Lorenzo Cirigliano, Gábor Timár, Claudio Castellano
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some critical properties of the transition, in particular for heterogeneous substrates, have not been fully elucidated and contradictory results appear in the literature. In this paper we present, by means of a generating functions approach, a thorough and complete investigation of percolation critical properties in random networks. We determine all critical exponents, the associated critical amplitude ratios and the form of the cluster size distribution for networks of any level of heterogeneity. We uncover, in particular for highly heterogeneous networks, subtle crossover phenomena, nontrivial scaling forms and violations of hyperscaling. In this way we clarify the origin of inconsistencies in the previous literature.
{"title":"Scaling and universality for percolation in random networks: a unified view","authors":"Lorenzo Cirigliano, Gábor Timár, Claudio Castellano","doi":"arxiv-2408.05125","DOIUrl":"https://doi.org/arxiv-2408.05125","url":null,"abstract":"Percolation processes on random networks have been the subject of intense\u0000research activity over the last decades: the overall phenomenology of standard\u0000percolation on uncorrelated and unclustered topologies is well known. Still\u0000some critical properties of the transition, in particular for heterogeneous\u0000substrates, have not been fully elucidated and contradictory results appear in\u0000the literature. In this paper we present, by means of a generating functions\u0000approach, a thorough and complete investigation of percolation critical\u0000properties in random networks. We determine all critical exponents, the\u0000associated critical amplitude ratios and the form of the cluster size\u0000distribution for networks of any level of heterogeneity. We uncover, in\u0000particular for highly heterogeneous networks, subtle crossover phenomena,\u0000nontrivial scaling forms and violations of hyperscaling. In this way we clarify\u0000the origin of inconsistencies in the previous literature.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943339","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}
The formation of dynamical patterns is one of the most striking features of non-equilibrium physical systems. Recent work has shown that such patterns arise generically from forces that violate Newton's third law, known as non-reciprocal interactions. These non-equilibrium phenomena are challenging for modern theories. Here, we introduce a model mixture of active (self-propelled) and passive (diffusive) particles with non-reciprocal effective interactions, which is amenable to exact mathematical analysis. We exploit state-of-the-art methods to derive exact hydrodynamic equations for the particle densities. We study the resulting collective behavior, including the linear stability of homogeneous states and phase coexistence in large systems. This reveals a novel phase diagram with the spinodal associated with active phase separation protruding through the associated binodal, heralding the emergence of dynamical steady states. We analyze these states in the thermodynamic limit of large system size, showing, for example, that sharp interfaces may travel at finite velocities, but traveling phase-separated states are forbidden. The model's mathematical tractability enables precise new conclusions beyond those available by numerical simulation of particle models or field theories.
{"title":"Dynamical patterns in active-passive particle mixtures with non-reciprocal interactions: Exact hydrodynamic analysis","authors":"James Mason, Robert L. Jack, Maria Bruna","doi":"arxiv-2408.03932","DOIUrl":"https://doi.org/arxiv-2408.03932","url":null,"abstract":"The formation of dynamical patterns is one of the most striking features of\u0000non-equilibrium physical systems. Recent work has shown that such patterns\u0000arise generically from forces that violate Newton's third law, known as\u0000non-reciprocal interactions. These non-equilibrium phenomena are challenging\u0000for modern theories. Here, we introduce a model mixture of active\u0000(self-propelled) and passive (diffusive) particles with non-reciprocal\u0000effective interactions, which is amenable to exact mathematical analysis. We\u0000exploit state-of-the-art methods to derive exact hydrodynamic equations for the\u0000particle densities. We study the resulting collective behavior, including the\u0000linear stability of homogeneous states and phase coexistence in large systems.\u0000This reveals a novel phase diagram with the spinodal associated with active\u0000phase separation protruding through the associated binodal, heralding the\u0000emergence of dynamical steady states. We analyze these states in the\u0000thermodynamic limit of large system size, showing, for example, that sharp\u0000interfaces may travel at finite velocities, but traveling phase-separated\u0000states are forbidden. The model's mathematical tractability enables precise new\u0000conclusions beyond those available by numerical simulation of particle models\u0000or field theories.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943343","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 investigate the observables of the one-dimensional model for anomalous transport in semiconductor devices where diffusion arises from scattering at dislocations at fixed random positions, known as L'evy-Lorentz gas. Due to complex stochasticity in the system, direct investigations of such non-trivial dynamics are not possible; therefore, to gain insight into the microscopic properties, we use deterministic dynamics known as the Slicer Map and Fly-and-Die dynamics. We analytically derive the generalized position auto-correlation function of these dynamics and study the special case, the 3-point position correlation function. For this, we derive single parameter-dependent scaling and compare it with the numerically estimated 3-point position auto-correlation of the L'evy-Lorentz gas, for which the analytical expression is still an open question. Here we obtained a remarkable agreement between them, irrespective of any functional relationship with time. Moreover, we demonstrate that the position moments and the position auto-correlations of these systems scale in the same fashion, provided the times are large enough and far enough apart. Other observables, such as velocity moments and correlations, are reported to distinguish the systems.
