Giulia Garcia Lorenzana, Ada Altieri, Giulio Biroli, Michel Fruchart, Vincenzo Vitelli
Disordered systems generically exhibit aging and a glass transition. Previous studies have long suggested that non-reciprocity tends to destroy glassiness. Here, we show that this is not always the case using a bipartite spherical Sherrington-Kirpatrick model that describes the antagonistic coupling between two identical complex agents modeled as macroscopic spin glasses. Our dynamical mean field theory calculations reveal an exceptional-point mediated transition from a static disorder phase to an oscillating amorphous phase as well as non-reciprocal aging with slow dynamics and oscillations.
{"title":"Non-reciprocal spin-glass transition and aging","authors":"Giulia Garcia Lorenzana, Ada Altieri, Giulio Biroli, Michel Fruchart, Vincenzo Vitelli","doi":"arxiv-2408.17360","DOIUrl":"https://doi.org/arxiv-2408.17360","url":null,"abstract":"Disordered systems generically exhibit aging and a glass transition. Previous\u0000studies have long suggested that non-reciprocity tends to destroy glassiness.\u0000Here, we show that this is not always the case using a bipartite spherical\u0000Sherrington-Kirpatrick model that describes the antagonistic coupling between\u0000two identical complex agents modeled as macroscopic spin glasses. Our dynamical\u0000mean field theory calculations reveal an exceptional-point mediated transition\u0000from a static disorder phase to an oscillating amorphous phase as well as\u0000non-reciprocal aging with slow dynamics and oscillations.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220852","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}
Temperature chaos (TC) in spin glasses has been claimed to exist no matter how small the temperature change, $Delta T$. However, experimental studies exhibit a finite value of $Delta T$ for the transition to TC. This paper explores the onset of TC with much higher accuracy over a large temperature range. We find that TC is always present, though small for the smallest $Delta T$ that we can reliably measure. However, it grows rapidly as $Delta T$ increases, the region of rapid growth coinciding with the $Delta T$ predicted from renormalization group arguments and observed experimentally. We are able to transcend the full range for the onset of TC, from fully reversible to fully chaotic.
{"title":"Nature of the onset to temperature chaos","authors":"Jiaming He, Hongze Li, Raymond Lee Orbach","doi":"arxiv-2408.16874","DOIUrl":"https://doi.org/arxiv-2408.16874","url":null,"abstract":"Temperature chaos (TC) in spin glasses has been claimed to exist no matter\u0000how small the temperature change, $Delta T$. However, experimental studies\u0000exhibit a finite value of $Delta T$ for the transition to TC. This paper\u0000explores the onset of TC with much higher accuracy over a large temperature\u0000range. We find that TC is always present, though small for the smallest $Delta\u0000T$ that we can reliably measure. However, it grows rapidly as $Delta T$\u0000increases, the region of rapid growth coinciding with the $Delta T$ predicted\u0000from renormalization group arguments and observed experimentally. We are able\u0000to transcend the full range for the onset of TC, from fully reversible to fully\u0000chaotic.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220854","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}
Autoregressive models are a class of generative model that probabilistically predict the next output of a sequence based on previous inputs. The autoregressive sequence is by definition one-dimensional (1D), which is natural for language tasks and hence an important component of modern architectures like recurrent neural networks (RNNs) and transformers. However, when language models are used to predict outputs on physical systems that are not intrinsically 1D, the question arises of which choice of autoregressive sequence -- if any -- is optimal. In this paper, we study the reconstruction of critical correlations in the two-dimensional (2D) Ising model, using RNNs and transformers trained on binary spin data obtained near the thermal phase transition. We compare the training performance for a number of different 1D autoregressive sequences imposed on finite-size 2D lattices. We find that paths with long 1D segments are more efficient at training the autoregressive models compared to space-filling curves that better preserve the 2D locality. Our results illustrate the potential importance in choosing the optimal autoregressive sequence ordering when training modern language models for tasks in physics.
