Over a century ago, Einstein formulated a precise mathematical model for describing Brownian motion. While this model adequately explains the diffusion of micron-sized particles in fluids, its limitations become apparent when applied to molecular self-diffusion in fluids. The foundational principles of Gaussianity and Markovianity, central to the Brownian diffusion paradigm, are insufficient for describing molecular diffusion, particularly in complex fluids characterized by intricate intermolecular interactions and hindered relaxation processes. This perspective delves into the nuanced behavior observed in diverse complex fluids, including molecular self-assembly, deep eutectic solvents, and ionic liquids, with a specific focus on modeling self-diffusion within these media. We explore the potential of extending diffusion models to incorporate non-Gaussian and non-Markovian effects by augmenting the Brownian model using non-local diffusion equations. Further, we validate the applicability of these models by utilizing them to describe results from quasielastic neutron scattering and MD simulations.
{"title":"Breaking the Brownian Barrier: Models and Manifestations of Molecular Diffusion in Complex Fluids","authors":"Harish Srinivasan, V. K. Sharma, S. Mitra","doi":"arxiv-2409.04199","DOIUrl":"https://doi.org/arxiv-2409.04199","url":null,"abstract":"Over a century ago, Einstein formulated a precise mathematical model for\u0000describing Brownian motion. While this model adequately explains the diffusion\u0000of micron-sized particles in fluids, its limitations become apparent when\u0000applied to molecular self-diffusion in fluids. The foundational principles of\u0000Gaussianity and Markovianity, central to the Brownian diffusion paradigm, are\u0000insufficient for describing molecular diffusion, particularly in complex fluids\u0000characterized by intricate intermolecular interactions and hindered relaxation\u0000processes. This perspective delves into the nuanced behavior observed in\u0000diverse complex fluids, including molecular self-assembly, deep eutectic\u0000solvents, and ionic liquids, with a specific focus on modeling self-diffusion\u0000within these media. We explore the potential of extending diffusion models to\u0000incorporate non-Gaussian and non-Markovian effects by augmenting the Brownian\u0000model using non-local diffusion equations. Further, we validate the\u0000applicability of these models by utilizing them to describe results from\u0000quasielastic neutron scattering and MD simulations.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"2012 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196237","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}
Luis Quiroga, Fernando J. Gómez-Ruiz, Ivan A. Bocanegra-Garay, Ferney J. Rodríguez, Carlos Tejedor
We investigate the impact of introducing a local cavity within the center of a topological chain, revealing profound effects on the system's quantum states. Notably, the cavity induces a scissor-like effect that bisects the chain, liberating Majorana zero modes (MZMs) within the bulk. Our results demonstrate that this setup enables the observation of non-trivial fusion rules and braiding -- key signatures of non-Abelian anyons -- facilitated by the spatially selective ultra-strong coupling of the cavity photon field. These MZM characteristics can be directly probed through fermionic parity readouts and photon Berry phases, respectively. Furthermore, by leveraging the symmetry properties of fermion modes within a two-site cavity, we propose a novel method for generating MZM-polariton Schr"odinger cat states. Our findings present a significant advancement in the control of topological quantum systems, offering new avenues for both fundamental research and potential quantum computing applications.
