Pub Date : 2024-09-02DOI: 10.1088/1751-8121/ad72ba
Kenta Shiina, Hiroyuki Mori, Yutaka Okabe, Hwee Kuan Lee
We present a super-resolution method for spin systems using a flow-based generative model that is a deep generative model with reversible neural network architecture. Starting from spin configurations on a two-dimensional square lattice, our model generates spin configurations of a larger lattice. As a flow-based generative model precisely estimates the distribution of the generated configurations, it can be combined with Monte Carlo simulation to generate large lattice configurations according to the Boltzmann distribution. Hence, the long-range correlation on a large configuration is reduced into the shorter one through the flow-based generative model. This alleviates the critical slowing down near the critical temperature. We demonstrated an 8 times increased lattice size in the linear dimensions using our super-resolution scheme repeatedly. We numerically show that by performing simulations for 16×16 configurations, our model can sample lattice configurations at 128×128 on which the thermal average of physical quantities has good agreement with the one evaluated by the traditional Metropolis–Hasting Monte Carlo simulation.
{"title":"Super-resolution of spin configurations based on flow-based generative models","authors":"Kenta Shiina, Hiroyuki Mori, Yutaka Okabe, Hwee Kuan Lee","doi":"10.1088/1751-8121/ad72ba","DOIUrl":"https://doi.org/10.1088/1751-8121/ad72ba","url":null,"abstract":"We present a super-resolution method for spin systems using a flow-based generative model that is a deep generative model with reversible neural network architecture. Starting from spin configurations on a two-dimensional square lattice, our model generates spin configurations of a larger lattice. As a flow-based generative model precisely estimates the distribution of the generated configurations, it can be combined with Monte Carlo simulation to generate large lattice configurations according to the Boltzmann distribution. Hence, the long-range correlation on a large configuration is reduced into the shorter one through the flow-based generative model. This alleviates the critical slowing down near the critical temperature. We demonstrated an 8 times increased lattice size in the linear dimensions using our super-resolution scheme repeatedly. We numerically show that by performing simulations for <inline-formula>\u0000<tex-math><?CDATA $16times 16$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mn>16</mml:mn><mml:mo>×</mml:mo><mml:mn>16</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"aad72baieqn1.gif\"></inline-graphic></inline-formula> configurations, our model can sample lattice configurations at <inline-formula>\u0000<tex-math><?CDATA $128times 128$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mn>128</mml:mn><mml:mo>×</mml:mo><mml:mn>128</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"aad72baieqn2.gif\"></inline-graphic></inline-formula> on which the thermal average of physical quantities has good agreement with the one evaluated by the traditional Metropolis–Hasting Monte Carlo simulation.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"6 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-30DOI: 10.1088/1751-8121/ad6c01
Nicholas R Beaton, Kai Ishihara, Mahshid Atapour, Jeremy W Eng, Mariel Vazquez, Koya Shimokawa, Christine E Soteros
Based on polymer scaling theory and numerical evidence, Orlandini, Tesi, Janse van Rensburg and Whittington conjectured in 1996 that the limiting entropy of knot-type K lattice polygons is the same as that for unknot polygons, and that the entropic critical exponent increases by one for each prime knot in the knot decomposition of K. This Knot Entropy (KE) conjecture is consistent with the idea that for unconfined polymers, knots occur in a localized way (the knotted part is relatively small compared to polymer length). For full confinement (to a sphere or box), numerical evidence suggests that knots are much less localized. Numerical evidence for nanochannel or tube confinement is mixed, depending on how the size of a knot is measured. Here we outline the proof that the KE conjecture holds for polygons in the ∞×2×1 lattice tube and show that knotting is localized when a connected-sum measure of knot size is used. Similar results are established for linked polygons. This is the first model for which the knot entropy conjecture has been proved.
