Jakub Vrabel, Ori Shem-Ur, Yaron Oz, David Krueger
We extend the concept of loss landscape mode connectivity to the input space of deep neural networks. Mode connectivity was originally studied within parameter space, where it describes the existence of low-loss paths between different solutions (loss minimizers) obtained through gradient descent. We present theoretical and empirical evidence of its presence in the input space of deep networks, thereby highlighting the broader nature of the phenomenon. We observe that different input images with similar predictions are generally connected, and for trained models, the path tends to be simple, with only a small deviation from being a linear path. Our methodology utilizes real, interpolated, and synthetic inputs created using the input optimization technique for feature visualization. We conjecture that input space mode connectivity in high-dimensional spaces is a geometric effect that takes place even in untrained models and can be explained through percolation theory. We exploit mode connectivity to obtain new insights about adversarial examples and demonstrate its potential for adversarial detection. Additionally, we discuss applications for the interpretability of deep networks.
{"title":"Input Space Mode Connectivity in Deep Neural Networks","authors":"Jakub Vrabel, Ori Shem-Ur, Yaron Oz, David Krueger","doi":"arxiv-2409.05800","DOIUrl":"https://doi.org/arxiv-2409.05800","url":null,"abstract":"We extend the concept of loss landscape mode connectivity to the input space\u0000of deep neural networks. Mode connectivity was originally studied within\u0000parameter space, where it describes the existence of low-loss paths between\u0000different solutions (loss minimizers) obtained through gradient descent. We\u0000present theoretical and empirical evidence of its presence in the input space\u0000of deep networks, thereby highlighting the broader nature of the phenomenon. We\u0000observe that different input images with similar predictions are generally\u0000connected, and for trained models, the path tends to be simple, with only a\u0000small deviation from being a linear path. Our methodology utilizes real,\u0000interpolated, and synthetic inputs created using the input optimization\u0000technique for feature visualization. We conjecture that input space mode\u0000connectivity in high-dimensional spaces is a geometric effect that takes place\u0000even in untrained models and can be explained through percolation theory. We\u0000exploit mode connectivity to obtain new insights about adversarial examples and\u0000demonstrate its potential for adversarial detection. Additionally, we discuss\u0000applications for the interpretability of deep networks.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"181 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Coarse-grained models have played an important role in the study of the behavior of DNA at length scales beyond a few hundred base pairs. Traditionally, these models have relied on structurally featureless and sequence-independent approaches, such as the twistable worm-like chain. However, research over the past decade has illuminated the substantial impact of DNA sequence even at the kilo-base pair scale. Several robust sequence-dependent models have emerged, capturing intricacies at the base pair-step level. Here we introduce an analytical framework for coarse-graining such models to the 2 to 40-base pair scale while preserving essential structural and dynamical features. These faithful coarse-grained parametrizations enable efficient sampling of large molecules. Rather than providing a fully parametrized model, we present the methodology and software necessary for mapping any base pair-step model to the desired level of coarse-graining. Finally, we provide application examples of our method, including estimates of the persistence length and effective torsional stiffness of DNA in a setup mimicking a freely orbiting tweezer, as well as simulations of intrinsically helical DNA.