{"title":"Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding and Majorana-Schrödinger Cat States","authors":"Luis Quiroga, Fernando J. Gómez-Ruiz, Ivan A. Bocanegra-Garay, Ferney J. Rodríguez, Carlos Tejedor","doi":"arxiv-2409.04515","DOIUrl":"https://doi.org/arxiv-2409.04515","url":null,"abstract":"We investigate the impact of introducing a local cavity within the center of\u0000a topological chain, revealing profound effects on the system's quantum states.\u0000Notably, the cavity induces a scissor-like effect that bisects the chain,\u0000liberating Majorana zero modes (MZMs) within the bulk. Our results demonstrate\u0000that this setup enables the observation of non-trivial fusion rules and\u0000braiding -- key signatures of non-Abelian anyons -- facilitated by the\u0000spatially selective ultra-strong coupling of the cavity photon field. These MZM\u0000characteristics can be directly probed through fermionic parity readouts and\u0000photon Berry phases, respectively. Furthermore, by leveraging the symmetry\u0000properties of fermion modes within a two-site cavity, we propose a novel method\u0000for generating MZM-polariton Schr\"odinger cat states. Our findings present a\u0000significant advancement in the control of topological quantum systems, offering\u0000new avenues for both fundamental research and potential quantum computing\u0000applications.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196181","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}
Abdelwahab Kawafi, Lars Kürten, Levke Ortlieb, Yushi Yang, Abraham Mauleon Amieva, James E. Hallett, C. Patrick Royall
Colloidoscope is a deep learning pipeline employing a 3D residual Unet architecture, designed to enhance the tracking of dense colloidal suspensions through confocal microscopy. This methodology uses a simulated training dataset that reflects a wide array of real-world imaging conditions, specifically targeting high colloid volume fraction and low-contrast scenarios where traditional detection methods struggle. Central to our approach is the use of experimental signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and point-spread-functions (PSFs) to accurately quantify and simulate the experimental data. Our findings reveal that Colloidoscope achieves superior recall in particle detection (finds more particles) compared to conventional heuristic methods. Simultaneously, high precision is maintained (high fraction of true positives.) The model demonstrates a notable robustness to photobleached samples, thereby prolonging the imaging time and number of frames than may be acquired. Furthermore, Colloidoscope maintains small scale resolution sufficient to classify local structural motifs. Evaluated across both simulated and experimental datasets, Colloidoscope brings the advancements in computer vision offered by deep learning to particle tracking at high volume fractions. We offer a promising tool for researchers in the soft matter community, this model is deployed and available to use pretrained: https://github.com/wahabk/colloidoscope.
{"title":"Colloidoscope: Detecting Dense Colloids in 3d with Deep Learning","authors":"Abdelwahab Kawafi, Lars Kürten, Levke Ortlieb, Yushi Yang, Abraham Mauleon Amieva, James E. Hallett, C. Patrick Royall","doi":"arxiv-2409.04603","DOIUrl":"https://doi.org/arxiv-2409.04603","url":null,"abstract":"Colloidoscope is a deep learning pipeline employing a 3D residual Unet\u0000architecture, designed to enhance the tracking of dense colloidal suspensions\u0000through confocal microscopy. This methodology uses a simulated training dataset\u0000that reflects a wide array of real-world imaging conditions, specifically\u0000targeting high colloid volume fraction and low-contrast scenarios where\u0000traditional detection methods struggle. Central to our approach is the use of\u0000experimental signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and\u0000point-spread-functions (PSFs) to accurately quantify and simulate the\u0000experimental data. Our findings reveal that Colloidoscope achieves superior\u0000recall in particle detection (finds more particles) compared to conventional\u0000heuristic methods. Simultaneously, high precision is maintained (high fraction\u0000of true positives.) The model demonstrates a notable robustness to\u0000photobleached samples, thereby prolonging the imaging time and number of frames\u0000than may be acquired. Furthermore, Colloidoscope maintains small scale\u0000resolution sufficient to classify local structural motifs. Evaluated across\u0000both simulated and experimental datasets, Colloidoscope brings the advancements\u0000in computer vision offered by deep learning to particle tracking at high volume\u0000fractions. We offer a promising tool for researchers in the soft matter\u0000community, this model is deployed and available to use pretrained:\u0000https://github.com/wahabk/colloidoscope.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196180","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}
Penghua Ying, Wenjiang Zhou, Lucas Svensson, Erik Fransson, Fredrik Eriksson, Ke Xu, Ting Liang, Bai Song, Shunda Chen, Paul Erhart, Zheyong Fan
Path-integral molecular dynamics (PIMD) simulations are crucial for accurately capturing nuclear quantum effects in materials. However, their computational intensity and reliance on multiple software packages often limit their applicability at large scales. Here, we present an integration of PIMD methods, including thermostatted ring-polymer molecular dynamics (TRPMD), into the open-source GPUMD package, combined with highly accurate and efficient machine-learned neuroevolution potential (NEP) models. This approach achieves almost the accuracy of first-principles calculations with the computational efficiency of empirical potentials, enabling large-scale atomistic simulations that incorporate nuclear quantum effects. We demonstrate the efficacy of the combined NEP-PIMD approach by examining various thermal properties of diverse materials, including lithium hydride (LiH), three porous metal-organic frameworks (MOFs), and elemental aluminum. For LiH, our NEP-PIMD simulations successfully capture the isotope effect, reproducing the experimentally observed dependence of the lattice parameter on the reduced mass. For MOFs, our results reveal that achieving good agreement with experimental data requires consideration of both nuclear quantum effects and dispersive interactions. For aluminum, the TRPMD method effectively captures thermal expansion and phonon properties, aligning well with quantum mechanical predictions. This efficient NEP-PIMD approach opens new avenues for exploring complex material properties influenced by nuclear quantum effects, with potential applications across a broad range of materials.