{"title":"Autoregressive model path dependence near Ising criticality","authors":"Yi Hong Teoh, Roger G. Melko","doi":"arxiv-2408.15715","DOIUrl":"https://doi.org/arxiv-2408.15715","url":null,"abstract":"Autoregressive models are a class of generative model that probabilistically\u0000predict the next output of a sequence based on previous inputs. The\u0000autoregressive sequence is by definition one-dimensional (1D), which is natural\u0000for language tasks and hence an important component of modern architectures\u0000like recurrent neural networks (RNNs) and transformers. However, when language\u0000models are used to predict outputs on physical systems that are not\u0000intrinsically 1D, the question arises of which choice of autoregressive\u0000sequence -- if any -- is optimal. In this paper, we study the reconstruction of\u0000critical correlations in the two-dimensional (2D) Ising model, using RNNs and\u0000transformers trained on binary spin data obtained near the thermal phase\u0000transition. We compare the training performance for a number of different 1D\u0000autoregressive sequences imposed on finite-size 2D lattices. We find that paths\u0000with long 1D segments are more efficient at training the autoregressive models\u0000compared to space-filling curves that better preserve the 2D locality. Our\u0000results illustrate the potential importance in choosing the optimal\u0000autoregressive sequence ordering when training modern language models for tasks\u0000in physics.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220853","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 random energy model (REM) is the simplest spin glass model which exhibits replica symmetry breaking. It is well known since the 80's that its overlaps are non-selfaveraging and that their statistics satisfy the predictions of the replica theory. All these statistical properties can be understood by considering that the low energy levels are the points generated by a Poisson process with an exponential density. Here we first show how, by replacing the exponential density by a sum of two exponentials, the overlaps statistics are modified. One way to reconcile these results with the replica theory is to allow the blocks in the Parisi matrix to fluctuate. Other examples where the sizes of these blocks should fluctuate include the finite size corrections of the REM, the case of discrete energies and the overlaps between two temperatures. In all these cases, the blocks sizes not only fluctuate but need to take complex values if one wishes to reproduce the results of our replica-free calculations.
随机能量模型（REM）是最简单的自旋玻璃模型，表现出复制对称性破缺。自上世纪 80 年代以来，人们就清楚地知道它的重叠是非自平均的，而且其统计特性满足复制理论的预测。考虑到低能级是由具有指数密度的泊松过程产生的点，就可以理解所有这些统计特性。在这里，我们首先展示了用两个指数之和取代指数密度后，重叠统计是如何被修正的。将这些结果与复制理论相协调的一种方法是允许帕里西矩阵中的块发生波动。这些块的大小应该波动的其他例子包括 REM 的有限尺寸修正、离散能量的情况以及两个温度之间的重叠。在所有这些情况下，如果要重现我们的无复制品计算结果，这些块的大小不仅会波动，而且需要取复杂的值。
{"title":"Generalizations of Parisi's replica symmetry breaking and overlaps in random energy models","authors":"Bernard Derrida, Peter Mottishaw","doi":"arxiv-2408.15125","DOIUrl":"https://doi.org/arxiv-2408.15125","url":null,"abstract":"The random energy model (REM) is the simplest spin glass model which exhibits\u0000replica symmetry breaking. It is well known since the 80's that its overlaps\u0000are non-selfaveraging and that their statistics satisfy the predictions of the\u0000replica theory. All these statistical properties can be understood by\u0000considering that the low energy levels are the points generated by a Poisson\u0000process with an exponential density. Here we first show how, by replacing the\u0000exponential density by a sum of two exponentials, the overlaps statistics are\u0000modified. One way to reconcile these results with the replica theory is to\u0000allow the blocks in the Parisi matrix to fluctuate. Other examples where the\u0000sizes of these blocks should fluctuate include the finite size corrections of\u0000the REM, the case of discrete energies and the overlaps between two\u0000temperatures. In all these cases, the blocks sizes not only fluctuate but need\u0000to take complex values if one wishes to reproduce the results of our\u0000replica-free calculations.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227453","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}
While electric power grids play a key role in the decarbonization of society, it remains unclear how recent trends, such as the strong integration of renewable energies, can affect their stability. Power oscillation modes, which are key to the stability of the grid, are traditionally studied numerically with the conventional view-point of two regimes of extended (inter-area) or localized (intra-area) modes. In this article we introduce an analogy based on stochastic quantum models and demonstrate its applicability to power systems. We show from simple models that at low frequency the mean free path induced by disorder is inversely cubic in the frequency. This stems from the Courant-Fisher-Weyl theorem, which predicts a strong protection of the lowest frequency modes from disorder. As a consequence a power oscillation, induced by some local disruption of the grid, can propagate in a ballistic, diffusive or localised regime. In contrast with the conventional view-point, the existence of these three regimes is confirmed in a realistic model of the European power grid.
