plays a crucial role in the dynamical evolution of molecules impinging on the surface in the range of low–intermediate collision kinetic energies. The study focuses on the collisions of H2, O2, N2 and CO, initially in their ground and excited vibro-rotational levels, on a graphite surface. The resulting dispersion coefficients, which control the capture of impinging molecules, are compared and found in good agreement with those available in the literature. New selectivity and peculiarities of scattered molecules, crucial to control the kinetics of elementary chemical processes occurring at the gas–surface interfaces under thermal and sub-thermal conditions, of interest in different applied fields, are highlighted. [ABSTRACT FROM AUTHOR]

We study the low-field ground-state (GS) properties of the antiferromagnetic transverse-field Ising model with long-range interactions (afLRTFIM) on the triangular lattice. We use the method of perturbative continuous unitary transformations (pCUT) to derive an effective model for the degenerate GS space of the antiferromagnetic nearest-neighbour (NN) Ising model on a finite system, by treating the transverse-field (TF) and the long-range interactions (LRI) as a perturbation. We determine a level-crossing between the gapped plain stripe phase at small TF and the gapped clock-ordered phase at intermediate TF at hc≅0.129 for α=6, N=36 spins in order three perturbation theory on the finite system. We discuss the qualitative layout of the quantum phase diagram of the afLRTFIM on the triangular lattice.

We present a comparative analysis of the plethora of nonextensive and/or nonadditive entropies which go beyond the standard Boltzmann–Gibbs formulation. After defining the basic notions of additivity, extensivity, and composability, we discuss the properties of these entropies and their mutual relations, if they exist. The results are presented in two informative tables that are of strong interest to the gravity and cosmology community in the context of the recently intensively explored horizon entropies for black hole and cosmological models. Gravitational systems admit long-range interactions, which usually lead to a break of the standard additivity rule for thermodynamic systems composed of subsystems in Boltzmann–Gibbs thermodynamics. The features of additivity, extensivity, and composability are listed systematically. A brief discussion on the validity of the notion of equilibrium temperature for nonextensive systems is also presented.

Abstract Objectives Triple-negative breast cancer (TNBC) is a highly aggressive breast cancer subtype with limited treatment options. Unlike other breast cancer subtypes, the scarcity of specific therapies and greater frequencies of distant metastases contribute to its aggressiveness. We aimed to find epigenetic changes that aid in the understanding of the dissemination process of these cancers. Data description Using CRISPR/Cas9, our experimental approach led us to identify and disrupt an insulator element, IE8, whose activity seemed relevant for cell invasion. The experiments were performed in two well-established TNBC cellular models, the MDA-MB-231 and the MDA-MB-436. To gain insights into the underlying molecular mechanisms of TNBC invasion ability, we generated and characterized high-resolution chromatin interaction (Hi-C) and chromatin accessibility (ATAC-seq) maps in both cell models and complemented these datasets with gene expression profiling (RNA-seq) in MDA-MB-231, the cell line that showed more significant changes in chromatin accessibility. Altogether, our data provide a comprehensive resource for understanding the spatial organization of the genome in TNBC cells, which may contribute to accelerating the discovery of TNBC-specific alterations triggering advances for this devastating disease.

Abstract Background Long-range interactions between promoters and cis-regulatory elements, such as enhancers, play critical roles in gene regulation. However, the role of three-dimensional (3D) chromatin structure in orchestrating changes in transcriptional regulation during direct cell reprogramming is not fully understood. Results Here, we performed integrated analyses of chromosomal architecture, epigenetics, and gene expression using Hi-C, promoter Capture Hi-C (PCHi-C), ChIP-seq, and RNA-seq during trans-differentiation of Pre-B cells into macrophages with a β-estradiol inducible C/EBPαER transgene. Within 1h of β-estradiol induction, C/EBPα translocated from the cytoplasm to the nucleus, binding to thousands of promoters and putative regulatory elements, resulting in the downregulation of Pre-B cell-specific genes and induction of macrophage-specific genes. Hi-C results were remarkably consistent throughout trans-differentiation, revealing only a small number of TAD boundary location changes, and A/B compartment switches despite significant changes in the expression of thousands of genes. PCHi-C revealed widespread changes in promoter-anchored loops with decreased interactions in parallel with decreased gene expression, and new and increased promoter-anchored interactions in parallel with increased expression of macrophage-specific genes. Conclusions Overall, our data demonstrate that C/EBPα-induced trans-differentiation involves few changes in genome architecture at the level of TADs and A/B compartments, in contrast with widespread reorganization of thousands of promoter-anchored loops in association with changes in gene expression and cell identity.