{"title":"Highly efficient path-integral molecular dynamics simulations with GPUMD using neuroevolution potentials: Case studies on thermal properties of materials","authors":"Penghua Ying, Wenjiang Zhou, Lucas Svensson, Erik Fransson, Fredrik Eriksson, Ke Xu, Ting Liang, Bai Song, Shunda Chen, Paul Erhart, Zheyong Fan","doi":"arxiv-2409.04430","DOIUrl":"https://doi.org/arxiv-2409.04430","url":null,"abstract":"Path-integral molecular dynamics (PIMD) simulations are crucial for\u0000accurately capturing nuclear quantum effects in materials. However, their\u0000computational intensity and reliance on multiple software packages often limit\u0000their applicability at large scales. Here, we present an integration of PIMD\u0000methods, including thermostatted ring-polymer molecular dynamics (TRPMD), into\u0000the open-source GPUMD package, combined with highly accurate and efficient\u0000machine-learned neuroevolution potential (NEP) models. This approach achieves\u0000almost the accuracy of first-principles calculations with the computational\u0000efficiency of empirical potentials, enabling large-scale atomistic simulations\u0000that incorporate nuclear quantum effects. We demonstrate the efficacy of the\u0000combined NEP-PIMD approach by examining various thermal properties of diverse\u0000materials, including lithium hydride (LiH), three porous metal-organic\u0000frameworks (MOFs), and elemental aluminum. For LiH, our NEP-PIMD simulations\u0000successfully capture the isotope effect, reproducing the experimentally\u0000observed dependence of the lattice parameter on the reduced mass. For MOFs, our\u0000results reveal that achieving good agreement with experimental data requires\u0000consideration of both nuclear quantum effects and dispersive interactions. For\u0000aluminum, the TRPMD method effectively captures thermal expansion and phonon\u0000properties, aligning well with quantum mechanical predictions. This efficient\u0000NEP-PIMD approach opens new avenues for exploring complex material properties\u0000influenced by nuclear quantum effects, with potential applications across a\u0000broad range of materials.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196185","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 consider a lattice model in which a tracer particle moves in the presence of randomly distributed immobile obstacles. The crowding effect due to the obstacles interplays with the quasi-confinement imposed by wrapping the lattice onto a cylinder. We compute the velocity autocorrelation function and show that already in equilibrium the system exhibits a dimensional crossover from two- to one-dimensional as time progresses. A pulling force is switched on and we characterize analytically the stationary state in terms of the stationary velocity and diffusion coefficient. Stochastic simulations are used to discuss the range of validity of the analytic results. Our calculation, exact to first order in the obstacle density, holds for arbitrarily large forces and confinement size.