{"title":"Stochastic quantum models for the dynamics of power grids","authors":"Pierrick Guichard, Nicolas Retière, Didier Mayou","doi":"arxiv-2408.14921","DOIUrl":"https://doi.org/arxiv-2408.14921","url":null,"abstract":"While electric power grids play a key role in the decarbonization of society,\u0000it remains unclear how recent trends, such as the strong integration of\u0000renewable energies, can affect their stability. Power oscillation modes, which\u0000are key to the stability of the grid, are traditionally studied numerically\u0000with the conventional view-point of two regimes of extended (inter-area) or\u0000localized (intra-area) modes. In this article we introduce an analogy based on\u0000stochastic quantum models and demonstrate its applicability to power systems.\u0000We show from simple models that at low frequency the mean free path induced by\u0000disorder is inversely cubic in the frequency. This stems from the\u0000Courant-Fisher-Weyl theorem, which predicts a strong protection of the lowest\u0000frequency modes from disorder. As a consequence a power oscillation, induced by\u0000some local disruption of the grid, can propagate in a ballistic, diffusive or\u0000localised regime. In contrast with the conventional view-point, the existence\u0000of these three regimes is confirmed in a realistic model of the European power\u0000grid.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227454","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}
Martino Salomone Centonze, Alessandro Treves, Elena Agliari, Adriano Barra
Pyramidal cells that emit spikes when the animal is at specific locations of the environment are known as "place cells": these neurons are thought to provide an internal representation of space via "cognitive maps". Here, we consider the Battaglia-Treves neural network model for cognitive map storage and reconstruction, instantiated with McCulloch & Pitts binary neurons. To quantify the information processing capabilities of these networks, we exploit spin-glass techniques based on Guerra's interpolation: in the low-storage regime (i.e., when the number of stored maps scales sub-linearly with the network size and the order parameters self-average around their means) we obtain an exact phase diagram in the noise vs inhibition strength plane (in agreement with previous findings) by adapting the Hamilton-Jacobi PDE-approach. Conversely, in the high-storage regime, we find that -- for mild inhibition and not too high noise -- memorization and retrieval of an extensive number of spatial maps is indeed possible, since the maximal storage capacity is shown to be strictly positive. These results, holding under the replica-symmetry assumption, are obtained by adapting the standard interpolation based on stochastic stability and are further corroborated by Monte Carlo simulations (and replica-trick outcomes for the sake of completeness). Finally, by relying upon an interpretation in terms of hidden units, in the last part of the work, we adapt the Battaglia-Treves model to cope with more general frameworks, such as bats flying in long tunnels.
{"title":"Guerra interpolation for place cells","authors":"Martino Salomone Centonze, Alessandro Treves, Elena Agliari, Adriano Barra","doi":"arxiv-2408.13856","DOIUrl":"https://doi.org/arxiv-2408.13856","url":null,"abstract":"Pyramidal cells that emit spikes when the animal is at specific locations of\u0000the environment are known as \"place cells\": these neurons are thought to\u0000provide an internal representation of space via \"cognitive maps\". Here, we\u0000consider the Battaglia-Treves neural network model for cognitive map storage\u0000and reconstruction, instantiated with McCulloch & Pitts binary neurons. To\u0000quantify the information processing capabilities of these networks, we exploit\u0000spin-glass techniques based on Guerra's interpolation: in the low-storage\u0000regime (i.e., when the number of stored maps scales sub-linearly with the\u0000network size and the order parameters self-average around their means) we\u0000obtain an exact phase diagram in the noise vs inhibition strength plane (in\u0000agreement with previous findings) by adapting the Hamilton-Jacobi PDE-approach.\u0000Conversely, in the high-storage regime, we find that -- for mild inhibition and\u0000not too high noise -- memorization and retrieval of an extensive number of\u0000spatial maps is indeed possible, since the maximal storage capacity is shown to\u0000be strictly positive. These results, holding under the replica-symmetry\u0000assumption, are obtained by adapting the standard interpolation based on\u0000stochastic stability and are further corroborated by Monte Carlo simulations\u0000(and replica-trick outcomes for the sake of completeness). Finally, by relying\u0000upon an interpretation in terms of hidden units, in the last part of the work,\u0000we adapt the Battaglia-Treves model to cope with more general frameworks, such\u0000as bats flying in long tunnels.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220855","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}
An Niza El Aisnadaa, Kajjana Boonpalit Robin van der Kruit, Koen M. Draijer, Jon Lopez-Zorrilla, Masahiro Miyauchi, Akira Yamaguchi, Nongnuch Artrith