{"title":"Generalized autocorrelation function in the family of deterministic and stochastic anomalous diffusion processes","authors":"Muhammad Tayyab","doi":"arxiv-2408.02989","DOIUrl":"https://doi.org/arxiv-2408.02989","url":null,"abstract":"We investigate the observables of the one-dimensional model for anomalous\u0000transport in semiconductor devices where diffusion arises from scattering at\u0000dislocations at fixed random positions, known as L'evy-Lorentz gas. Due to\u0000complex stochasticity in the system, direct investigations of such non-trivial\u0000dynamics are not possible; therefore, to gain insight into the microscopic\u0000properties, we use deterministic dynamics known as the Slicer Map and\u0000Fly-and-Die dynamics. We analytically derive the generalized position\u0000auto-correlation function of these dynamics and study the special case, the\u00003-point position correlation function. For this, we derive single\u0000parameter-dependent scaling and compare it with the numerically estimated\u00003-point position auto-correlation of the L'evy-Lorentz gas, for which the\u0000analytical expression is still an open question. Here we obtained a remarkable\u0000agreement between them, irrespective of any functional relationship with time.\u0000Moreover, we demonstrate that the position moments and the position\u0000auto-correlations of these systems scale in the same fashion, provided the\u0000times are large enough and far enough apart. Other observables, such as\u0000velocity moments and correlations, are reported to distinguish the systems.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943344","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}
Using the framework of stochastic thermodynamics we study heat production related to the stochastic motion of a particle driven by repulsive, nonlinear, time-delayed feedback. Recently it has been shown that this type of feedback can lead to persistent motion above a threshold in parameter space [Physical Review E 107, 024611 (2023)]. Here we investigate, numerically and by analytical methods, the rate of heat production in the different regimes around the threshold to persistent motion. We find a nonzero average heat production rate, $langle dot{q}rangle$, already below the threshold, indicating the nonequilibrium character of the system even at small feedback. In this regime, we compare to analytical results for a corresponding linearized delayed system and a small-delay approximation which provides a reasonable description of $langle dot{q}rangle$ at small repulsion (or delay time). Beyond the threshold, the rate of heat production is much larger and shows a maximum as function of the delay time. In this regime, $langle dot{q}rangle$ can be approximated by that of a system subject to a constant force stemming from the long-time velocity in the deterministic limit. The distribution of dissipated heat, however, is non-Gaussian, contrary to the constant-force case.
利用随机热力学框架，我们研究了与粒子在排斥性、非线性、延时反馈驱动下的随机运动有关的热量产生。最近的研究表明，这种类型的反馈会导致超过参数空间阈值的持续运动[PhysicalReview E 107, 024611 (2023)]。在此，我们通过数值和分析方法研究了持续运动阈值附近不同状态下的产热速率。我们发现在阈值以下就有一个非零的平均产热率（$langle dot{q}rangle$），这表明即使在小反馈时系统也是平衡的。在这种情况下，我们比较了相应线性化延迟系统的分析结果和小延迟近似值，后者对小排斥力（或延迟时间）下的$langle dot{q}rangle$ 提供了合理的描述。超过阈值后，产热速率会更大，并显示出与延迟时间函数相关的最大值。在这种情况下，$langle dot{q}rangle$可以近似于一个系统在确定性极限下受到的源于长时速度的恒定力。然而，耗散热的分布是非高斯分布，这与恒力情况相反。
{"title":"Heat production in a stochastic system with nonlinear time-delayed feedback","authors":"Robin A. Kopp, Sabine H. L. Klapp","doi":"arxiv-2408.03316","DOIUrl":"https://doi.org/arxiv-2408.03316","url":null,"abstract":"Using the framework of stochastic thermodynamics we study heat production\u0000related to the stochastic motion of a particle driven by repulsive, nonlinear,\u0000time-delayed feedback. Recently it has been shown that this type of feedback\u0000can lead to persistent motion above a threshold in parameter space [Physical\u0000Review E 107, 024611 (2023)]. Here we investigate, numerically and by\u0000analytical methods, the rate of heat production in the different regimes around\u0000the threshold to persistent motion. We find a nonzero average heat production\u0000rate, $langle dot{q}rangle$, already below the threshold, indicating the\u0000nonequilibrium character of the system even at small feedback. In this regime,\u0000we compare to analytical results for a corresponding linearized delayed system\u0000and a small-delay approximation which provides a reasonable description of\u0000$langle dot{q}rangle$ at small repulsion (or delay time). Beyond the\u0000threshold, the rate of heat production is much larger and shows a maximum as\u0000function of the delay time. In this regime, $langle dot{q}rangle$ can be\u0000approximated by that of a system subject to a constant force stemming from the\u0000long-time velocity in the deterministic limit. The distribution of dissipated\u0000heat, however, is non-Gaussian, contrary to the constant-force case.