The RNA secondary structure is like a blueprint that holds the key to unlocking the mysteries of RNA function and 3D structure. It serves as a crucial foundation for investigating the complex world of RNA, making it an indispensable component of research in this exciting field. However, pseudoknots cannot be accurately predicted by conventional prediction methods based on free energy minimization, which results in a performance bottleneck. To this end, we propose a deep learning-based method called TransUFold to train directly on RNA data annotated with structure information. It employs an encoder-decoder network architecture, named Vision Transformer, to extract long-range interactions in RNA sequences and utilizes convolutions with lateral connections to supplement short-range interactions. Then, a post-processing program is designed to constrain the model's output to produce realistic and effective RNA secondary structures, including pseudoknots. After training TransUFold on benchmark datasets, we outperform other methods in test data on the same family. Additionally, we achieve better results on longer sequences up to 1600 nt, demonstrating the outstanding performance of Vision Transformer in extracting long-range interactions in RNA sequences. Finally, our analysis indicates that TransUFold produces effective pseudoknot structures in long sequences. As more high-quality RNA structures become available, deep learning-based prediction methods like Vision Transformer can exhibit better performance.

Quantized vortices are the hallmark of superfluidity, and are often sought out as the first observable feature in new superfluid systems. Following the recent experimental observation of vortices in Bose–Einstein condensates comprised of atoms with inherent long-range dipole-dipole interactions [Nat. Phys. 18, 1453-1458 (2022)], we thoroughly investigate vortex properties in the three-dimensional dominantly dipolar regime, where beyond-mean-field effects are crucial for stability, and investigate the interplay between trap geometry and magnetic field tilt angle.

Background: Long-range interactions between promoters and cis-regulatory elements, such as enhancers, play critical roles in gene regulation. However, the role of three-dimensional (3D) chromatin structure in orchestrating changes in transcriptional regulation during direct cell reprogramming is not fully understood. Results: Here, we performed integrated analyses of chromosomal architecture, epigenetics, and gene expression using Hi-C, promoter Capture Hi-C (PCHi-C), ChIP-seq, and RNA-seq during trans-differentiation of Pre-B cells into macrophages with a β-estradiol inducible C/EBPαER transgene. Within 1h of β-estradiol induction, C/EBPα translocated from the cytoplasm to the nucleus, binding to thousands of promoters and putative regulatory elements, resulting in the downregulation of Pre-B cell-specific genes and induction of macrophage-specific genes. Hi-C results were remarkably consistent throughout trans-differentiation, revealing only a small number of TAD boundary location changes, and A/B compartment switches despite significant changes in the expression of thousands of genes. PCHi-C revealed widespread changes in promoter-anchored loops with decreased interactions in parallel with decreased gene expression, and new and increased promoter-anchored interactions in parallel with increased expression of macrophage-specific genes. Conclusions: Overall, our data demonstrate that C/EBPα-induced trans-differentiation involves few changes in genome architecture at the level of TADs and A/B compartments, in contrast with widespread reorganization of thousands of promoter-anchored loops in association with changes in gene expression and cell identity. [ABSTRACT FROM AUTHOR]

The adsorption of nitrogen molecules on a (100) tungsten surface has been studied using a new potential energy surface in which long-range interactions are suitably characterized and represented by the Improved Lennard–Jones function. The new potential energy surface is used to carry out molecular dynamics simulations by adopting a semiclassical collisional method that explicitly includes the interaction with the surface phonons. The results of the sticking probability, evaluated as a function of the collision energy, are in good agreement with those obtained in the experiments and improve the already good comparison recently obtained with calculations performed using interactions from the Density Functional Theory method and corrected for long-range van der Waals contributions. The dependence of trapping probability on the surface temperature for a well-defined collision energy has also been investigated. [ABSTRACT FROM AUTHOR]

