Pub Date : 2016-12-15DOI: 10.1007/978-3-319-23947-7_6
G. Baxter, D. Cellai, S. N. Dorogovtsev, A. Goltsev, J. Mendes
{"title":"A unified approach to percolation processes on multiplex networks","authors":"G. Baxter, D. Cellai, S. N. Dorogovtsev, A. Goltsev, J. Mendes","doi":"10.1007/978-3-319-23947-7_6","DOIUrl":"https://doi.org/10.1007/978-3-319-23947-7_6","url":null,"abstract":"","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"52 1","pages":"101-123"},"PeriodicalIF":0.0,"publicationDate":"2016-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89263613","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}
When spatial constraint for the constituents (e.g., atom or particle) of system is once given, disordered structure for non-interacting system in equilibrium states is symmetric with respect to equiatomic composition. Meanwhile, when the interaction between constituents is introduced, this symmetry is typically broken, naturally appearing compositional asymmetry. Although this asymmetry, depending on temperature, comes from multibody interactions in the system, we here clarify that the asymmetry near equiatomic composition can be universally well-characterized by two specially selected microscopic structure, which can be known a priori without any information about interactions or temperature: The key role is the class of spatial constraint. Based on the facts, we provide analytical expression of temperature dependence of disordered structure, and demonstrate its validity and applicability by predicting short-range order parameters of practical alloys compared with full thermodynamic simulation.
{"title":"Compositional asymmetry of disordered structure: Role of spatial constraint","authors":"Koretaka Yuge","doi":"10.14723/TMRSJ.42.85","DOIUrl":"https://doi.org/10.14723/TMRSJ.42.85","url":null,"abstract":"When spatial constraint for the constituents (e.g., atom or particle) of system is once given, disordered structure for non-interacting system in equilibrium states is symmetric with respect to equiatomic composition. Meanwhile, when the interaction between constituents is introduced, this symmetry is typically broken, naturally appearing compositional asymmetry. Although this asymmetry, depending on temperature, comes from multibody interactions in the system, we here clarify that the asymmetry near equiatomic composition can be universally well-characterized by two specially selected microscopic structure, which can be known a priori without any information about interactions or temperature: The key role is the class of spatial constraint. Based on the facts, we provide analytical expression of temperature dependence of disordered structure, and demonstrate its validity and applicability by predicting short-range order parameters of practical alloys compared with full thermodynamic simulation.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84015099","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}
Pub Date : 2016-10-27DOI: 10.1103/PhysRevB.95.054303
S. Geraedts, R. Bhatt
The dynamics of the highly excited states of a system projected into a single Landau level are analyzed. An analysis of level spacing ratios for finite size systems shows a clear crossover from extend (GUE) to localized (Poisson) statistics, indicating a many body localization transition. However, the location of this transition depends very strongly on system size, and appears to scale to infinite disorder in the thermodynamic limit. This result does not depend on the properties of the ground state (such as whether the ground state exhibits topological order), as expected for a transition of highly-excited eigenstates. We therefore conclude that many body localization does not exist in these systems. Our results demonstrate that a sub-thermodynamic number of single particle effectively extended states is sufficient to cause all many body states to become extended.
{"title":"Absence of Many-Body Localization in a Single Landau Level","authors":"S. Geraedts, R. Bhatt","doi":"10.1103/PhysRevB.95.054303","DOIUrl":"https://doi.org/10.1103/PhysRevB.95.054303","url":null,"abstract":"The dynamics of the highly excited states of a system projected into a single Landau level are analyzed. An analysis of level spacing ratios for finite size systems shows a clear crossover from extend (GUE) to localized (Poisson) statistics, indicating a many body localization transition. However, the location of this transition depends very strongly on system size, and appears to scale to infinite disorder in the thermodynamic limit. This result does not depend on the properties of the ground state (such as whether the ground state exhibits topological order), as expected for a transition of highly-excited eigenstates. We therefore conclude that many body localization does not exist in these systems. Our results demonstrate that a sub-thermodynamic number of single particle effectively extended states is sufficient to cause all many body states to become extended.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83996201","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}
Pub Date : 2016-10-18DOI: 10.1093/OSO/9780198797319.003.0010
H. Schomerus
Over the past decades, a great body of theoretical and mathematical work has been devoted to random-matrix descriptions of open quantum systems. In these notes, based on lectures delivered at the Les Houches Summer School "Stochastic Processes and Random Matrices" in July 2015, we review the physical origins and mathematical structures of the underlying models, and collect key predictions which give insight into the typical system behaviour. In particular, we aim to give an idea how the different features are interlinked. The notes mainly focus on elastic scattering but also include a short detour to interacting systems, which we motivate by the overarching question of ergodicity. The first chapters introduce general notions from random matrix theory, such as the ten universality classes and ensembles of hermitian, unitary, positive-definite and non-hermitian matrices. We then review microscopic scattering models that form the basis for statistical descriptions, and consider signatures of random scattering in decay, dynamics and transport. The last chapter briefly touches on Anderson localization and localization in interacting systems.