{"title":"Dimensional crossover via confinement in the lattice Lorentz gas","authors":"A. Squarcini, A. Tinti, P. Illien, O. Bénichou, T. Franosch","doi":"arxiv-2409.04289","DOIUrl":"https://doi.org/arxiv-2409.04289","url":null,"abstract":"We consider a lattice model in which a tracer particle moves in the presence\u0000of randomly distributed immobile obstacles. The crowding effect due to the\u0000obstacles interplays with the quasi-confinement imposed by wrapping the lattice\u0000onto a cylinder. We compute the velocity autocorrelation function and show that\u0000already in equilibrium the system exhibits a dimensional crossover from two- to\u0000one-dimensional as time progresses. A pulling force is switched on and we\u0000characterize analytically the stationary state in terms of the stationary\u0000velocity and diffusion coefficient. Stochastic simulations are used to discuss\u0000the range of validity of the analytic results. Our calculation, exact to first\u0000order in the obstacle density, holds for arbitrarily large forces and\u0000confinement size.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196183","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}
Partial solvability plays an important role in the context of statistical mechanics, since it has turned out to be closely related to the emergence of quantum many-body scar states, i.e., exceptional energy eigenstates which do not obey the strong version of the eigenstate themalization hypothesis. We show that partial solvability of a quantum many-body system can be maintained even when the system is coupled to boundary dissipators under certain conditions. We propose two mechanisms that support partially solvable structures in boundary dissipative systems: The first one is based on the restricted spectrum generating algebra, while the second one is based on the Hilbert space fragmentation. From these structures, we derive exact eigenmodes of the Gorini-Kossakowski-Sudarshan-Lindblad equation for a family of quantum spin chain models with boundary dissipators, where we find various intriguing phenomena arising from the partial solvability of the open quantum systems, including persistent oscillations (quantum synchronization) and the existence of the matrix product operator symmetry. We discuss how the presence of solvable eigenmodes affects long-time behaviors of observables in boundary dissipative spin chains based on numerical simulations using the quantum trajectory method.
{"title":"Boundary dissipative spin chains with partial solvability inherited from system Hamiltonians","authors":"Chihiro Matsui, Naoto Tsuji","doi":"arxiv-2409.03208","DOIUrl":"https://doi.org/arxiv-2409.03208","url":null,"abstract":"Partial solvability plays an important role in the context of statistical\u0000mechanics, since it has turned out to be closely related to the emergence of\u0000quantum many-body scar states, i.e., exceptional energy eigenstates which do\u0000not obey the strong version of the eigenstate themalization hypothesis. We show\u0000that partial solvability of a quantum many-body system can be maintained even\u0000when the system is coupled to boundary dissipators under certain conditions. We\u0000propose two mechanisms that support partially solvable structures in boundary\u0000dissipative systems: The first one is based on the restricted spectrum\u0000generating algebra, while the second one is based on the Hilbert space\u0000fragmentation. From these structures, we derive exact eigenmodes of the\u0000Gorini-Kossakowski-Sudarshan-Lindblad equation for a family of quantum spin\u0000chain models with boundary dissipators, where we find various intriguing\u0000phenomena arising from the partial solvability of the open quantum systems,\u0000including persistent oscillations (quantum synchronization) and the existence\u0000of the matrix product operator symmetry. We discuss how the presence of\u0000solvable eigenmodes affects long-time behaviors of observables in boundary\u0000dissipative spin chains based on numerical simulations using the quantum\u0000trajectory method.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196190","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 motility of living things and synthetic self-propelled objects is often described using Active Brownian particles. To capture the interaction of these particles with their often complex environment, this model can be augmented with empirical forces or torques, for example, to describe their alignment with an obstacle or wall after a collision. Here, we assess the quality of these empirical models by comparing their output predictions with trajectories of rod-shaped active particles that scatter sterically at a flat wall. We employ a classical least-squares method to evaluate the instantaneous torque. In addition, we lay out a Bayesian inference procedure to construct the posterior distribution of plausible model parameters. In contrast to the least squares fit, the Bayesian approach does not require orientational data of the active particle and can readily be applied to experimental tracking data.