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943340","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 introduce an aggregation process based on emph{templating}, where a specified number of constituent clusters must assemble on a larger aggregate, which serves as a scaffold, for a reaction to occur. A simple example is a dimer scaffold, upon which two monomers meet and create another dimer, while dimers and larger aggregates undergo in irreversible aggregation with mass-independent rates. In the mean-field approximation, templating aggregation has unusual kinetics in which the cluster and monomer densities, $c(t)$ and $m(t)$ respectively, decay with time as $csim m^2sim t^{-2/3}$. These starkly contrast to the corresponding behaviors in conventional aggregation, $csim sqrt{m}sim t^{-1}$. We then treat three natural extensions of templating: (a) the reaction in which $L$ monomers meet and react on an $L$-mer scaffold to create two $L$-mers, (b) multistage scaffold reactions, and (c) templated ligation, in which clusters of all masses serve as scaffolds and binary aggregation is absent.
{"title":"Templating Aggregation","authors":"P. L. Krapivsky, S. Redner","doi":"arxiv-2408.02910","DOIUrl":"https://doi.org/arxiv-2408.02910","url":null,"abstract":"We introduce an aggregation process based on emph{templating}, where a\u0000specified number of constituent clusters must assemble on a larger aggregate,\u0000which serves as a scaffold, for a reaction to occur. A simple example is a\u0000dimer scaffold, upon which two monomers meet and create another dimer, while\u0000dimers and larger aggregates undergo in irreversible aggregation with\u0000mass-independent rates. In the mean-field approximation, templating aggregation\u0000has unusual kinetics in which the cluster and monomer densities, $c(t)$ and\u0000$m(t)$ respectively, decay with time as $csim m^2sim t^{-2/3}$. These starkly\u0000contrast to the corresponding behaviors in conventional aggregation, $csim\u0000sqrt{m}sim t^{-1}$. We then treat three natural extensions of templating: (a)\u0000the reaction in which $L$ monomers meet and react on an $L$-mer scaffold to\u0000create two $L$-mers, (b) multistage scaffold reactions, and (c) templated\u0000ligation, in which clusters of all masses serve as scaffolds and binary\u0000aggregation is absent.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"70 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943342","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}
Large language models show a surprising in-context learning ability -- being able to use a prompt to form a prediction for a query, yet without additional training, in stark contrast to old-fashioned supervised learning. Providing a mechanistic interpretation and linking the empirical phenomenon to physics are thus challenging and remain unsolved. We study a simple yet expressive transformer with linear attention, and map this structure to a spin glass model with real-valued spins, where the couplings and fields explain the intrinsic disorder in data. The spin glass model explains how the weight parameters interact with each other during pre-training, and most importantly why an unseen function can be predicted by providing only a prompt yet without training. Our theory reveals that for single instance learning, increasing the task diversity leads to the emergence of the in-context learning, by allowing the Boltzmann distribution to converge to a unique correct solution of weight parameters. Therefore the pre-trained transformer displays a prediction power in a novel prompt setting. The proposed spin glass model thus establishes a foundation to understand the empirical success of large language models.