基于聚合物缩放理论和数值证据，Orlandini、Tesi、Janse van Rensburg 和 Whittington 于 1996 年猜想，结型 K 网格多边形的极限熵与无结多边形的极限熵相同，K 的结分解中每增加一个质结，熵临界指数就增加一个。这一 "结熵（KE）"猜想与以下观点一致：对于非封闭聚合物，结是以局部方式出现的（与聚合物长度相比，结的部分相对较小）。对于完全封闭（球形或箱形），数值证据表明，结的局部性要小得多。对于纳米通道或管状约束，数值证据则喜忧参半，这取决于如何测量结的大小。在此，我们概述了 KE 猜想在 ∞×2×1 网格管中的多边形中成立的证明，并表明当使用结大小的连接和测量时，结是局部的。类似的结果也适用于连接多边形。这是第一个证明结熵猜想的模型。
{"title":"A first proof of knot localization for polymers in a nanochannel","authors":"Nicholas R Beaton, Kai Ishihara, Mahshid Atapour, Jeremy W Eng, Mariel Vazquez, Koya Shimokawa, Christine E Soteros","doi":"10.1088/1751-8121/ad6c01","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6c01","url":null,"abstract":"Based on polymer scaling theory and numerical evidence, Orlandini, Tesi, Janse van Rensburg and Whittington conjectured in 1996 that the limiting entropy of knot-type <italic toggle=\"yes\">K</italic> lattice polygons is the same as that for unknot polygons, and that the entropic critical exponent increases by one for each prime knot in the knot decomposition of <italic toggle=\"yes\">K</italic>. This Knot Entropy (KE) conjecture is consistent with the idea that for unconfined polymers, knots occur in a localized way (the knotted part is relatively small compared to polymer length). For full confinement (to a sphere or box), numerical evidence suggests that knots are much less localized. Numerical evidence for nanochannel or tube confinement is mixed, depending on how the size of a knot is measured. Here we outline the proof that the KE conjecture holds for polygons in the <inline-formula>\u0000<tex-math><?CDATA $inftytimes2times1$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi mathvariant=\"normal\">∞</mml:mi><mml:mo>×</mml:mo><mml:mn>2</mml:mn><mml:mo>×</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"aad6c01ieqn1.gif\"></inline-graphic></inline-formula> lattice tube and show that knotting is localized when a connected-sum measure of knot size is used. Similar results are established for linked polygons. This is the first model for which the knot entropy conjecture has been proved.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"242 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-29DOI: 10.1088/1751-8121/ad7077
Ryo Takakura
In this study, we consider generalized probabilistic theories (GPTs) and focus on a class of theories called regular polygon theories, which can be regarded as natural generalizations of a two-level quantum system (a qubit system). In the usual CHSH setting for quantum theory, the CHSH value is known to be optimized by maximally entangled states. This research will reveal that the same observations are obtained also in regular polygon theories. Our result gives a physical meaning to the concept of ‘maximal entanglement’ in regular polygon theories.
{"title":"Optimal CHSH values for regular polygon theories in generalized probabilistic theories","authors":"Ryo Takakura","doi":"10.1088/1751-8121/ad7077","DOIUrl":"https://doi.org/10.1088/1751-8121/ad7077","url":null,"abstract":"In this study, we consider generalized probabilistic theories (GPTs) and focus on a class of theories called regular polygon theories, which can be regarded as natural generalizations of a two-level quantum system (a qubit system). In the usual CHSH setting for quantum theory, the CHSH value is known to be optimized by maximally entangled states. This research will reveal that the same observations are obtained also in regular polygon theories. Our result gives a physical meaning to the concept of ‘maximal entanglement’ in regular polygon theories.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"25 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-29DOI: 10.1088/1751-8121/ad6f7c
Sven Gnutzmann, Uzy Smilansky
Given an arbitrary V × V Hermitian matrix H, considered as a finite discrete quantum Hamiltonian, we use methods from graph and ergodic theories to construct a quantum Poincaré map at energy E and a corresponding stochastic classical Poincaré–Markov map at the same energy on an appropriate discrete phase space. This phase space D consists of the directed edges of a graph with V vertices that are in one-to-one correspondence with the non-vanishing off-diagonal elements of H. The correspondence between quantum Poincaré map and classical Poincaré–Markov map is an alternative to the standard quantum–classical correspondence based on a classical limit ℏ→0. Most importantly it can be constructed where no such limit exists. Using standard methods from ergodic theory we then proceed to derive an expression for the Lyapunov exponentΛ(E) of the classical map. It measures the rate of loss of classical information in the dynamics and relates it to the separation of stochastic classical trajectories in the phase space. We suggest that loss of information in the underlying classical dynamics is an indicator for quantum information scrambling.