{"title":"Bayesian inference of wall torques for active Brownian particles","authors":"Sascha Lambert, Merle Duchene, Stefan Klumpp","doi":"arxiv-2409.03533","DOIUrl":"https://doi.org/arxiv-2409.03533","url":null,"abstract":"The motility of living things and synthetic self-propelled objects is often\u0000described using Active Brownian particles. To capture the interaction of these\u0000particles with their often complex environment, this model can be augmented\u0000with empirical forces or torques, for example, to describe their alignment with\u0000an obstacle or wall after a collision. Here, we assess the quality of these\u0000empirical models by comparing their output predictions with trajectories of\u0000rod-shaped active particles that scatter sterically at a flat wall. We employ a\u0000classical least-squares method to evaluate the instantaneous torque. In\u0000addition, we lay out a Bayesian inference procedure to construct the posterior\u0000distribution of plausible model parameters. In contrast to the least squares\u0000fit, the Bayesian approach does not require orientational data of the active\u0000particle and can readily be applied to experimental tracking data.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196187","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 discuss local magnetic field quenches using perturbative methods of finite time path field theory in the following spin chains: Ising and XY in a transverse magnetic field. Their common characteristics are: i) they are integrable via mapping to second quantized noninteracting fermion problem; ii) when the ground state is nondegenerate (true for finite chains except in special cases) it can be represented as a vacuum of Bogoliubov fermions. By switching on a local magnetic field perturbation at finite time, the problem becomes nonintegrable and must be approached via numeric or perturbative methods. Using the formalism of finite time path field theory based on Wigner transforms of projected functions, we show how to: i) calculate the basic "bubble" diagram in the Loschmidt echo of a quenched chain to any order in the perturbation; ii) resum the generalized Schwinger-Dyson equation for the fermion two point retarded functions in the "bubble" diagram, hence achieving the resummation of perturbative expansion of Loschmidt echo for a wide range of perturbation strengths under certain analiticity assumptions. Limitations of the assumptions and possible generalizations beyond it and also for other spin chains are further discussed.
{"title":"Finite time path field theory perturbative methods for local quantum spin chain quenches","authors":"Domagoj Kuić, Alemka Knapp, Diana Šaponja-Milutinović","doi":"arxiv-2409.03832","DOIUrl":"https://doi.org/arxiv-2409.03832","url":null,"abstract":"We discuss local magnetic field quenches using perturbative methods of finite\u0000time path field theory in the following spin chains: Ising and XY in a\u0000transverse magnetic field. Their common characteristics are: i) they are\u0000integrable via mapping to second quantized noninteracting fermion problem; ii)\u0000when the ground state is nondegenerate (true for finite chains except in\u0000special cases) it can be represented as a vacuum of Bogoliubov fermions. By\u0000switching on a local magnetic field perturbation at finite time, the problem\u0000becomes nonintegrable and must be approached via numeric or perturbative\u0000methods. Using the formalism of finite time path field theory based on Wigner\u0000transforms of projected functions, we show how to: i) calculate the basic\u0000\"bubble\" diagram in the Loschmidt echo of a quenched chain to any order in the\u0000perturbation; ii) resum the generalized Schwinger-Dyson equation for the\u0000fermion two point retarded functions in the \"bubble\" diagram, hence achieving\u0000the resummation of perturbative expansion of Loschmidt echo for a wide range of\u0000perturbation strengths under certain analiticity assumptions. Limitations of\u0000the assumptions and possible generalizations beyond it and also for other spin\u0000chains are further discussed.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196231","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 kinetic theory description of a low density gas of hard spheres or disks, confined between two parallel plates separated a distance smaller than twice the diameter of the particles, is addressed starting from the Liouville equation of the system. The associated BBGKY hierarchy of equations for the reduced distribution functions is expanded in powers of a parameter measuring the density of the system in the appropriate dimensionless units. The Boltzmann level of description is obtained by keeping only the two lowest orders in the parameter. In particular, the one-particle distribution function obeys a couple of equations. Contrary to what happens with a Boltzmann-like kinetic equation that has been proposed for the same system on a heuristic basis, the kinetic theory formulated here admits stationary solutions that are consistent with equilibrium statistical mechanics, both in absence and presence of external fields. In the latter case, the density profile is rather complex due to the coupling between the inhomogeneities generated by the confinement and by the external fields. The general theory formulated provides a solid basis for the study of the properties of strongly confined dilute gases.