{"title":"Random matrix approaches to open quantum systems","authors":"H. Schomerus","doi":"10.1093/OSO/9780198797319.003.0010","DOIUrl":"https://doi.org/10.1093/OSO/9780198797319.003.0010","url":null,"abstract":"Over the past decades, a great body of theoretical and mathematical work has been devoted to random-matrix descriptions of open quantum systems. In these notes, based on lectures delivered at the Les Houches Summer School \"Stochastic Processes and Random Matrices\" in July 2015, we review the physical origins and mathematical structures of the underlying models, and collect key predictions which give insight into the typical system behaviour. In particular, we aim to give an idea how the different features are interlinked. The notes mainly focus on elastic scattering but also include a short detour to interacting systems, which we motivate by the overarching question of ergodicity. The first chapters introduce general notions from random matrix theory, such as the ten universality classes and ensembles of hermitian, unitary, positive-definite and non-hermitian matrices. We then review microscopic scattering models that form the basis for statistical descriptions, and consider signatures of random scattering in decay, dynamics and transport. The last chapter briefly touches on Anderson localization and localization in interacting systems.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78764992","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}
Pub Date : 2016-10-06DOI: 10.1103/PhysRevB.95.054433
Cosimo Lupo, F. Ricci-Tersenghi
Numerical simulations of spin glass models with continuous variables set the problem of a reliable but efficient discretization of such variables. In particular, the main question is how fast physical observables computed in the discretized model converge toward the ones of the continuous model when the number of states of the discretized model increases. We answer this question for the XY model and its discretization, the $q$-states clock model, in the mean-field setting provided by random graphs. It is found that the convergence of physical observables is exponentially fast in the number $q$ of states of the clock model, so allowing a very reliable approximation of the XY model by using a rather small number of states. Furthermore, such an exponential convergence is found to be independent from the disorder distribution used. Only at $T=0$ the convergence is slightly slower (stretched exponential). We also study the 1RSB solution of the $q$-states clock model in the low temperature spin glass phase.
{"title":"Approximating the XY model on a random graph with a $q$-states clock model","authors":"Cosimo Lupo, F. Ricci-Tersenghi","doi":"10.1103/PhysRevB.95.054433","DOIUrl":"https://doi.org/10.1103/PhysRevB.95.054433","url":null,"abstract":"Numerical simulations of spin glass models with continuous variables set the problem of a reliable but efficient discretization of such variables. In particular, the main question is how fast physical observables computed in the discretized model converge toward the ones of the continuous model when the number of states of the discretized model increases. We answer this question for the XY model and its discretization, the $q$-states clock model, in the mean-field setting provided by random graphs. It is found that the convergence of physical observables is exponentially fast in the number $q$ of states of the clock model, so allowing a very reliable approximation of the XY model by using a rather small number of states. Furthermore, such an exponential convergence is found to be independent from the disorder distribution used. Only at $T=0$ the convergence is slightly slower (stretched exponential). We also study the 1RSB solution of the $q$-states clock model in the low temperature spin glass phase.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"192 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79650109","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}
Random electron systems show rich phases such as Anderson insulator, diffusive metal, quantum and anomalous quantum Hall insulator, Weyl semimetal, as well as strong/weak topological insulators. Eigenfunctions of each matter phase have specific features, but due to the random nature of systems, judging the matter phase from eigenfunctions is difficult. Here we propose the deep learning algorithm to capture the features of eigenfunctions. Localization-delocalization transition as well as disordered Chern insulator-Anderson insulator transition is discussed.
{"title":"Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems","authors":"T. Ohtsuki, T. Ohtsuki","doi":"10.7566/JPSJ.85.123706","DOIUrl":"https://doi.org/10.7566/JPSJ.85.123706","url":null,"abstract":"Random electron systems show rich phases such as Anderson insulator, diffusive metal, quantum and anomalous quantum Hall insulator, Weyl semimetal, as well as strong/weak topological insulators. Eigenfunctions of each matter phase have specific features, but due to the random nature of systems, judging the matter phase from eigenfunctions is difficult. Here we propose the deep learning algorithm to capture the features of eigenfunctions. Localization-delocalization transition as well as disordered Chern insulator-Anderson insulator transition is discussed.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"51 1-2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72604598","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}
Configurational polyhedora (CP) is a hyperpolyhedra on multidimensional configuration space, whose vertex (and edges) corresponds to upper or lower limit value of correlation functions for all possible atomic configuration on given lattice. In classical systems where physical property including internal energy and elastic modulus can be a linear map for structures considered, it is known that atomic configuration having highest (or lowerst) physical quantity should always locate on one of the vertices at absolute zero temperature. The present study extend the idea of CP to finite-temperature property (especially, focusing on internal energy), and successfully provides demonstration of how temperature dependence of internal energy in equilibrium state for alloys is interpreted in terms of the density of states for non-interacting system along specially selected direction on cofiguration space.