{"title":"Spin glass model of in-context learning","authors":"Yuhao Li, Ruoran Bai, Haiping Huang","doi":"arxiv-2408.02288","DOIUrl":"https://doi.org/arxiv-2408.02288","url":null,"abstract":"Large language models show a surprising in-context learning ability -- being\u0000able to use a prompt to form a prediction for a query, yet without additional\u0000training, in stark contrast to old-fashioned supervised learning. Providing a\u0000mechanistic interpretation and linking the empirical phenomenon to physics are\u0000thus challenging and remain unsolved. We study a simple yet expressive\u0000transformer with linear attention, and map this structure to a spin glass model\u0000with real-valued spins, where the couplings and fields explain the intrinsic\u0000disorder in data. The spin glass model explains how the weight parameters\u0000interact with each other during pre-training, and most importantly why an\u0000unseen function can be predicted by providing only a prompt yet without\u0000training. Our theory reveals that for single instance learning, increasing the\u0000task diversity leads to the emergence of the in-context learning, by allowing\u0000the Boltzmann distribution to converge to a unique correct solution of weight\u0000parameters. Therefore the pre-trained transformer displays a prediction power\u0000in a novel prompt setting. The proposed spin glass model thus establishes a\u0000foundation to understand the empirical success of large language models.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943350","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 developed a computer code for the thermodynamic hierarchical equations of motion (T-HEOM) derived from a spin subsystem coupled to multiple Drude baths at different temperatures, which are connected to or disconnected from the subsystem as a function of time. The code can simulate the reduced dynamics of the subsystem under isothermal, isentropic, thermostatic, and entropic conditions. The thermodynamic extensive and intensive variables were calculated as physical observables, and the Gibbs and Helmholtz energies were evaluated as intensive and extensive work. The contribution of energies from the system-bath interaction was evaluated separately from the subsystem using the hierarchical elements of T-HEOM. The accuracy of the calculated results for the equilibrium distribution and two-body correlation functions of the subsystem was verified by comparison with the results obtained from the time-convolution-less Redfield equation. Non-Markovian effects in thermostatic processes were investigated by sequentially turning on and off the baths of different temperatures with different switching times and system-bath coupling. As a demonstration, a comparison was made by simulating the case where the temperature of one bath was varied over time and the case where similar temperature changes were achieved by turning on and off the baths at different temperatures. In addition, the Carnot engine was simulated under quasi-static conditions. To analyze the work done for the subsystem in the cycle, thermodynamic work diagrams were plotted as functions of intensive and extensive variables. The C++ source codes are provided as supplementary material.
{"title":"Thermodynamic hierarchical equations of motion and their application to Carnot engine","authors":"Shoki Koyanagi, Yoshitaka Tanimura","doi":"arxiv-2408.02249","DOIUrl":"https://doi.org/arxiv-2408.02249","url":null,"abstract":"We developed a computer code for the thermodynamic hierarchical equations of\u0000motion (T-HEOM) derived from a spin subsystem coupled to multiple Drude baths\u0000at different temperatures, which are connected to or disconnected from the\u0000subsystem as a function of time. The code can simulate the reduced dynamics of\u0000the subsystem under isothermal, isentropic, thermostatic, and entropic\u0000conditions. The thermodynamic extensive and intensive variables were calculated\u0000as physical observables, and the Gibbs and Helmholtz energies were evaluated as\u0000intensive and extensive work. The contribution of energies from the system-bath\u0000interaction was evaluated separately from the subsystem using the hierarchical\u0000elements of T-HEOM. The accuracy of the calculated results for the equilibrium\u0000distribution and two-body correlation functions of the subsystem was verified\u0000by comparison with the results obtained from the time-convolution-less Redfield\u0000equation. Non-Markovian effects in thermostatic processes were investigated by\u0000sequentially turning on and off the baths of different temperatures with\u0000different switching times and system-bath coupling. As a demonstration, a\u0000comparison was made by simulating the case where the temperature of one bath\u0000was varied over time and the case where similar temperature changes were\u0000achieved by turning on and off the baths at different temperatures. In\u0000addition, the Carnot engine was simulated under quasi-static conditions. To\u0000analyze the work done for the subsystem in the cycle, thermodynamic work\u0000diagrams were plotted as functions of intensive and extensive variables. The\u0000C++ source codes are provided as supplementary material.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943346","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}
The equilibrium and nonequilibrium properties of an Ising ferromagnetic cubic shell have been extensively studied by Monte Carlo simulation using Metropolis single spin flip algorithm. Although geometrically the Euclidean dimension of the cubical shell is three, interestingly, the Ising ferromagnetic cubic shell undergoes ferromagnetic phase transition at a temperature which is very close to that for two-dimensional Ising ferromagnet. Surprisingly, the Ising ferromagnetic cubic shell shows a strange (neither exponential nor stretched exponential) kind of relaxation behaviour, instead of exponential relaxation as usually observed in the two dimensional Ising ferromagnet. The metastable lifetime of a ferromagnetic Ising cubical shell is studied as a function of the applied magnetic field. Here also, the cubic shell behaves more likely a two-dimensional object as found from statistical analysis and comparison with Becker-D"oring prediction of classical nucleation theory.
