Pub Date : 2019-06-10DOI: 10.1103/physrevb.102.214309
M. G. Izzo, B. Wehinger, S. Cazzato, A. Matic, C. Masciovecchio, A. Gessini, G. Ruocco
Acoustic excitations in topologically disordered media at mesoscale present anomalous features with respect to the Debye's theory. In a three-dimensional medium an acoustic excitation is characterized by its phase velocity, intensity and polarization. The so-called Rayleigh anomalies, which manifest in attenuation and retardation of the acoustic excitations, affect the first two properties. The topological disorder is, however, expected to influence also the third one. Acoustic excitations with a well-defined polarization in the continuum limit present indeed a so-called mixing of polarizations at nanoscale, as attested by experimental observations and Molecular Dynamics simulations. We provide a comprehensive experimental characterization of acoustic dynamics properties of a selected glass, 1-octyl-3-methylimidazolium chloride glass, whose heterogeneous structure at nanoscale is well-assessed. Distinctive features, which can be related to the occurrence of the Rayleigh anomalies and of the mixing of polarizations are observed. We develop, in the framework of the Random Media Theory, an analytical model that allows a quantitative description of all the Rayleigh anomalies and the mixing of polarizations. Contrast between theoretical and experimental features for the selected glass reveals an excellent agreement. The quantitative theoretical approach permits thus to demonstrate how the mixing of polarizations generates distinctive feature in the dynamic structure factor of glasses and to unambiguously identify them. The robustness of the proposed theoretical approach is validated by its ability to describe as well transverse acoustic dynamics.
{"title":"Rayleigh scattering and disorder-induced mixing of polarizations in amorphous solids at the nanoscale: 1-octyl-3-methylimidazolium chloride glass","authors":"M. G. Izzo, B. Wehinger, S. Cazzato, A. Matic, C. Masciovecchio, A. Gessini, G. Ruocco","doi":"10.1103/physrevb.102.214309","DOIUrl":"https://doi.org/10.1103/physrevb.102.214309","url":null,"abstract":"Acoustic excitations in topologically disordered media at mesoscale present anomalous features with respect to the Debye's theory. In a three-dimensional medium an acoustic excitation is characterized by its phase velocity, intensity and polarization. The so-called Rayleigh anomalies, which manifest in attenuation and retardation of the acoustic excitations, affect the first two properties. The topological disorder is, however, expected to influence also the third one. Acoustic excitations with a well-defined polarization in the continuum limit present indeed a so-called mixing of polarizations at nanoscale, as attested by experimental observations and Molecular Dynamics simulations. We provide a comprehensive experimental characterization of acoustic dynamics properties of a selected glass, 1-octyl-3-methylimidazolium chloride glass, whose heterogeneous structure at nanoscale is well-assessed. Distinctive features, which can be related to the occurrence of the Rayleigh anomalies and of the mixing of polarizations are observed. We develop, in the framework of the Random Media Theory, an analytical model that allows a quantitative description of all the Rayleigh anomalies and the mixing of polarizations. Contrast between theoretical and experimental features for the selected glass reveals an excellent agreement. The quantitative theoretical approach permits thus to demonstrate how the mixing of polarizations generates distinctive feature in the dynamic structure factor of glasses and to unambiguously identify them. The robustness of the proposed theoretical approach is validated by its ability to describe as well transverse acoustic dynamics.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90684111","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 : 2019-01-30DOI: 10.21468/SCIPOSTPHYS.8.6.087
Jeremy B. Goetz, Yi Zhang, M. Lawler
Detecting the subtle yet phase defining features in Scanning Tunneling Microscopy and Spectroscopy data remains an important challenge in quantum materials. We meet the challenge of detecting nematic order from local density of states data with supervised machine learning and artificial neural networks for the difficult scenario without sharp features such as visible lattice Bragg peaks or Friedel oscillation signatures in the Fourier transform spectrum. We train the artificial neural networks to classify simulated data of isotropic and anisotropic two-dimensional metals in the presence of disorder. The supervised machine learning succeeds only with at least one hidden layer in the ANN architecture, demonstrating it is a higher level of complexity than nematic order detected from Bragg peaks which requires just two neurons. We apply the finalized ANN to experimental STM data on CaFe2As2, and it predicts nematic symmetry breaking with 99% confidence (probability 0.99), in agreement with previous analysis. Our results suggest ANNs could be a useful tool for the detection of nematic order in STM data and a variety of other forms of symmetry breaking.