粗粒度模型在研究长度超过几百个碱基对的 DNA 行为中发挥了重要作用。传统上，这些模型依赖于无结构特征和不依赖序列的方法，如扭曲的蠕虫链。然而，过去十年的研究表明，即使在千碱基对尺度上，DNA 序列也会产生重大影响。已经出现了几种依赖于序列的稳健模型，可以捕捉到碱基对级的复杂性。在这里，我们介绍了一种分析框架，用于将此类模型粗粒化到 2 到 40 碱基对尺度，同时保留基本的结构和动力学特征。这些忠实的粗粒度参数化可以实现大分子的高效采样。我们没有提供完全参数化的模型，而是介绍了将任何碱基对步骤模型映射到所需粗粒度水平所需的方法和软件。最后，我们提供了我们的方法的应用实例，包括在模仿自由轨道镊子的设置中对 DNA 的持续长度和有效扭转刚度的估计，以及对本征螺旋 DNA 的模拟。
{"title":"Systematic Coarse-Graining of Sequence-Dependent Structure and Elasticity of Double-Stranded DNA","authors":"Enrico Skoruppa, Helmut Schiessel","doi":"arxiv-2409.05510","DOIUrl":"https://doi.org/arxiv-2409.05510","url":null,"abstract":"Coarse-grained models have played an important role in the study of the\u0000behavior of DNA at length scales beyond a few hundred base pairs.\u0000Traditionally, these models have relied on structurally featureless and\u0000sequence-independent approaches, such as the twistable worm-like chain.\u0000However, research over the past decade has illuminated the substantial impact\u0000of DNA sequence even at the kilo-base pair scale. Several robust\u0000sequence-dependent models have emerged, capturing intricacies at the base\u0000pair-step level. Here we introduce an analytical framework for coarse-graining\u0000such models to the 2 to 40-base pair scale while preserving essential\u0000structural and dynamical features. These faithful coarse-grained\u0000parametrizations enable efficient sampling of large molecules. Rather than\u0000providing a fully parametrized model, we present the methodology and software\u0000necessary for mapping any base pair-step model to the desired level of\u0000coarse-graining. Finally, we provide application examples of our method,\u0000including estimates of the persistence length and effective torsional stiffness\u0000of DNA in a setup mimicking a freely orbiting tweezer, as well as simulations\u0000of intrinsically helical DNA.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we solve the joint probability density for the passive and active particles with harmonic, viscous, and perturbative forces. After deriving the Fokker-Planck equation for a passive and a run-and-tumble particles, we approximately get and analyze the solution for the joint distribution density subject to an exponential correlated Gaussian force in three kinds of time limit domains. Mean squared displacement (velocity) for a particle with harmonic and viscous forces behaviors in the form of super-diffusion, consistent with a particle having viscous and perturbative forces. A passive particle with both harmonic, viscous forces and viscous, perturbative forces has the Gaussian form with mean squared velocity ~t. Particularly, In our case of a run-and-tumble particle, the mean squared displacement scales as super-diffusion, while the mean squared velocity has a normal diffusive form.In addition, the kurtosis, the correlation coefficient, and the moment from moment equation are numerically calculated.
{"title":"On the motion of passive and active particles with harmonic and viscous forces","authors":"Jae-Won Jung, Sung Kyu Seo, Kyungsik Kim","doi":"arxiv-2409.05164","DOIUrl":"https://doi.org/arxiv-2409.05164","url":null,"abstract":"In this paper, we solve the joint probability density for the passive and\u0000active particles with harmonic, viscous, and perturbative forces. After\u0000deriving the Fokker-Planck equation for a passive and a run-and-tumble\u0000particles, we approximately get and analyze the solution for the joint\u0000distribution density subject to an exponential correlated Gaussian force in\u0000three kinds of time limit domains. Mean squared displacement (velocity) for a\u0000particle with harmonic and viscous forces behaviors in the form of\u0000super-diffusion, consistent with a particle having viscous and perturbative\u0000forces. A passive particle with both harmonic, viscous forces and viscous,\u0000perturbative forces has the Gaussian form with mean squared velocity ~t.\u0000Particularly, In our case of a run-and-tumble particle, the mean squared\u0000displacement scales as super-diffusion, while the mean squared velocity has a\u0000normal diffusive form.In addition, the kurtosis, the correlation coefficient,\u0000and the moment from moment equation are numerically calculated.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tomasz Masłowski, Hadi Cheraghi, Jesko Sirker, Nicholas Sedlmayr
Dynamical quantum phase transitions are non-analyticities in a dynamical free energy (or return rate) which occur at critical times. Although extensively studied in one dimension, the exact nature of the non-analyticity in two and three dimensions has not yet been fully investigated. In two dimensions, results so far are known only for relatively simple two-band models. Here we study the general two- and three-dimensional cases. We establish the relation between the non-analyticities in different dimensions, and the functional form of the densities of Fisher zeroes. We show, in particular, that entering a critical region where the density of Fisher zeroes is non-zero at the boundary always leads to a cusp in the derivative of the return rate while the return rate itself is smooth. We illustrate our results by obtaining analytical results for exemplary two- and three-dimensional models.
