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arXiv: Statistical Mechanics最新文献

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Dynamics of Rod like Particles in Supercooled Liquids -- Probing Dynamic Heterogeneity and Amorphous Order 过冷液体中棒状粒子的动力学——探究动态非均匀性和非晶态秩序
arXiv: Statistical Mechanics Pub Date : 2020-05-22 DOI: 10.1103/PhysRevApplied.16.034022
Anoop Mutneja, S. Karmakar
{"title":"Dynamics of Rod like Particles in Supercooled Liquids -- Probing Dynamic Heterogeneity and Amorphous Order","authors":"Anoop Mutneja, S. Karmakar","doi":"10.1103/PhysRevApplied.16.034022","DOIUrl":"https://doi.org/10.1103/PhysRevApplied.16.034022","url":null,"abstract":"Probing dynamic and static correlation in glass-forming supercooled liquids has been a challenge for decades in spite of extensive research. Dynamic correlation which manifests itself as Dynamic Heterogeneity is ubiquitous in a vast variety of systems starting from molecular glass-forming liquids, dense colloidal systems to collections of cells. On the other hand, the mere concept of static correlation in these dense disordered systems remain somewhat elusive and its existence is still actively debated. We propose a novel method to extract both dynamic and static correlations using rod-like particles as probe. This method can be implemented in molecular glass-forming liquids in experiments as well as in other soft matter systems including biologically relevant systems. We also rationalize the observed log-normal like distribution of rotational decorrelation time of elongated probe molecules in reported experimental studies along with a proposal of a novel methodology to extract dynamic and static correlation lengths in experiments.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81243260","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}
引用次数: 1
A kinetic model for epidemic spread 流行病传播的动力学模型
arXiv: Statistical Mechanics Pub Date : 2020-05-20 DOI: 10.2140/memocs.2020.8.249
M. Pulvirenti, S. Simonella
{"title":"A kinetic model for epidemic spread","authors":"M. Pulvirenti, S. Simonella","doi":"10.2140/memocs.2020.8.249","DOIUrl":"https://doi.org/10.2140/memocs.2020.8.249","url":null,"abstract":"We present a Boltzmann equation for mixtures of three species of particles reducing to the Kermack-McKendrick (SIR) equations for the time-evolution of the density of infected agents in an isolated population. The kinetic model is potentially more detailed and might provide information on space mixing of the agents.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"94 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91034802","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}
引用次数: 12
Scalar Active Mixtures: The Nonreciprocal Cahn-Hilliard Model 标量活性混合:非互反Cahn-Hilliard模型
arXiv: Statistical Mechanics Pub Date : 2020-05-14 DOI: 10.1103/PHYSREVX.10.041009
Suropriya Saha, J. Agudo-Canalejo, R. Golestanian
{"title":"Scalar Active Mixtures: The Nonreciprocal Cahn-Hilliard Model","authors":"Suropriya Saha, J. Agudo-Canalejo, R. Golestanian","doi":"10.1103/PHYSREVX.10.041009","DOIUrl":"https://doi.org/10.1103/PHYSREVX.10.041009","url":null,"abstract":"Pair interactions between active particles need not follow Newton's third law. In this work we propose a continuum model of pattern formation due to non-reciprocal interaction between multiple species of scalar active matter. The classical Cahn-Hilliard model is minimally modified by supplementing the equilibrium Ginzburg-Landau dynamics with particle number conserving currents which cannot be derived from a free energy, reflecting the microscopic departure from action-reaction symmetry. The strength of the asymmetry in the interaction determines whether the steady state exhibits a macroscopic phase separation or a traveling density wave displaying global polar order. The latter structure, which is equivalent to an active self-propelled smectic phase, coarsens via annihilation of defects, whereas the former structure undergoes Ostwald ripening. The emergence of traveling density waves, which is a clear signature of broken time-reversal symmetry in this active system, is a generic feature of any multi-component mixture with microscopic non-reciprocal interactions.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91065453","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}
引用次数: 66
Sustaining a temperature difference 维持温差
arXiv: Statistical Mechanics Pub Date : 2020-05-13 DOI: 10.21468/SCIPOSTPHYS.9.3.030
M. Polettini, Alberto Garilli
{"title":"Sustaining a temperature difference","authors":"M. Polettini, Alberto Garilli","doi":"10.21468/SCIPOSTPHYS.9.3.030","DOIUrl":"https://doi.org/10.21468/SCIPOSTPHYS.9.3.030","url":null,"abstract":"We derive an expression for the minimal rate of entropy that sustains two reservoirs at different temperatures $T_0$ and $T_ell$. The law displays an intuitive $ell^{-1}$ dependency on the relative distance and a characterisic $log^2 (T_ell/T_0)$ dependency on the boundary temperatures. First we give a back-of-envelope argument based on the Fourier Law (FL) of conduction, showing that the least-dissipation profile is exponential. Then we revisit a model of a chain of oscillators, each coupled to a heat reservoir. In the limit of large damping we reobtain the exponential and squared-log behaviors, providing a self-consistent derivation of the FL. For small damping \"equipartition frustration\" leads to a well-known balistic behaviour, whose incompatibility with the FL posed a long-time challenge.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87788779","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}