Objectives: Triple-negative breast cancer (TNBC) is a highly aggressive breast cancer subtype with limited treatment options. Unlike other breast cancer subtypes, the scarcity of specific therapies and greater frequencies of distant metastases contribute to its aggressiveness. We aimed to find epigenetic changes that aid in the understanding of the dissemination process of these cancers. Data description: Using CRISPR/Cas9, our experimental approach led us to identify and disrupt an insulator element, IE8, whose activity seemed relevant for cell invasion. The experiments were performed in two well-established TNBC cellular models, the MDA-MB-231 and the MDA-MB-436. To gain insights into the underlying molecular mechanisms of TNBC invasion ability, we generated and characterized high-resolution chromatin interaction (Hi-C) and chromatin accessibility (ATAC-seq) maps in both cell models and complemented these datasets with gene expression profiling (RNA-seq) in MDA-MB-231, the cell line that showed more significant changes in chromatin accessibility. Altogether, our data provide a comprehensive resource for understanding the spatial organization of the genome in TNBC cells, which may contribute to accelerating the discovery of TNBC-specific alterations triggering advances for this devastating disease. [ABSTRACT FROM AUTHOR]

The RNA secondary structure is like a blueprint that holds the key to unlocking the mysteries of RNA function and 3D structure. It serves as a crucial foundation for investigating the complex world of RNA, making it an indispensable component of research in this exciting field. However, pseudoknots cannot be accurately predicted by conventional prediction methods based on free energy minimization, which results in a performance bottleneck. To this end, we propose a deep learning-based method called TransUFold to train directly on RNA data annotated with structure information. It employs an encoder-decoder network architecture, named Vision Transformer, to extract long-range interactions in RNA sequences and utilizes convolutions with lateral connections to supplement short-range interactions. Then, a post-processing program is designed to constrain the model's output to produce realistic and effective RNA secondary structures, including pseudoknots. After training TransUFold on benchmark datasets, we outperform other methods in test data on the same family. Additionally, we achieve better results on longer sequences up to 1600 nt, demonstrating the outstanding performance of Vision Transformer in extracting long-range interactions in RNA sequences. Finally, our analysis indicates that TransUFold produces effective pseudoknot structures in long sequences. As more high-quality RNA structures become available, deep learning-based prediction methods like Vision Transformer can exhibit better performance. [ABSTRACT FROM AUTHOR]

We show that defect modes in infinite systems of resonators have corresponding modes in finite systems which converge as the size of the system increases. We study the generalized capacitance matrix as a model for three-dimensional coupled resonators with long-range interactions and consider defect modes that are induced by compact perturbations. If such a mode exists, then there are elements of the discrete spectrum of the corresponding truncated finite system that converge to each element of the pure point spectrum. The rate of convergence depends on the dimension of the lattice. When the dimension of the lattice is equal to that of the physical space, the convergence is exponential. Conversely, when the dimension of the lattice is less than that of the physical space, the convergence is only algebraic, because of long-range interactions arising due to coupling with the far field. [ABSTRACT FROM AUTHOR]

In the vast majority of biologically relevant cases of receptor-ligand complex formation, the binding site of the receptor is a small part of its surface, and moreover, formation of a biologically active complex often requires a specific orientation of the ligand relative to the binding site. Before the formation of the initial form of the complex, only long-range, electrostatic and hydrodynamic interactions can act between the ligand approaching the binding site and the receptor. In this context, the question arises whether as a result of these interactions, there is a pre-orientation of the ligand towards the binding site, which to some extent would accelerate the formation of the complex. The role of electrostatic interactions in the orientation of the ligand relative to the binding site of the receptor is well documented. The analogous role of hydrodynamic interactions, although assessed as very significant by Brune and Kim (PNAS 91, 2930–2934, (1994)), is still debatable. In this article, I present the current state of knowledge on this subject and consider the possibilities of demonstrating the orienting effect of hydrodynamic interactions in the processes of receptor–ligand association, in an experimental way supported by computer simulations. [ABSTRACT FROM AUTHOR]

The influence of dispersive long-range interactions on liquid bulk phase transport and excess properties of six binary Lennard–Jones (LJ) mixtures was studied by molecular dynamics simulation and equation of state modelling. For the transport properties, the self-diffusion coefficients, mutual diffusion coefficients, shear viscosity, and thermal conductivity were considered. For the excess properties, the excess energy, volume, Gibbs energy, and entropy were studied. Moreover, the thermodynamic factor was studied. The two components had the same size parameter in all cases, but different dispersion energies and different cross-interaction parameters. Thereby, the six resulting mixtures show three types of phase behaviour: ideal, high- and low-boiling azeotrope. For studying the influence of the dispersive long-range interactions, the results of the full LJ potential were compared to the LJ truncated and shifted (LJTS) potential applying the corresponding states principle. The dispersive long-range interactions have a significant influence on the self-diffusion and the mutual diffusion coefficients, whereas the shear viscosity and the thermal conductivity are hardly affected. For all investigated properties, the dispersive long-range interactions have practically no influence on the composition dependency. [ABSTRACT FROM AUTHOR]