{"title":"Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models","authors":"Tomasz Masłowski, Hadi Cheraghi, Jesko Sirker, Nicholas Sedlmayr","doi":"arxiv-2409.09070","DOIUrl":"https://doi.org/arxiv-2409.09070","url":null,"abstract":"Dynamical quantum phase transitions are non-analyticities in a dynamical free\u0000energy (or return rate) which occur at critical times. Although extensively\u0000studied in one dimension, the exact nature of the non-analyticity in two and\u0000three dimensions has not yet been fully investigated. In two dimensions,\u0000results so far are known only for relatively simple two-band models. Here we\u0000study the general two- and three-dimensional cases. We establish the relation\u0000between the non-analyticities in different dimensions, and the functional form\u0000of the densities of Fisher zeroes. We show, in particular, that entering a\u0000critical region where the density of Fisher zeroes is non-zero at the boundary\u0000always leads to a cusp in the derivative of the return rate while the return\u0000rate itself is smooth. We illustrate our results by obtaining analytical\u0000results for exemplary two- and three-dimensional models.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
David Evans, José Martín-Roca, Nathan J. Harmer, Chantal Valeriani, Mark A. Miller
Non-equilibrium clustering and percolation are investigated in an archetypal model of two-dimensional active matter using dynamic simulations of self-propelled Brownian repulsive particles. We concentrate on the single-phase region up to moderate levels of activity, before motility-induced phase separation (MIPS) sets in. Weak activity promotes cluster formation and lowers the percolation threshold. However, driving the system further out of equilibrium partly reverses this effect, resulting in a minimum in the critical density for the formation of system-spanning clusters and introducing re-entrant percolation as a function of activity in the pre-MIPS regime. This non-monotonic behaviour arises from competition between activity-induced effective attraction (which eventually leads to MIPS) and activity-driven cluster breakup. Using an adapted iterative Boltzmann inversion method, we derive effective potentials to map weakly active cases onto a passive (equilibrium) model with conservative attraction, which can be characterised by Monte Carlo simulations. While the active and passive systems have practically identical radial distribution functions, we find decisive differences in higher-order structural correlations, to which the percolation threshold is highly sensitive. For sufficiently strong activity, no passive pairwise potential can reproduce the radial distribution function of the active system.
{"title":"Re-entrant percolation in active Brownian hard disks","authors":"David Evans, José Martín-Roca, Nathan J. Harmer, Chantal Valeriani, Mark A. Miller","doi":"arxiv-2409.04141","DOIUrl":"https://doi.org/arxiv-2409.04141","url":null,"abstract":"Non-equilibrium clustering and percolation are investigated in an archetypal\u0000model of two-dimensional active matter using dynamic simulations of\u0000self-propelled Brownian repulsive particles. We concentrate on the single-phase\u0000region up to moderate levels of activity, before motility-induced phase\u0000separation (MIPS) sets in. Weak activity promotes cluster formation and lowers\u0000the percolation threshold. However, driving the system further out of\u0000equilibrium partly reverses this effect, resulting in a minimum in the critical\u0000density for the formation of system-spanning clusters and introducing\u0000re-entrant percolation as a function of activity in the pre-MIPS regime. This\u0000non-monotonic behaviour arises from competition between activity-induced\u0000effective attraction (which eventually leads to MIPS) and activity-driven\u0000cluster breakup. Using an adapted iterative Boltzmann inversion method, we\u0000derive effective potentials to map weakly active cases onto a passive\u0000(equilibrium) model with conservative attraction, which can be characterised by\u0000Monte Carlo simulations. While the active and passive systems have practically\u0000identical radial distribution functions, we find decisive differences in\u0000higher-order structural correlations, to which the percolation threshold is\u0000highly sensitive. For sufficiently strong activity, no passive pairwise\u0000potential can reproduce the radial distribution function of the active system.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Squarcini, A. Tinti, P. Illien, O. Bénichou, T. Franosch
We study a lattice model describing the non-equilibrium dynamics emerging from the pulling of a tracer particle through a disordered medium occupied by randomly placed obstacles. The model is considered in a restricted geometry pertinent for the investigation of confinement-induced effects. We analytically derive exact results for the characteristic function of the moments valid to first order in the obstacle density. By calculating the velocity autocorrelation function and its long-time tail we find that already in equilibrium the system exhibits a dimensional crossover. This picture is further confirmed by the approach of the drift velocity to its terminal value attained in the non-equilibrium stationary state. At large times the diffusion coefficient is affected by both the driving and confinement in a way that we quantify analytically. The force-induced diffusion coefficient depends sensitively on the presence of confinement. The latter is able to modify qualitatively the non-analytic behavior in the force observed for the unbounded model. We then examine the fluctuations of the tracer particle along the driving force. We show that in the intermediate regime superdiffusive anomalous behavior persists even in the presence of confinement. Stochastic simulations are employed in order to test the validity of the analytic results, exact to first order in the obstacle density and valid for arbitrary force and confinement.