{"title":"What will be the Euclidean dimension of an Ising ferromagnetic cubic shell?","authors":"Ishita Tikader, Muktish Acharyya","doi":"arxiv-2408.01804","DOIUrl":"https://doi.org/arxiv-2408.01804","url":null,"abstract":"The equilibrium and nonequilibrium properties of an Ising ferromagnetic cubic\u0000shell have been extensively studied by Monte Carlo simulation using Metropolis\u0000single spin flip algorithm. Although geometrically the Euclidean dimension of\u0000the cubical shell is three, interestingly, the Ising ferromagnetic cubic shell\u0000undergoes ferromagnetic phase transition at a temperature which is very close\u0000to that for two-dimensional Ising ferromagnet. Surprisingly, the Ising\u0000ferromagnetic cubic shell shows a strange (neither exponential nor stretched\u0000exponential) kind of relaxation behaviour, instead of exponential relaxation as\u0000usually observed in the two dimensional Ising ferromagnet. The metastable\u0000lifetime of a ferromagnetic Ising cubical shell is studied as a function of the\u0000applied magnetic field. Here also, the cubic shell behaves more likely a\u0000two-dimensional object as found from statistical analysis and comparison with\u0000Becker-D\"oring prediction of classical nucleation theory.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943345","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 discuss quantum friction in a system formed by two metallic surfaces separated by a ferromagnetic intermedium of a certain thickness. The internal degrees of freedom in the two metallic surfaces are assumed to be plasmons, while the excitations in the intermediate material are magnons, modeling plasmons coupled to magnons. During relative sliding, one surface moves uniformly parallel to the other, causing friction in the system. By calculating the effective action of the magnons, we can determine the particle production probability, which shows a positive correlation between the probability and the sliding speed. Finally, we derive the frictional force of the system, with both theoretical and numerical results indicating that the friction, like the particle production probability, also has a positive correlation with the speed.
{"title":"The magnon mediated plasmon friction: a functional integral approach","authors":"Yang Wang, Ruanjing Zhang, Feiyi Liu","doi":"arxiv-2408.01405","DOIUrl":"https://doi.org/arxiv-2408.01405","url":null,"abstract":"In this paper, we discuss quantum friction in a system formed by two metallic\u0000surfaces separated by a ferromagnetic intermedium of a certain thickness. The\u0000internal degrees of freedom in the two metallic surfaces are assumed to be\u0000plasmons, while the excitations in the intermediate material are magnons,\u0000modeling plasmons coupled to magnons. During relative sliding, one surface\u0000moves uniformly parallel to the other, causing friction in the system. By\u0000calculating the effective action of the magnons, we can determine the particle\u0000production probability, which shows a positive correlation between the\u0000probability and the sliding speed. Finally, we derive the frictional force of\u0000the system, with both theoretical and numerical results indicating that the\u0000friction, like the particle production probability, also has a positive\u0000correlation with the speed.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943347","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 apply the real space Renormalisation Group (RNG) technique to a variety of one-dimensional Ising chains. We begin by recapitulating the work of Nauenberg for an ordered Ising chain, namely the decimation approach. We extend this work to certain non-trivial situation namely, the Alternate Ising Chain and Fibonacci Ising chain. Our approach is pedagogical and accessible to undergraduate students who have had a first course in statistical mechanics.
{"title":"Real Space Renormalization Group for One-Dimensional Ising Chains","authors":"Shraddha singh, Vijay Singh","doi":"arxiv-2408.01021","DOIUrl":"https://doi.org/arxiv-2408.01021","url":null,"abstract":"We apply the real space Renormalisation Group (RNG) technique to a variety of\u0000one-dimensional Ising chains. We begin by recapitulating the work of Nauenberg\u0000for an ordered Ising chain, namely the decimation approach. We extend this work\u0000to certain non-trivial situation namely, the Alternate Ising Chain and\u0000Fibonacci Ising chain. Our approach is pedagogical and accessible to\u0000undergraduate students who have had a first course in statistical mechanics.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"70 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943349","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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