给定一个任意的 V × V 赫米矩阵 H，将其视为有限离散量子哈密顿，我们利用图论和遍历理论的方法，在适当的离散相空间上构建能量 E 的量子波卡列图和相同能量的相应随机经典波卡列-马尔科夫图。这个相空间 D 由一个有 V 个顶点的图的有向边组成，这些顶点与 H 的非消失对角元素一一对应。量子波因卡雷图与经典波因卡雷-马尔科夫图之间的对应关系是基于经典极限ℏ→0 的标准量子-经典对应关系的另一种选择。最重要的是，它可以在不存在这种极限的地方构建。利用遍历理论的标准方法，我们可以推导出经典映射的莱普诺夫指数Λ(E) 的表达式。它衡量了动力学中经典信息的损失率，并将其与相空间中随机经典轨迹的分离联系起来。我们认为，底层经典动力学中的信息损失是量子信息扰乱的一个指标。
{"title":"Information scrambling and chaos induced by a Hermitian matrix","authors":"Sven Gnutzmann, Uzy Smilansky","doi":"10.1088/1751-8121/ad6f7c","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6f7c","url":null,"abstract":"Given an arbitrary <italic toggle=\"yes\">V</italic> × <italic toggle=\"yes\">V</italic> Hermitian matrix <italic toggle=\"yes\">H</italic>, considered as a finite discrete quantum Hamiltonian, we use methods from graph and ergodic theories to construct a <italic toggle=\"yes\">quantum Poincaré map</italic> at energy <italic toggle=\"yes\">E</italic> and a corresponding stochastic <italic toggle=\"yes\">classical Poincaré–Markov map</italic> at the same energy on an appropriate discrete <italic toggle=\"yes\">phase space</italic>. This phase space <inline-formula>\u0000<tex-math><?CDATA $mathcal{D}$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:mrow></mml:math><inline-graphic xlink:href=\"aad6f7cieqn1.gif\"></inline-graphic></inline-formula> consists of the directed edges of a graph with <italic toggle=\"yes\">V</italic> vertices that are in one-to-one correspondence with the non-vanishing off-diagonal elements of <italic toggle=\"yes\">H</italic>. The correspondence between quantum Poincaré map and classical Poincaré–Markov map is an alternative to the standard quantum–classical correspondence based on a classical limit <inline-formula>\u0000<tex-math><?CDATA $hbar to 0$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>ℏ</mml:mi><mml:mo accent=\"false\" stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"aad6f7cieqn2.gif\"></inline-graphic></inline-formula>. Most importantly it can be constructed where no such limit exists. Using standard methods from ergodic theory we then proceed to derive an expression for the <italic toggle=\"yes\">Lyapunov exponent</italic> <inline-formula>\u0000<tex-math><?CDATA $Lambda(E)$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi mathvariant=\"normal\">Λ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"aad6f7cieqn3.gif\"></inline-graphic></inline-formula> of the classical map. It measures the rate of loss of classical information in the dynamics and relates it to the separation of stochastic <italic toggle=\"yes\">classical trajectories</italic> in the phase space. We suggest that loss of information in the underlying classical dynamics is an indicator for quantum information scrambling.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"74 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-29DOI: 10.1088/1751-8121/ad707f
C J Bradly, E J Janse van Rensburg
Polymers in confined spaces are compressed and have reduced conformational entropy, and will partially or fully escape from confinement if conditions are suitable. This is in particular the case for a polymer grafted in a pore. The escape of the polymer from the pore may be considered a partial translocation from the pore into bulk solution, and the resulting conformational readjustment of the polymer has characteristics of a thermodynamic phase transition. In this paper a lattice self-avoiding walk model of a star polymer grafted in a pore is examined numerically using the PERM algorithm. We show that the arms of the grafted lattice star escape one at a time as the length of the pore is reduced, consistent with earlier results in the literature. Critical points for the escape transitions are estimated for square and cubic lattice models and we also examine various properties of the model as it undergoes the escape transition.
{"title":"The escape transition of a lattice star polymer grafted in a pore","authors":"C J Bradly, E J Janse van Rensburg","doi":"10.1088/1751-8121/ad707f","DOIUrl":"https://doi.org/10.1088/1751-8121/ad707f","url":null,"abstract":"Polymers in confined spaces are compressed and have reduced conformational entropy, and will partially or fully escape from confinement if conditions are suitable. This is in particular the case for a polymer grafted in a pore. The escape of the polymer from the pore may be considered a partial translocation from the pore into bulk solution, and the resulting conformational readjustment of the polymer has characteristics of a thermodynamic phase transition. In this paper a lattice self-avoiding walk model of a star polymer grafted in a pore is examined numerically using the PERM algorithm. We show that the arms of the grafted lattice star escape one at a time as the length of the pore is reduced, consistent with earlier results in the literature. Critical points for the escape transitions are estimated for square and cubic lattice models and we also examine various properties of the model as it undergoes the escape transition.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"42 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Trapped-ion has shown great advantages in building quantum computers. While high fidelity entangling-gate has been realized for a few ions, how to maintain the high fidelity for large scale trapped-ions remains an open problem. Here, we present an analysis of arbitrary scale ion chains and focus on motional-related errors, reported as one of the leading error sources in state-of-the-art experiments. We theoretically analyze two-qubit entangling-gate infidelity in a large ion crystal under the phase insensitive configuration. To verify our result, we develop an efficient numerical simulation algorithm that avoids exponential increases in of the Hilbert space dimension. For the motional heating error, we derive a much tighter bound of gate infidelity than previously estimated O(NΓτ), and we give an intuitive understanding from the trajectories in the phase space of motional modes. Our discoveries may inspire the scheme of pulse design against incoherent errors and shed light on the way toward constructing scalable quantum computers with large ion crystals.