{"title":"Time-dependent dynamics in the confined lattice Lorentz gas","authors":"A. Squarcini, A. Tinti, P. Illien, O. Bénichou, T. Franosch","doi":"arxiv-2409.04293","DOIUrl":"https://doi.org/arxiv-2409.04293","url":null,"abstract":"We study a lattice model describing the non-equilibrium dynamics emerging\u0000from the pulling of a tracer particle through a disordered medium occupied by\u0000randomly placed obstacles. The model is considered in a restricted geometry\u0000pertinent for the investigation of confinement-induced effects. We analytically\u0000derive exact results for the characteristic function of the moments valid to\u0000first order in the obstacle density. By calculating the velocity\u0000autocorrelation function and its long-time tail we find that already in\u0000equilibrium the system exhibits a dimensional crossover. This picture is\u0000further confirmed by the approach of the drift velocity to its terminal value\u0000attained in the non-equilibrium stationary state. At large times the diffusion\u0000coefficient is affected by both the driving and confinement in a way that we\u0000quantify analytically. The force-induced diffusion coefficient depends\u0000sensitively on the presence of confinement. The latter is able to modify\u0000qualitatively the non-analytic behavior in the force observed for the unbounded\u0000model. We then examine the fluctuations of the tracer particle along the\u0000driving force. We show that in the intermediate regime superdiffusive anomalous\u0000behavior persists even in the presence of confinement. Stochastic simulations\u0000are employed in order to test the validity of the analytic results, exact to\u0000first order in the obstacle density and valid for arbitrary force and\u0000confinement.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Three types of cycles are identified in the quantum jump trajectories of the Scovil--Schulz-DuBois (SSDB) machine: an R-cycle as refrigeration, an H-cycle as a heat engine, and an N-cycle in which the machine is neutral. The statistics of these cycles are investigated via a semi-Markov process method. We find that in the large time limit, whether the machine operates as a heat engine or refrigerator depends on a balance between the numbers of R-cycles and H-cycles per unit time. Further increasing the hot bath temperature above a certain threshold does not increase the machine's power output. The cause is that, in this situation, the N-cycle has a greater probability than the H-cycle and R-cycle. Although the SSDB machine operates by randomly switching among these three cycles, at the level of a single quantum jump trajectory, its heat engine efficiency and the refrigerator's coefficient of performance remain constant.