{"title":"Extension of Configurational Polyhedra to Finite Temperature Property","authors":"Koretaka Yuge, Kazuya Kojima, Kazuhito Takeuchi, Tetsuya Taikei","doi":"10.14723/TMRSJ.41.363","DOIUrl":"https://doi.org/10.14723/TMRSJ.41.363","url":null,"abstract":"Configurational polyhedora (CP) is a hyperpolyhedra on multidimensional configuration space, whose vertex (and edges) corresponds to upper or lower limit value of correlation functions for all possible atomic configuration on given lattice. In classical systems where physical property including internal energy and elastic modulus can be a linear map for structures considered, it is known that atomic configuration having highest (or lowerst) physical quantity should always locate on one of the vertices at absolute zero temperature. The present study extend the idea of CP to finite-temperature property (especially, focusing on internal energy), and successfully provides demonstration of how temperature dependence of internal energy in equilibrium state for alloys is interpreted in terms of the density of states for non-interacting system along specially selected direction on cofiguration space.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86774820","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}
Pub Date : 2016-08-24DOI: 10.1007/978-3-319-56422-7_31
Y. Tarasov, D. Iakushev, S. Melnik, O. Usatenko
{"title":"The plasmon-polariton mirroring due to strong fluctuations of the surface impedance","authors":"Y. Tarasov, D. Iakushev, S. Melnik, O. Usatenko","doi":"10.1007/978-3-319-56422-7_31","DOIUrl":"https://doi.org/10.1007/978-3-319-56422-7_31","url":null,"abstract":"","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"120 1","pages":"417-429"},"PeriodicalIF":0.0,"publicationDate":"2016-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87772120","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 ensemble teacher learning, ensemble teachers have only uncertain information about the true teacher, and this information is given by an ensemble consisting of an infinite number of ensemble teachers whose variety is sufficiently rich. In this learning, a student learns from an ensemble teacher that is iteratively selected randomly from a pool of many ensemble teachers. An interesting point of ensemble teacher learning is the asymptotic behavior of the student to approach the true teacher by learning from ensemble teachers. The student performance is improved by using the Hebbian learning rule in the learning. However, the perceptron learning rule cannot improve the student performance. On the other hand, we proposed a perceptron learning rule with a margin. This learning rule is identical to the perceptron learning rule when the margin is zero and identical to the Hebbian learning rule when the margin is infinity. Thus, this rule connects the perceptron learning rule and the Hebbian learning rule continuously through the size of the margin. Using this rule, we study changes in the learning behavior from the perceptron learning rule to the Hebbian learning rule by considering several margin sizes. From the results, we show that by setting a margin of kappa > 0, the effect of an ensemble appears and becomes significant when a larger margin kappa is used.
{"title":"Statistical Mechanics of On-line Ensemble Teacher Learning through a Novel Perceptron Learning Rule","authors":"K. Hara, S. Miyoshi","doi":"10.1143/JPSJ.81.064002","DOIUrl":"https://doi.org/10.1143/JPSJ.81.064002","url":null,"abstract":"In ensemble teacher learning, ensemble teachers have only uncertain information about the true teacher, and this information is given by an ensemble consisting of an infinite number of ensemble teachers whose variety is sufficiently rich. In this learning, a student learns from an ensemble teacher that is iteratively selected randomly from a pool of many ensemble teachers. An interesting point of ensemble teacher learning is the asymptotic behavior of the student to approach the true teacher by learning from ensemble teachers. The student performance is improved by using the Hebbian learning rule in the learning. However, the perceptron learning rule cannot improve the student performance. On the other hand, we proposed a perceptron learning rule with a margin. This learning rule is identical to the perceptron learning rule when the margin is zero and identical to the Hebbian learning rule when the margin is infinity. Thus, this rule connects the perceptron learning rule and the Hebbian learning rule continuously through the size of the margin. Using this rule, we study changes in the learning behavior from the perceptron learning rule to the Hebbian learning rule by considering several margin sizes. From the results, we show that by setting a margin of kappa > 0, the effect of an ensemble appears and becomes significant when a larger margin kappa is used.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82922309","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}
Disordered non-interacting systems are classified into ten symmetry classes, with the unitary class being the most fundamental. The three and four dimensional unitary universality classes are attracting renewed interest because of their relation to three dimensional Weyl semi-metals and four dimensional topological insulators. Determining the critical exponent of the correlation/localistion length for the Anderson transition in these classes is important both theoretically and experimentally. Using the transfer matrix technique, we report numerical estimations of the critical exponent in a U(1) model in three and four dimensions.
{"title":"Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes","authors":"K. Slevin, T. Ohtsuki","doi":"10.7566/JPSJ.85.104712","DOIUrl":"https://doi.org/10.7566/JPSJ.85.104712","url":null,"abstract":"Disordered non-interacting systems are classified into ten symmetry classes, with the unitary class being the most fundamental. The three and four dimensional unitary universality classes are attracting renewed interest because of their relation to three dimensional Weyl semi-metals and four dimensional topological insulators. Determining the critical exponent of the correlation/localistion length for the Anderson transition in these classes is important both theoretically and experimentally. Using the transfer matrix technique, we report numerical estimations of the critical exponent in a U(1) model in three and four dimensions.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87029718","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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