引用次数: 0
Kibble–Zurek Mechanism in a Dissipative Transverse Ising Chain 耗散横向Ising链中的Kibble-Zurek机制
arXiv: Statistical Mechanics Pub Date : 2020-05-12 DOI: 10.7566/JPSJ.89.104002
Hiroki Oshiyama, N. Shibata, S. Suzuki
{"title":"Kibble–Zurek Mechanism in a Dissipative Transverse Ising Chain","authors":"Hiroki Oshiyama, N. Shibata, S. Suzuki","doi":"10.7566/JPSJ.89.104002","DOIUrl":"https://doi.org/10.7566/JPSJ.89.104002","url":null,"abstract":"We study the Kibble-Zurek mechanism in the transverse Ising chain coupled to a dissipative boson bath, making use of a new numerical method with the infinite time evolving block decimation combined with the discrete-time path integral. We first show the ground-state phase diagram and confirm that a quantum phase transition takes place in the presence of the system-bath coupling. Then we present the time dependence of the energy expectation value of the spin Hamiltonian and the scaling of the kink density with respect to the time period over which the spin Hamiltonian crosses a quantum phase transition. The energy of spins starts to grow from the energy at the ground state of the full system near a quantum phase transition. The kink density decays as a power law with respect to the time period. These results confirm that the Kibble-Zurek mechanism happens. We discuss the exponent for the decay of the kink density in comparison with a theoretical result with the quantum Monte-Carlo simulation. A comparison to an experimental study is also briefly mentioned.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81802689","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}
引用次数: 8
Analysis of the Hopfield Model with Discrete Coupling 具有离散耦合的Hopfield模型分析
arXiv: Statistical Mechanics Pub Date : 2020-05-11 DOI: 10.7566/JPSJ.90.094602
Ryuta Sasaki, T. Aonishi
{"title":"Analysis of the Hopfield Model with Discrete Coupling","authors":"Ryuta Sasaki, T. Aonishi","doi":"10.7566/JPSJ.90.094602","DOIUrl":"https://doi.org/10.7566/JPSJ.90.094602","url":null,"abstract":"Growing demand for high-speed Ising-computing-specific hardware has prompted a need for determining how the accuracy depends on a hardware implementation with physically limited resources. For instance, in digital hardware such as field-programmable gate arrays, as the number of bits representing the coupling strength is reduced, the density of integrated Ising spins and the speed of computing can be increased while the calculation accuracy becomes lower. To optimize the accuracy-efficiency trade-off, we have to estimate the change in performance of the Ising computing machine depending on the number of bits representing the coupling strength. In this study, we tackle this issue by focusing on the Hopfield model with discrete coupling. The Hopfield model is a canonical Ising computing model. Previous studies have analyzed the effect of a few nonlinear functions (e.g. sign) for mapping the coupling strength on the Hopfield model with statistical mechanics methods, but not the effect of discretization of the coupling strength in detail. Here, we derived the order parameter equations of the Hopfield model with discrete coupling by using the replica method and clarified the relationship between the number of bits representing the coupling strength and the critical memory capacity.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"333 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78924688","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}
引用次数: 0
Coarse-grained second-order response theory 粗粒度二阶响应理论
arXiv: Statistical Mechanics Pub Date : 2020-05-11 DOI: 10.1103/physrevresearch.2.043123
Fenna Muller, U. Basu, Peter Sollich, M. Kruger
{"title":"Coarse-grained second-order response theory","authors":"Fenna Muller, U. Basu, Peter Sollich, M. Kruger","doi":"10.1103/physrevresearch.2.043123","DOIUrl":"https://doi.org/10.1103/physrevresearch.2.043123","url":null,"abstract":"While linear response theory, manifested by the fluctuation dissipation theorem, can be applied on any length scale, nonlinear response theory is fundamentally of microscopic nature. We develop an exact theoretical framework for analyzing nonlinear (second order) response of coarse grained observables to time-dependent perturbations, using a path-integral formalism. The resulting expressions involve correlations of the observable with coarse grained path weights. The time symmetric part of these weights depends on paths and perturbation protocol in a complex manner, and, furthermore, the absence of Markovianity prevents slicing of the coarse grained path integral. Despite this, we show that the response function can be expressed in terms of path weights corresponding to a single-step perturbation. This formalism thus leads to an extrapolation scheme, which circumvents the mentioned difficulties, and where measuring linear responses of coarse-grained variables suffices to determine their second order response. We illustrate the validity of the formalism with the examples of an exactly solvable four-state model and the near-critical Ising model.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72786665","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}