我们在斯科维尔-舒尔茨-杜博瓦（SSDB）机器的量子跃迁轨迹中发现了三种循环：作为制冷机的 R 循环、作为热机的 H 循环以及机器处于中性状态的 N 循环。我们发现，在大时限内，机器是作为热机还是制冷机运行取决于单位时间内 R 循环和 H 循环数量之间的平衡。将热浴温度进一步提高到某个临界值以上并不会增加机器的功率输出。原因在于，在这种情况下，N 循环的概率大于 H 循环和 R 循环。虽然 SSDB 机器通过在这三个循环之间随机切换来运行，但在单量子跃迁轨迹的水平上，其热机效率和冰箱的性能系数保持不变。
{"title":"Stochastic Scovil--Schulz-DuBois machine","authors":"Fei Liu","doi":"arxiv-2409.04124","DOIUrl":"https://doi.org/arxiv-2409.04124","url":null,"abstract":"Three types of cycles are identified in the quantum jump trajectories of the\u0000Scovil--Schulz-DuBois (SSDB) machine: an R-cycle as refrigeration, an H-cycle\u0000as a heat engine, and an N-cycle in which the machine is neutral. The\u0000statistics of these cycles are investigated via a semi-Markov process method.\u0000We find that in the large time limit, whether the machine operates as a heat\u0000engine or refrigerator depends on a balance between the numbers of R-cycles and\u0000H-cycles per unit time. Further increasing the hot bath temperature above a\u0000certain threshold does not increase the machine's power output. The cause is\u0000that, in this situation, the N-cycle has a greater probability than the H-cycle\u0000and R-cycle. Although the SSDB machine operates by randomly switching among\u0000these three cycles, at the level of a single quantum jump trajectory, its heat\u0000engine efficiency and the refrigerator's coefficient of performance remain\u0000constant.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"181 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that a variety of non-monotonic ratchet effects can arise when mesophase pattern-forming systems, which exhibit anisotropic crystal, stripe, and bubble reigmes, are coupled to one-dimensional asymmetric substrates under ac driving. The ratchet efficiency and direction of motion are determined by how well the mesophase morphology matches the periodicity and shape of the substrate. Stripe states that are aligned with the substrate show the strongest ratchet effect, large bubbles show a weak ratchet effect, and small bubbles show a strong ratchet effect with an efficiency that oscillates as a function of ac drive amplitude. We map out the different rectification phases as a function of the pattern morphology, substrate strength, and ac drive amplitude. The pronounced ratchet effects that we observe in some regimes can be exploited for pattern sorting in hard and soft matter systems.
{"title":"Stripe and Bubble Ratchets on Asymmetric Substrates","authors":"C. Reichhardt, C. J. O. Reichhardt","doi":"arxiv-2409.04646","DOIUrl":"https://doi.org/arxiv-2409.04646","url":null,"abstract":"We show that a variety of non-monotonic ratchet effects can arise when\u0000mesophase pattern-forming systems, which exhibit anisotropic crystal, stripe,\u0000and bubble reigmes, are coupled to one-dimensional asymmetric substrates under\u0000ac driving. The ratchet efficiency and direction of motion are determined by\u0000how well the mesophase morphology matches the periodicity and shape of the\u0000substrate. Stripe states that are aligned with the substrate show the strongest\u0000ratchet effect, large bubbles show a weak ratchet effect, and small bubbles\u0000show a strong ratchet effect with an efficiency that oscillates as a function\u0000of ac drive amplitude. We map out the different rectification phases as a\u0000function of the pattern morphology, substrate strength, and ac drive amplitude.\u0000The pronounced ratchet effects that we observe in some regimes can be exploited\u0000for pattern sorting in hard and soft matter systems.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"70 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
W. S. Oliveira, J. Pimentel de Lima, Raimundo R. dos Santos
We theoretically investigate the quantum percolation problem on Lieb lattices in two and three dimensions. We study the statistics of the energy levels through random matrix theory, and determine the level spacing distributions, which, with the aid of finite-size scaling theory, allows us to obtain accurate estimates for site- and bond percolation thresholds and critical exponents. Our numerical investigation supports a localized-delocalized transition at finite threshold, which decreases as the average coordination number increases. The precise determination of the localization length exponent enables us to claim that quantum site- and bond-percolation problems on Lieb lattices belong to the same universality class, with $nu$ decreasing with lattice dimensionality, $d$, similarly to the classical percolation problem. In addition, we verify that, in three dimensions, quantum percolation on Lieb lattices belongs to the same universality class as the Anderson impurity model.