The accumulated knowledge about the structure of protein-DNA complexes allowed us to understand the mechanisms of protein-DNA recognition and searching for a specific site on DNA. Obviously, the mechanism of specific DNA recognition by a protein must satisfy two requirements. First, the probability of incorrect binding should be very small. Second, the time to find the "correct" binding site should not be too long. If we assume that protein recognition of a precise site on DNA occurs at some distance from DNA and calculate global minima, we can avoid local minima at short distances. The only long-range interaction is the interaction of charges. The location of charges on DNA in three-dimensional space depends on the local conformation of DNA and thus reflects the DNA sequence and sets the spatial pattern for recognition. Various factors such as counter ion concentration, ionic strength, and pH can affect protein recognition of DNA. Nowadays, the theory of long-range interactions makes it possible to calculate the best mutual spatial arrangement of protein and DNA molecules by charged groups and avoid misplaced binding. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to show how the combination of the well-known results for convergence to equilibrium and conditional regularity, in addition to a short-time existence result, lead to a quick proof of the existence of global smooth solutions for the non cutoff Boltzmann equation when the initial data is close to equilibrium. We include a short-time existence result for polynomially-weighted $ L^\infty $ initial data. From this, we deduce that if the initial data is sufficiently close to a Maxwellian in this norm, then a smooth solution exists globally in time.

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum–optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.

We study generalizations of the forest fire model introduced in [4] and [10] by allowing the rates at which the trees grow to depend on their location, introducing long-range burning, as well as a continuous-space generalization of the model. We establish that in all the models in consideration the expected time required to reach a site at distance x from the origin is of order $(\!\log x)^{(\!\log 2)^{-1}+\delta}$ for any $\delta>0$. [ABSTRACT FROM AUTHOR]

We consider the jellium model of N particles on a line confined in an external harmonic potential and with a pairwise one-dimensional Coulomb repulsion of strength α > 0. Using a Coulomb gas method, we study the statistics of s = (1 / N) ∑ i = 1 N f (x i) where f (x), in principle, is an arbitrary smooth function. While the mean of s is easy to compute, the variance is nontrivial due to the long-range Coulomb interactions. In this paper we demonstrate that the fluctuations around this mean are Gaussian with a variance Var (s) ≈ b / N 3 for large N. In this paper, we provide an exact compact formula for the constant b = 1 / (4 α) ∫ − 2 α 2 α [ f ′ (x) ] 2 d x. In addition, we also calculate the full large deviation function characterizing the tails of the full distribution P (s , N) for several different examples of f (x). Our analytical predictions are confirmed by numerical simulations. [ABSTRACT FROM AUTHOR]

We study the non-equilibrium dynamics of a one-dimensional Bose gas with long-range interactions that decay as $(\frac{1}{r^{\alpha}})$ $(0.5 \lt \alpha \lt 4.0$ ). We investigate exotic dynamics when the interactions are suddenly switched from strongly repulsive to strongly attractive, a procedure known to generate super-Tonks-Girardeau gases in systems with contact interactions. We find that relaxation is achieved through a complex intermediate dynamics demonstrated by violent fragmentation and chaotic delocalization. We establish that the relaxed state exhibits classical gaseous characteristics and an asymptotic state associated with unbounded entropy production. The phase diagram shows an exponential boundary between the coherent (quantum) gas and the chaotic (classical) gas. We show the universality of the dynamics by also presenting analogous results for spinless fermions. Weaker quench protocols give a certain degree of control over the relaxation process and induce a slower initial entropy growth. Our study showcases the complex relaxation behavior of tunable long-range interacting systems that could be engineered in state-of-the-art experiments, e.g. in trapped ions or Rydberg atoms.