{"title":"Dynamics and kinetic theory of hard spheres under strong confinement","authors":"J. Javier Brey, M. I. García de Soria, P. Maynar","doi":"arxiv-2409.03452","DOIUrl":"https://doi.org/arxiv-2409.03452","url":null,"abstract":"The kinetic theory description of a low density gas of hard spheres or disks,\u0000confined between two parallel plates separated a distance smaller than twice\u0000the diameter of the particles, is addressed starting from the Liouville\u0000equation of the system. The associated BBGKY hierarchy of equations for the\u0000reduced distribution functions is expanded in powers of a parameter measuring\u0000the density of the system in the appropriate dimensionless units. The Boltzmann\u0000level of description is obtained by keeping only the two lowest orders in the\u0000parameter. In particular, the one-particle distribution function obeys a couple\u0000of equations. Contrary to what happens with a Boltzmann-like kinetic equation\u0000that has been proposed for the same system on a heuristic basis, the kinetic\u0000theory formulated here admits stationary solutions that are consistent with\u0000equilibrium statistical mechanics, both in absence and presence of external\u0000fields. In the latter case, the density profile is rather complex due to the\u0000coupling between the inhomogeneities generated by the confinement and by the\u0000external fields. The general theory formulated provides a solid basis for the\u0000study of the properties of strongly confined dilute gases.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196188","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}
This paper deals with themes such as approximate counting/evaluation of the total number of flat-foldings for random origami diagrams, evaluation of the values averaged over various instances, obtaining forcing sets for general origami diagrams, and evaluation of average computational complexity. An approach to the above problems using a physical model and an efficient size reduction method for them is proposed. Using a statistical mechanics model and a numerical method of approximate enumeration based on it, we give the result of approximate enumeration of the total number of flat-foldings of single-vertex origami diagram with random width of angles gathering around the central vertex, and obtain its size dependence for an asymptotic prediction towards the limit of infinite size. In addition, an outlook with respect to the chained determination of local stacking orders of facets caused by the constraint that prohibits the penetration of them is also provided from the viewpoint of organizing the terms included in the physical model. A method to efficiently solve the problem of the determination or enumeration of flat-foldings is discussed based on the above perspectives. This is thought to be closely related to forcing sets.
{"title":"An Efficient Enumeration of Flat-Foldings : Study on Random Single Vertex Origami","authors":"Chihiro Nakajima","doi":"arxiv-2409.03240","DOIUrl":"https://doi.org/arxiv-2409.03240","url":null,"abstract":"This paper deals with themes such as approximate counting/evaluation of the\u0000total number of flat-foldings for random origami diagrams, evaluation of the\u0000values averaged over various instances, obtaining forcing sets for general\u0000origami diagrams, and evaluation of average computational complexity. An\u0000approach to the above problems using a physical model and an efficient size\u0000reduction method for them is proposed. Using a statistical mechanics model and\u0000a numerical method of approximate enumeration based on it, we give the result\u0000of approximate enumeration of the total number of flat-foldings of\u0000single-vertex origami diagram with random width of angles gathering around the\u0000central vertex, and obtain its size dependence for an asymptotic prediction\u0000towards the limit of infinite size. In addition, an outlook with respect to the\u0000chained determination of local stacking orders of facets caused by the\u0000constraint that prohibits the penetration of them is also provided from the\u0000viewpoint of organizing the terms included in the physical model. A method to\u0000efficiently solve the problem of the determination or enumeration of\u0000flat-foldings is discussed based on the above perspectives. This is thought to\u0000be closely related to forcing sets.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"76 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196223","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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