{"title":"Detecting nematic order in STM/STS data with artificial intelligence","authors":"Jeremy B. Goetz, Yi Zhang, M. Lawler","doi":"10.21468/SCIPOSTPHYS.8.6.087","DOIUrl":"https://doi.org/10.21468/SCIPOSTPHYS.8.6.087","url":null,"abstract":"Detecting the subtle yet phase defining features in Scanning Tunneling Microscopy and Spectroscopy data remains an important challenge in quantum materials. We meet the challenge of detecting nematic order from local density of states data with supervised machine learning and artificial neural networks for the difficult scenario without sharp features such as visible lattice Bragg peaks or Friedel oscillation signatures in the Fourier transform spectrum. We train the artificial neural networks to classify simulated data of isotropic and anisotropic two-dimensional metals in the presence of disorder. The supervised machine learning succeeds only with at least one hidden layer in the ANN architecture, demonstrating it is a higher level of complexity than nematic order detected from Bragg peaks which requires just two neurons. We apply the finalized ANN to experimental STM data on CaFe2As2, and it predicts nematic symmetry breaking with 99% confidence (probability 0.99), in agreement with previous analysis. Our results suggest ANNs could be a useful tool for the detection of nematic order in STM data and a variety of other forms of symmetry breaking.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"61 1","pages":"087"},"PeriodicalIF":0.0,"publicationDate":"2019-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85784149","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 : 2018-12-21DOI: 10.13130/MALATESTA-ENRICO-MARIA_PHD2018-12-21
E. Malatesta
This PhD thesis is organized as follows. In the first two chapters I will review some basic notions of statistical physics of disordered systems, such as random graph theory, the mean-field approximation, spin glasses and combinatorial optimization. The replica method will also be introduced and applied to the Sherrington-Kirkpatrick model, one of the simplest mean-field models of spin-glasses. The second part of the thesis deals with mean-field combinatorial optimization problems. The attention will be focused on the study of finite-size corrections of random integer matching problems (chapter 3) and fractional ones (chapter 4). In chapter 5 I will discuss a very general relation connecting multi-overlaps and the moments of the cavity magnetization distribution. In the third part we consider random Euclidean optimization problems. I will start solving the traveling-salesman-problem (TSP) in one dimension both in its bipartite and monopartite version (chapter 6). In chapter 7 I will discuss the possible optimal solutions of the 2-factor problem. In chapter 8 I will solve the bipartite TSP in two dimensions, in the limit of large number of points. Chapter 9 contains some conclusions.
{"title":"RANDOM COMBINATORIAL OPTIMIZATION PROBLEMS: MEAN FIELD AND FINITE-DIMENSIONAL RESULTS","authors":"E. Malatesta","doi":"10.13130/MALATESTA-ENRICO-MARIA_PHD2018-12-21","DOIUrl":"https://doi.org/10.13130/MALATESTA-ENRICO-MARIA_PHD2018-12-21","url":null,"abstract":"This PhD thesis is organized as follows. In the first two chapters I will review some basic notions of statistical physics of disordered systems, such as random graph theory, the mean-field approximation, spin glasses and combinatorial optimization. The replica method will also be introduced and applied to the Sherrington-Kirkpatrick model, one of the simplest mean-field models of spin-glasses. The second part of the thesis deals with mean-field combinatorial optimization problems. The attention will be focused on the study of finite-size corrections of random integer matching problems (chapter 3) and fractional ones (chapter 4). In chapter 5 I will discuss a very general relation connecting multi-overlaps and the moments of the cavity magnetization distribution. In the third part we consider random Euclidean optimization problems. I will start solving the traveling-salesman-problem (TSP) in one dimension both in its bipartite and monopartite version (chapter 6). In chapter 7 I will discuss the possible optimal solutions of the 2-factor problem. In chapter 8 I will solve the bipartite TSP in two dimensions, in the limit of large number of points. Chapter 9 contains some conclusions.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84421386","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 : 2018-09-18DOI: 10.20944/PREPRINTS201809.0327.V1
T. Chattaraj
In two dimensional disordered lattices, presence of interaction makes particles less localized than the non-interacting ones within the range of disorder strength W ≤ 4 and interaction strength V ≤ 4. If the interaction strength is higher, then particles localize more. Although, a localization-delocalization transition is not found, a transition with changes in the dominant correlations is observed. The nature of correlations between the particles as nearest neighbors become dominant beyond certain disorder strengths.