We consider a modified Boltzmann equation which contains, together with the collision operator, an additional drift term which is characterized by a matrix A. Furthermore, we consider a Maxwell gas, where the collision kernel has an angular singularity. Such an equation is used in the study of homoenergetic solutions to the Boltzmann equation. Under smallness assumptions on the drift term, we prove that the longtime asymptotics is given by self-similar solutions. We work in the framework of measure-valued solutions with finite moments of order p > 2 and show existence, uniqueness and stability of these self-similar solutions for sufficiently small A. Furthermore, we prove that they have finite moments of arbitrary order if A is small enough. In addition, the singular collision operator allows to prove smoothness of these self-similar solutions. Finally, we study the asymptotics of particular homoenergetic solutions. This extends previous results from the cutoff case to non-cutoff Maxwell gases. [ABSTRACT FROM AUTHOR]

DNA sequence variants (single nucleotide polymorphisms or variants, SNPs/SNVs; copy number variants, CNVs) associated to neurodevelopmental disorders (NDD) and traits often map on putative transcriptional regulatory elements, including, in particular, enhancers. However, the genes controlled by these enhancers remain poorly defined. Traditionally, the activity of a given enhancer, and the effect of its possible alteration associated to the sequence variants, has been thought to influence the nearest gene promoter. However, the obtainment of genome-wide long-range interaction maps in neural cells chromatin challenged this view, showing that a given enhancer is very frequently not connected to the nearest promoter, but to a more distant one, skipping genes in between. In this Perspective, we review some recent papers, who generated long-range interaction maps (by HiC, RNApolII ChIA-PET, Capture-HiC, or PLACseq), and overlapped the identified long-range interacting DNA segments with DNA sequence variants associated to NDD (such as schizophrenia, bipolar disorder and autism) and traits (intelligence). This strategy allowed to attribute the function of enhancers, hosting the NDD-related sequence variants, to a connected gene promoter lying far away on the linear chromosome map. Some of these enhancer-connected genes had indeed been already identified as contributive to the diseases, by the identification of mutations within the gene's protein-coding regions (exons), validating the approach. Significantly, however, the connected genes also include many genes that were not previously found mutated in their exons, pointing to novel candidate contributors to NDD and traits. Thus, long-range interaction maps, in combination with DNA variants detected in association with NDD, can be used as "pointers" to identify novel candidate disease-relevant genes. Functional manipulation of the long-range interaction network involving enhancers and promoters by CRISPR-Cas9-based approaches is beginning to probe for the functional significance of the identified interactions, and the enhancers and the genes involved, improving our understanding of neural development and its pathology. [ABSTRACT FROM AUTHOR]

It is sometimes the case that the dynamics of a physical system is described by equations of motion that do not derive from a Hamiltonian, and additionally, the degrees of freedom constituting the system interact with each other via long-range interactions. A concrete example is that of particles interacting with light as encountered in free-electron laser and cold-atom experiments. In the last couple of decades, long-range Hamiltonian systems have been found to present a peculiar relaxation dynamics, and in this work, we extend the study of the relaxation dynamics to non-Hamiltonian systems, more precisely, to systems with interactions of both Hamiltonian and non-Hamiltonian origin. Our model consists of N globally-coupled particles moving on a circle of unit radius. Since every particle is characterized by a single coordinate given by its location on the circle, the model is one-dimensional. We show that in the infinite-size limit (the limit N → ∞ ), the dynamics, similarly to the Hamiltonian case, is described by the Vlasov equation for the one-particle distribution function. In the Hamiltonian case, the system eventually reaches an equilibrium state, even though one has to wait for a long time diverging with N for this to happen. By contrast, in the non-Hamiltonian case, there is no equilibrium state that the system is expected to reach eventually; thus, the equations for the dynamical evolution remain the only tool to analyze the state of the system. We characterize this state with its average magnetization. We find that the relaxation dynamics depends strongly on the relative weight of the Hamiltonian and non-Hamiltonian contributions to the interaction. When the non-Hamiltonian part is predominant, the magnetization attains a vanishing value, suggesting that the system does not sustain states with constant magnetization, either stationary or rotating (for the fully non-Hamiltonian case, we can prove this on the basis of the Vlasov equation). On the other hand, when the Hamiltonian part is predominant, the magnetization presents long-lived strong oscillations, for which we provide a heuristic explanation. Furthermore, we find that the finite-size corrections are much more pronounced than those in the Hamiltonian case; we justify this by showing that the Lenard–Balescu equation, which gives leading-order corrections to the Vlasov equation, does not vanish, contrary to what occurs in one-dimensional Hamiltonian long-range systems. [ABSTRACT FROM AUTHOR]