Machine learning potentials (MLPs) offer efficient and accurate material simulations, but constructing the reference ab initio database remains a significant challenge, particularly for catalyst-adsorbate systems. Training an MLP with a small dataset can lead to overfitting, thus limiting its practical applications. This study explores the feasibility of developing computationally cost-effective and accurate MLPs for catalyst-adsorbate systems with a limited number of ab initio references by leveraging a transfer learning strategy from subsets of a comprehensive public database. Using the Open Catalyst Project 2020 (OC20) -- a dataset closely related to our system of interest -- we pre-trained MLP models on OC20 subsets using the {ae}net-PyTorch framework. We compared several strategies for database subset selection. Our findings indicate that MLPs constructed via transfer learning exhibit better generalizability than those constructed from scratch, as demonstrated by the consistency in the dynamics simulations. Remarkably, transfer learning enhances the stability and accuracy of MLPs for the CuAu/H2O system with approximately 600 reference data points. This approach achieved excellent extrapolation performance in molecular dynamics (MD) simulations for the larger CuAu/6H2O system, sustaining up to 250 ps, whereas MLPs without transfer learning lasted less than 50 ps. We also examine the potential limitations of this strategy. This work proposes an alternative, cost-effective approach for constructing MLPs for the challenging simulation of catalytic systems. Finally, we anticipate that this methodology will pave the way for broader applications in material science and catalysis research, facilitating more efficient and accurate simulations across various systems.
{"title":"A cost-effective strategy of enhancing machine learning potentials by transfer learning from a multicomponent dataset on ænet-PyTorch","authors":"An Niza El Aisnadaa, Kajjana Boonpalit Robin van der Kruit, Koen M. Draijer, Jon Lopez-Zorrilla, Masahiro Miyauchi, Akira Yamaguchi, Nongnuch Artrith","doi":"arxiv-2408.12939","DOIUrl":"https://doi.org/arxiv-2408.12939","url":null,"abstract":"Machine learning potentials (MLPs) offer efficient and accurate material\u0000simulations, but constructing the reference ab initio database remains a\u0000significant challenge, particularly for catalyst-adsorbate systems. Training an\u0000MLP with a small dataset can lead to overfitting, thus limiting its practical\u0000applications. This study explores the feasibility of developing computationally\u0000cost-effective and accurate MLPs for catalyst-adsorbate systems with a limited\u0000number of ab initio references by leveraging a transfer learning strategy from\u0000subsets of a comprehensive public database. Using the Open Catalyst Project\u00002020 (OC20) -- a dataset closely related to our system of interest -- we\u0000pre-trained MLP models on OC20 subsets using the {ae}net-PyTorch framework. We\u0000compared several strategies for database subset selection. Our findings\u0000indicate that MLPs constructed via transfer learning exhibit better\u0000generalizability than those constructed from scratch, as demonstrated by the\u0000consistency in the dynamics simulations. Remarkably, transfer learning enhances\u0000the stability and accuracy of MLPs for the CuAu/H2O system with approximately\u0000600 reference data points. This approach achieved excellent extrapolation\u0000performance in molecular dynamics (MD) simulations for the larger CuAu/6H2O\u0000system, sustaining up to 250 ps, whereas MLPs without transfer learning lasted\u0000less than 50 ps. We also examine the potential limitations of this strategy.\u0000This work proposes an alternative, cost-effective approach for constructing\u0000MLPs for the challenging simulation of catalytic systems. Finally, we\u0000anticipate that this methodology will pave the way for broader applications in\u0000material science and catalysis research, facilitating more efficient and\u0000accurate simulations across various systems.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220856","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}
Gradient-based meta-learning algorithms have gained popularity for their ability to train models on new tasks using limited data. Empirical observations indicate that such algorithms are able to learn a shared representation across tasks, which is regarded as a key factor in their success. However, the in-depth theoretical understanding of the learning dynamics and the origin of the shared representation remains underdeveloped. In this work, we investigate the meta-learning dynamics of the non-linear two-layer neural networks trained on streaming tasks in the teach-student scenario. Through the lens of statistical physics analysis, we characterize the macroscopic behavior of the meta-training processes, the formation of the shared representation, and the generalization ability of the model on new tasks. The analysis also points to the importance of the choice of certain hyper-parameters of the learning algorithms.