{"title":"Quantum percolation on Lieb Lattices","authors":"W. S. Oliveira, J. Pimentel de Lima, Raimundo R. dos Santos","doi":"arxiv-2409.04610","DOIUrl":"https://doi.org/arxiv-2409.04610","url":null,"abstract":"We theoretically investigate the quantum percolation problem on Lieb lattices\u0000in two and three dimensions. We study the statistics of the energy levels\u0000through random matrix theory, and determine the level spacing distributions,\u0000which, with the aid of finite-size scaling theory, allows us to obtain accurate\u0000estimates for site- and bond percolation thresholds and critical exponents. Our\u0000numerical investigation supports a localized-delocalized transition at finite\u0000threshold, which decreases as the average coordination number increases. The\u0000precise determination of the localization length exponent enables us to claim\u0000that quantum site- and bond-percolation problems on Lieb lattices belong to the\u0000same universality class, with $nu$ decreasing with lattice dimensionality,\u0000$d$, similarly to the classical percolation problem. In addition, we verify\u0000that, in three dimensions, quantum percolation on Lieb lattices belongs to the\u0000same universality class as the Anderson impurity model.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chemotactic biological or synthetic active matter shapes its environment by secretions of chemical signals from its self-propelled constituents, like cells, organisms or active colloids. From this indirect interaction collective effects emerge that can be used by the agents to migrate collectively, to form patterns or to search for targets more efficiently. Here, we use paradigmatic models to study the efficiency of collective search strategies of a large group of motile agents that release during their movement repulsive auto-chemotactic signals forcing them to move away from high concentrations of the chemical clue. We show that the repulsive chemotactic interactions improve the search efficiency, measured by the mean first passage time to find a randomly located target, by orders of magnitude depending on the strength of the chemotactic coupling. The mechanism for this improvement relies on two factors: the increase of the persistence length due to the agent's self-interaction with its own chemotactic field and by a more homogeneous distribution of the agents due to their mutual indirect repulsion mediated by the chemotactic field. At stronger particle-field coupling the chemotactic searchers self-organize into ballistically moving bands reminiscent of search-chains formed in search and rescue operations, whose efficiency depends on the number of searchers involved. Our comprehensive study of collective search strategies of large groups of interacting agents is not only relevant for chemotactic active matter but also for a wide range of fields like ethology, information engineering, robotics, and social engineering.
{"title":"Collective chemotactic search strategies","authors":"Hugues Meyer, Adam Wysocki, Heiko Rieger","doi":"arxiv-2409.04262","DOIUrl":"https://doi.org/arxiv-2409.04262","url":null,"abstract":"Chemotactic biological or synthetic active matter shapes its environment by\u0000secretions of chemical signals from its self-propelled constituents, like\u0000cells, organisms or active colloids. From this indirect interaction collective\u0000effects emerge that can be used by the agents to migrate collectively, to form\u0000patterns or to search for targets more efficiently. Here, we use paradigmatic\u0000models to study the efficiency of collective search strategies of a large group\u0000of motile agents that release during their movement repulsive auto-chemotactic\u0000signals forcing them to move away from high concentrations of the chemical\u0000clue. We show that the repulsive chemotactic interactions improve the search\u0000efficiency, measured by the mean first passage time to find a randomly located\u0000target, by orders of magnitude depending on the strength of the chemotactic\u0000coupling. The mechanism for this improvement relies on two factors: the\u0000increase of the persistence length due to the agent's self-interaction with its\u0000own chemotactic field and by a more homogeneous distribution of the agents due\u0000to their mutual indirect repulsion mediated by the chemotactic field. At\u0000stronger particle-field coupling the chemotactic searchers self-organize into\u0000ballistically moving bands reminiscent of search-chains formed in search and\u0000rescue operations, whose efficiency depends on the number of searchers\u0000involved. Our comprehensive study of collective search strategies of large\u0000groups of interacting agents is not only relevant for chemotactic active matter\u0000but also for a wide range of fields like ethology, information engineering,\u0000robotics, and social engineering.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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