We calculate the fully retarded one-photon exchange interaction potential between electrically neutral, identical atoms, one of which is assumed to be in an excited state, by matching the scattering matrix (S matrix) element with the effective Hamiltonian. Based on the Feynman prescription, we obtain the imaginary part of the interaction energy. Our results lead to precise formulas for the distance-dependent enhancement and suppression of the decay rates of entangled superradiant and subradiant Dicke states (Bell states), as a function of the interatomic distance. The formulas include a long-range tail due to entanglement. We apply the result to an example calculation involving two hydrogen atoms, one of which is in an excited P state. [ABSTRACT FROM AUTHOR]

The simultaneous presence of two active metal centres in diatomic catalysts (DACs) leads to the occurrence of specific interactions between active sites. Such interactions, referred to as long‐range interactions (LRIs), play an important role in determining the rate and selectivity of a reaction. The optimal combination of metal centres must be determined to achieve the targeted efficiency. To date, various types of DACs have been synthesised and applied in electrochemistry. However, LRIs have not been systematically summarised. Herein, the regulation, mechanism, and electrocatalytic applications of LRIs are comprehensively summarised and discussed. In addition to the basic information above, the challenges, opportunities, and future development of LRIs in DACs are proposed in order to present an overall view and reference for future research. [ABSTRACT FROM AUTHOR]

We study random displacements models with a long-range particle-media interaction potential 픲 ⁢ (r , θ) = 픣 ⁢ (θ) ⁢ r - A in polar coordinates, with a smooth function 픣 which can be sign-indefinite. Spectral and dynamical localization, with an asymptotically exponential decay of eigenfunction correlators, is proved under the optimal condition A > d . [ABSTRACT FROM AUTHOR]

Through the study of the real seismic behavior, we find that large mainshocks are often followed by aftershocks. Mainshocks occur instantaneously, while aftershocks feature relatively slow relaxation. Based on the Olami–Feder–Christensen with relaxation (OFCR) model, the long-range interactions and new energy distribution rule are added into our model. At the same time, we find that the statistical distributions of seismic magnitude, and time intervals of mainshock and aftershock conform to the power law behaviors. By comparing the curves of aftershock and mainshock behaviors, we find that they have similar distribution characteristics, which indicates that the study of aftershock behavior is of practical significance for the study of large earthquakes. Meanwhile long-range interactions OFCR model can provide a good supplement for the large earthquake data. [ABSTRACT FROM AUTHOR]

Considering light-mediated long-range interactions between cold atoms in a magneto-optical trap (MOT), we present numerical evidence of a nonequilibrium steady state (NESS) for sufficiently large number of atoms (> 10 8 ). This state manifests itself as the appearance of an anisotropic distribution of velocity when a MOT approaches the threshold beyond which self-oscillating instabilities occur. Our three-dimensional (3D) spatiotemporal model with nonlocal spatial dependencies stemming from the interatomic interactions has recently been compared successfully to predict different instability thresholds and regimes in experiments with rubidium atoms. The behavior of the NESS is studied as a function of the main MOT parameters, including its spatiotemporal characteristics. [ABSTRACT FROM AUTHOR]

Unitarity sets upper limits on partial-wave elastic and inelastic cross-sections, which are often violated by perturbative computations. We discuss the dynamics underlying these limits in the non-relativistic regime, namely long-range interactions, and show how the resummation of the 2-particle-irreducible diagrams arising from squaring inelastic processes unitarizes both elastic and inelastic cross-sections. We provide a simple prescription to obtain the unitarized cross-sections from those that do not include resummation of the squared inelastic processes. Our results are model-independent, apply to all partial waves, and affect elastic and inelastic cross-sections, with extensive implications for new physics scenarios, such as dark-matter freeze-out, indirect detection and self-interactions. [ABSTRACT FROM AUTHOR]

The adsorption of nitrogen molecules on a (100) tungsten surface has been studied using a new potential energy surface in which long-range interactions are suitably characterized and represented by the Improved Lennard–Jones function. The new potential energy surface is used to carry out molecular dynamics simulations by adopting a semiclassical collisional method that explicitly includes the interaction with the surface phonons. The results of the sticking probability, evaluated as a function of the collision energy, are in good agreement with those obtained in the experiments and improve the already good comparison recently obtained with calculations performed using interactions from the Density Functional Theory method and corrected for long-range van der Waals contributions. The dependence of trapping probability on the surface temperature for a well-defined collision energy has also been investigated.