{"title":"Localization Parameters for Interacting Particles in Disordered Two- Dimensional Lattices","authors":"T. Chattaraj","doi":"10.20944/PREPRINTS201809.0327.V1","DOIUrl":"https://doi.org/10.20944/PREPRINTS201809.0327.V1","url":null,"abstract":"In two dimensional disordered lattices, presence of interaction makes particles less localized than the non-interacting ones within the range of disorder strength W ≤ 4 and interaction strength V ≤ 4. If the interaction strength is higher, then particles localize more. Although, a localization-delocalization transition is not found, a transition with changes in the dominant correlations is observed. The nature of correlations between the particles as nearest neighbors become dominant beyond certain disorder strengths.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88627013","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 : 2018-01-10DOI: 10.1007/978-3-319-99731-5_13
Ajith Ramachandran, C. Danieli, S. Flach
{"title":"Fano Resonances in Flat Band Networks","authors":"Ajith Ramachandran, C. Danieli, S. Flach","doi":"10.1007/978-3-319-99731-5_13","DOIUrl":"https://doi.org/10.1007/978-3-319-99731-5_13","url":null,"abstract":"","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"305 1","pages":"311-329"},"PeriodicalIF":0.0,"publicationDate":"2018-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79812477","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 : 2018-01-01DOI: 10.4236/jemaa.2018.102003
C. Bédard, A. Destexhe
The macroscopic electric permittivity of a given medium may depend on frequency, but this frequency dependence cannot be arbitrary, its real and imaginary parts are related by the well-known Kramers-Kronig relations. Here, we show that an analogous paradigm applies to the macroscopic electric conductivity. If the causality principle is taken into account, there exists Kramers-Kronig relations for conductivity, which are mathematically equivalent to the Hilbert transform. These relations impose strong constraints that models of heterogeneous media should satisfy to have a physically plausible frequency dependence of the conductivity and permittivity. We illustrate these relations and constraints by a few examples of known physical media. These extended relations constitute important constraints to test the consistency of past and future experimental measurements of the electric properties of heterogeneous media.
{"title":"Kramers-Kronig relations and the properties of conductivity and permittivity in heterogeneous media","authors":"C. Bédard, A. Destexhe","doi":"10.4236/jemaa.2018.102003","DOIUrl":"https://doi.org/10.4236/jemaa.2018.102003","url":null,"abstract":"The macroscopic electric permittivity of a given medium may depend on frequency, but this frequency dependence cannot be arbitrary, its real and imaginary parts are related by the well-known Kramers-Kronig relations. Here, we show that an analogous paradigm applies to the macroscopic electric conductivity. If the causality principle is taken into account, there exists Kramers-Kronig relations for conductivity, which are mathematically equivalent to the Hilbert transform. These relations impose strong constraints that models of heterogeneous media should satisfy to have a physically plausible frequency dependence of the conductivity and permittivity. We illustrate these relations and constraints by a few examples of known physical media. These extended relations constitute important constraints to test the consistency of past and future experimental measurements of the electric properties of heterogeneous media.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"75 1","pages":"34-51"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75402612","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 : 2017-12-29DOI: 10.1016/j.physleta.2019.125987
A. Mukherjee, A. Nandy, A. Chakrabarti
{"title":"Controlled trapping of single particle states on a periodic substrate by deterministic stubbing","authors":"A. Mukherjee, A. Nandy, A. Chakrabarti","doi":"10.1016/j.physleta.2019.125987","DOIUrl":"https://doi.org/10.1016/j.physleta.2019.125987","url":null,"abstract":"","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89565905","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}
Most of the analytical studies on spin glasses are performed by using mean-field theory and renormalization group analysis. Analytical studies on finite-dimensional spin glasses are very challenging. In this short note, a possible exten- sion of the approaches on the phase transition in spin glasses is demonstrated. To validate our extension, we compared our estimates on the critical points with the existing numerical results.
{"title":"An extension of estimation of critical points in ground state for random spin systems","authors":"Masayuki Ohzeki, Yuta Kudo, Kazuyuki Tanaka","doi":"10.7566/JPSJ.87.015001","DOIUrl":"https://doi.org/10.7566/JPSJ.87.015001","url":null,"abstract":"Most of the analytical studies on spin glasses are performed by using mean-field theory and renormalization group analysis. Analytical studies on finite-dimensional spin glasses are very challenging. In this short note, a possible exten- sion of the approaches on the phase transition in spin glasses is demonstrated. To validate our extension, we compared our estimates on the critical points with the existing numerical results.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75427627","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 : 2017-09-29DOI: 10.1007/978-3-319-96914-5_2
E. Vincent, Vincent Dupuis Sphynx, Phenix
{"title":"Spin Glasses: Experimental Signatures and Salient Outcomes","authors":"E. Vincent, Vincent Dupuis Sphynx, Phenix","doi":"10.1007/978-3-319-96914-5_2","DOIUrl":"https://doi.org/10.1007/978-3-319-96914-5_2","url":null,"abstract":"","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"41 1","pages":"31-56"},"PeriodicalIF":0.0,"publicationDate":"2017-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74272930","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 : 2017-09-18DOI: 10.1016/j.rinp.2018.01.031
H. Yamada
{"title":"Wavepacket Dynamics in One-Dimensional System with Long-Range Correlated Disorder","authors":"H. Yamada","doi":"10.1016/j.rinp.2018.01.031","DOIUrl":"https://doi.org/10.1016/j.rinp.2018.01.031","url":null,"abstract":"","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"12 1","pages":"1006-1009"},"PeriodicalIF":0.0,"publicationDate":"2017-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75464668","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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