{"title":"Dynamics of Meta-learning Representation in the Teacher-student Scenario","authors":"Hui Wang, Cho Tung Yip, Bo Li","doi":"arxiv-2408.12545","DOIUrl":"https://doi.org/arxiv-2408.12545","url":null,"abstract":"Gradient-based meta-learning algorithms have gained popularity for their\u0000ability to train models on new tasks using limited data. Empirical observations\u0000indicate that such algorithms are able to learn a shared representation across\u0000tasks, which is regarded as a key factor in their success. However, the\u0000in-depth theoretical understanding of the learning dynamics and the origin of\u0000the shared representation remains underdeveloped. In this work, we investigate\u0000the meta-learning dynamics of the non-linear two-layer neural networks trained\u0000on streaming tasks in the teach-student scenario. Through the lens of\u0000statistical physics analysis, we characterize the macroscopic behavior of the\u0000meta-training processes, the formation of the shared representation, and the\u0000generalization ability of the model on new tasks. The analysis also points to\u0000the importance of the choice of certain hyper-parameters of the learning\u0000algorithms.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate the dynamics of non-interacting particles in a one-dimensional tight-binding chain in the presence of an electric field with random amplitude drawn from a Gaussian distribution, and explicitly focus on the nature of quantum transport. We derive an exact expression for the probability propagator and the mean-squared displacement in the clean limit and generalize it for the disordered case using the Liouville operator method. Our analysis reveals that in the presence a random static field, the system follows diffusive transport; however, an increase in the field strength causes a suppression in the transport and thus results in disorder-induced localization. We further extend the analysis for a time-dependent disordered electric field and show that the dynamics of mean-squared-displacement deviates from the parabolic path as the field strength increases, unlike the clean limit where ballistic transport occurs.
{"title":"Quantum transport under oscillatory drive with disordered amplitude","authors":"Vatsana Tiwari, Sushanta Dattagupta, Devendra Singh Bhakuni, Auditya Sharma","doi":"arxiv-2408.12653","DOIUrl":"https://doi.org/arxiv-2408.12653","url":null,"abstract":"We investigate the dynamics of non-interacting particles in a one-dimensional\u0000tight-binding chain in the presence of an electric field with random amplitude\u0000drawn from a Gaussian distribution, and explicitly focus on the nature of\u0000quantum transport. We derive an exact expression for the probability propagator\u0000and the mean-squared displacement in the clean limit and generalize it for the\u0000disordered case using the Liouville operator method. Our analysis reveals that\u0000in the presence a random static field, the system follows diffusive transport;\u0000however, an increase in the field strength causes a suppression in the\u0000transport and thus results in disorder-induced localization. We further extend\u0000the analysis for a time-dependent disordered electric field and show that the\u0000dynamics of mean-squared-displacement deviates from the parabolic path as the\u0000field strength increases, unlike the clean limit where ballistic transport\u0000occurs.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220858","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 study elastic electron scattering and localization by ubiquitous isotopic disorder in one-dimensional systems appearing due to interaction with phonon modes localized at isotope impurities. By using a tight-binding model with intersite hopping matrix element dependent on the interatomic distance, we find mass-dependent backscattering probability by single and pairs of isotopic impurities. For the pairs, in addition to the mass, the distance between the isotopes plays the critical role. Single impurities effectively attract electrons and can produce localized weakly bound electron states. In the presence of disorder, the electron free path at positive energies becomes finite and the corresponding Anderson localization at the spatial scale greatly exceeding the distance between the impurities becomes possible.
{"title":"Elastic electron scattering and localization in a chain with isotopic disorder","authors":"K. S. Denisov, E. Ya. Sherman","doi":"arxiv-2408.10909","DOIUrl":"https://doi.org/arxiv-2408.10909","url":null,"abstract":"We study elastic electron scattering and localization by ubiquitous isotopic\u0000disorder in one-dimensional systems appearing due to interaction with phonon\u0000modes localized at isotope impurities. By using a tight-binding model with\u0000intersite hopping matrix element dependent on the interatomic distance, we find\u0000mass-dependent backscattering probability by single and pairs of isotopic\u0000impurities. For the pairs, in addition to the mass, the distance between the\u0000isotopes plays the critical role. Single impurities effectively attract\u0000electrons and can produce localized weakly bound electron states. In the\u0000presence of disorder, the electron free path at positive energies becomes\u0000finite and the corresponding Anderson localization at the spatial scale greatly\u0000exceeding the distance between the impurities becomes possible.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220867","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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