引用次数: 2
Apparent superballistic dynamics in one-dimensional random walks with biased detachment 有偏分离的一维随机行走的表观超弹道动力学
arXiv: Statistical Mechanics Pub Date : 2020-05-08 DOI: 10.1103/PHYSREVRESEARCH.2.033520
C. Korosec, David A. Sivak, N. R. Forde
{"title":"Apparent superballistic dynamics in one-dimensional random walks with biased detachment","authors":"C. Korosec, David A. Sivak, N. R. Forde","doi":"10.1103/PHYSREVRESEARCH.2.033520","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.2.033520","url":null,"abstract":"The mean-squared displacement (MSD) is an averaged quantity widely used to assess anomalous diffusion. In many cases, such as molecular motors with finite processivity, dynamics of the system of interest produce trajectories of varying duration. Here we explore the effects of finite processivity on different measures of the MSD. We do so by investigating a deceptively simple dynamical system: a one-dimensional random walk (with equidistant jump lengths, symmetric move probabilities, and constant step duration) with an origin-directed detachment bias. By tuning the time dependence of the detachment bias, we find through analytical calculations and trajectory simulations that the system can exhibit a broad range of anomalous diffusion, extending beyond conventional diffusion to superdiffusion and even superballistic motion. We analytically determine that protocols with a time-increasing detachment lead to an ensemble-averaged velocity increasing in time, thereby providing the effective acceleration that is required to push the system above the ballistic threshold. MSD analysis of burnt-bridges ratchets similarly reveals superballistic behavior. Because superdiffusive MSDs are often used to infer biased, motor-like dynamics, these findings provide a cautionary tale for dynamical interpretation.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"47 4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90992995","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}
引用次数: 8
Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters 横向场Ising模型中的量子猝灭动力学:连接矩形团簇中的数值展开
arXiv: Statistical Mechanics Pub Date : 2020-05-06 DOI: 10.21468/SCIPOSTPHYS.9.3.031
Jonas Richter, Tjark Heitmann, R. Steinigeweg
{"title":"Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters","authors":"Jonas Richter, Tjark Heitmann, R. Steinigeweg","doi":"10.21468/SCIPOSTPHYS.9.3.031","DOIUrl":"https://doi.org/10.21468/SCIPOSTPHYS.9.3.031","url":null,"abstract":"We study quantum quenches in the transverse-field Ising model defined on different lattice geometries such as chains, two- and three-leg ladders, and two-dimensional square lattices. Starting from fully polarized initial states, we consider the dynamics of the transverse and the longitudinal magnetization for quenches to weak, strong, and critical values of the transverse field. To this end, we rely on an efficient combination of numerical linked cluster expansions (NLCEs) and a forward propagation of pure states in real time. As a main result, we demonstrate that NLCEs comprising solely rectangular clusters provide a promising approach to study the real-time dynamics of two-dimensional quantum many-body systems directly in the thermodynamic limit. By comparing to existing data from the literature, we unveil that NLCEs yield converged results on time scales which are competitive to other state-of-the-art numerical methods.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"81 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84977504","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}
引用次数: 8
Thermodynamically consistent gradient elasticity with an internal variable 具有内部变量的热力学一致梯度弹性
arXiv: Statistical Mechanics Pub Date : 2020-05-01 DOI: 10.2298/tam200204006v
P. V'an
{"title":"Thermodynamically consistent gradient elasticity with an internal variable","authors":"P. V'an","doi":"10.2298/tam200204006v","DOIUrl":"https://doi.org/10.2298/tam200204006v","url":null,"abstract":"The role of thermodynamics in continuum mechanics and the derivation of the proper constitutive relations is a discussed subject of Rational Mechanics. The classical literature did not use the accumulated knowledge of thermostatics and was very critical with the heuristic methods of irreversible thermodynamics. In this paper, a small strain gradient elasticity theory is constructed with memory effects and dissipation. The method is nonequilibrium thermodynamics with internal variables; therefore, the constitutive relations are compatible with thermodynamics by construction. Thermostatic Gibbs relation is introduced for elastic bodies with a single tensorial internal variable. The thermodynamic potentials are first-order weakly nonlocal, and the entropy production is calculated. Then the constitutive functions and the evolution equation of the internal variable is constructed. The second law analysis has shown a contribution of gradient terms to the stress, also without dissipation.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"158 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72587729","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}
引用次数: 3
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