In this paper, we review the importance of long-range zeolite framework interactions in theoretical predictions for a variety of zeolite-catalyzed processes, and we show why such interactions must be determined accurately in order to reproduce experimentally measured adsorption and activation energies. We begin with an overview of the different strategies that have been used to account for long-range coulombic and dispersive interactions of zeolite framework atoms with species adsorbed at an active site. These methods include full periodic-DFT calculations and multi-layer hybrid techniques. Electrostatic interactions are observed to have a more significant impact than dispersive interactions on the geometries of ion-pair transition states and adsorbed species. Stabilization of the TS relative to reactant complexes is also dictated by electrostatic interactions. Dispersion effects are found to significantly stabilize both transition and reactant states for adsorbed species, especially those which have dimensions that provide good fits within the zeolite pore or cavity. We also show that the relevance of particular active site configurations can be missed, if the effects of long-range interactions are neglected. As a case in point, we demonstrate that a site previously considered inactive for ethane dehydrogenation, [GaH2]+ may in fact be more active than previously thought, when the impact of long-range interactions on the predicted activation energy is taken into account. Finally, the use of hybrid quantum mechanics/molecular mechanics approaches on extended, finite zeolite clusters has emerged as an accurate, highly cost-effective, and versatile alternative towards overcoming some of the present-day limitations of periodic calculations.

The inelastic scattering of N2 molecules from silica surfaces, taken at 100 K, has been investigated by adopting a semiclassical collision model in conjunction with the appropriate treatment of the long-range interaction forces. Such forces promote the formation of the precursor state that controls all basic elementary processes occurring at the gas–surface interphase. The probabilities for the different elementary surface processes triggered by quartz are determined and compared with those recently obtained for another silica polymorph (cristobalite). In addition, the final roto-vibrational distributions of N2 molecules undergoing inelastic scattering have been characterized. N2 molecules, impinging on both considered surfaces in low-medium vibrational states, preserve the initial vibrational state, while those inelastically scattered are rotationally excited and translationally colder. The surface temperature effect, investigated by raising the temperature itself from 100 K up to 1000 K, emerges more sharply for the cristobalite polymorph, mainly for the molecules impinging in the ground roto-vibrational state and with low collision energies. [ABSTRACT FROM AUTHOR]

We investigate the classical equilibrium properties and metamorphosis of the ground state of interacting dipoles with fixed locations on a helix. The dipoles are shown to align themselves along separate intertwined dipole chains forming single, double, and higher-order helical chains. The number of dipole chains, and their properties such as chirality and length scale on which the chains wind around each other, can be tuned by the geometrical parameters. We demonstrate that all possible configurations form a self-similar bifurcation diagram which can be linked to the Sternâ€"Brocot tree and the underlying Farey sequence. We describe the mechanism responsible for this behavior and subsequently discuss corresponding implications and possible applications. [ABSTRACT FROM AUTHOR]

We propose a covariant definition of the fractional Kleinâ€"Gordon equation (KGE) with long-range interactions independent of the metric of the underlying manifold. As an example we consider the fractional KGE on AdS2+1, computing the explicit kernel representation of the fractional Laplaceâ€"Beltrami operator as well as the two-point propagator of the fractional KGE. Our results suggest that the propagator only exists if the mass is small compared to the inverse AdS radius, presumably because the AdS space expands faster with distance as a flat space of the same dimension. Our results are expected to be useful in particular for new applications of the AdS/CFT correspondence within statistical mechanics and quantum information. [ABSTRACT FROM AUTHOR]

We propose a covariant definition of the fractional Kleinâ€"Gordon equation (KGE) with long-range interactions independent of the metric of the underlying manifold. As an example we consider the fractional KGE on AdS2+1, computing the explicit kernel representation of the fractional Laplaceâ€"Beltrami operator as well as the two-point propagator of the fractional KGE. Our results suggest that the propagator only exists if the mass is small compared to the inverse AdS radius, presumably because the AdS space expands faster with distance as a flat space of the same dimension. Our results are expected to be useful in particular for new applications of the AdS/CFT correspondence within statistical mechanics and quantum information. [ABSTRACT FROM AUTHOR]