{"title":"Scaling of entangling-gate errors in large ion crystals","authors":"Wenhao He, Wenhao Zhang, Xiao Yuan, Yangchao Shen, Xiao-Ming Zhang","doi":"10.1088/1751-8121/ad6ab5","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6ab5","url":null,"abstract":"Trapped-ion has shown great advantages in building quantum computers. While high fidelity entangling-gate has been realized for a few ions, how to maintain the high fidelity for large scale trapped-ions remains an open problem. Here, we present an analysis of arbitrary scale ion chains and focus on motional-related errors, reported as one of the leading error sources in state-of-the-art experiments. We theoretically analyze two-qubit entangling-gate infidelity in a large ion crystal under the phase insensitive configuration. To verify our result, we develop an efficient numerical simulation algorithm that avoids exponential increases in of the Hilbert space dimension. For the motional heating error, we derive a much tighter bound of gate infidelity than previously estimated <inline-formula>\u0000<tex-math><?CDATA $O(NGammatau)$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>O</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>N</mml:mi><mml:mi mathvariant=\"normal\">Γ</mml:mi><mml:mi>τ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"aad6ab5ieqn1.gif\"></inline-graphic></inline-formula>, and we give an intuitive understanding from the trajectories in the phase space of motional modes. Our discoveries may inspire the scheme of pulse design against incoherent errors and shed light on the way toward constructing scalable quantum computers with large ion crystals.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"24 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The study of decoherence plays a key role in our understanding of the transition from the quantum to the classical world. Typically, one considers a system coupled to an external bath which forms a model for an open quantum system. While most of the studies pertain to a position coupling between the system and the environment, some involve a momentum coupling, giving rise to an anomalous diffusive model. Here we have gone beyond existing studies and analyzed the non-Markovian master equation, involving the quantum Langevin dynamics of a harmonically oscillating charged Brownian particle in the presence of a magnetic field and coupled to Ohmic (s = 1), sub-Ohmic (s < 1) and super-Ohmic (s > 1) heat baths via both position and momentum couplings. The presence of both position and momentum couplings leads to a stronger interaction with the environment, resulting in a faster loss of coherence compared to a situation where only position coupling is present. The rate of decoherence can be tuned by controlling the relative strengths of the position and momentum coupling parameters. In addition, the magnetic field results in the slowing down of the loss of information from the system, irrespective of the nature of coupling between the system and the bath. A faster decoherence rate is observed for higher values of the Ohmicity parameter ‘s’. Our results can be experimentally verified by designing a suitable ion trap setup.
{"title":"Decoherence of a charged Brownian particle in a magnetic field: an analysis of the roles of coupling via position and momentum variables","authors":"Suraka Bhattacharjee, Koushik Mandal, Supurna Sinha","doi":"10.1088/1751-8121/ad707e","DOIUrl":"https://doi.org/10.1088/1751-8121/ad707e","url":null,"abstract":"The study of decoherence plays a key role in our understanding of the transition from the quantum to the classical world. Typically, one considers a system coupled to an external bath which forms a model for an open quantum system. While most of the studies pertain to a position coupling between the system and the environment, some involve a momentum coupling, giving rise to an anomalous diffusive model. Here we have gone beyond existing studies and analyzed the non-Markovian master equation, involving the quantum Langevin dynamics of a harmonically oscillating charged Brownian particle in the presence of a magnetic field and coupled to Ohmic (<italic toggle=\"yes\">s</italic> = 1), sub-Ohmic (<italic toggle=\"yes\">s</italic> < 1) and super-Ohmic (<italic toggle=\"yes\">s</italic> > 1) heat baths via both position and momentum couplings. The presence of both position and momentum couplings leads to a stronger interaction with the environment, resulting in a faster loss of coherence compared to a situation where only position coupling is present. The rate of decoherence can be tuned by controlling the relative strengths of the position and momentum coupling parameters. In addition, the magnetic field results in the slowing down of the loss of information from the system, irrespective of the nature of coupling between the system and the bath. A faster decoherence rate is observed for higher values of the Ohmicity parameter ‘<italic toggle=\"yes\">s</italic>’. Our results can be experimentally verified by designing a suitable ion trap setup.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"57 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1088/1751-8121/ad6ab4
Laura Guislain, Eric Bertin
We study the effect of introducing separable quenched disorder on a non-equilibrium mean-field spin model exhibiting a phase transition to an oscillating state in the absence of disorder, due to non-reciprocal interactions. In the disordered model, the magnetisation and its time derivative no longer carry the signature of the phase transition to an oscillating state. However, thanks to the separable (Mattis-type) form of the disorder, the presence of oscillations can be revealed by introducing a specific, disorder-dependent observable. We also introduce generalised linear and non-linear susceptibilities associated either with the magnetisation or with its time derivative. While linear susceptibilities show no sign of a phase transition, the third-order susceptibilities present a clear signature of the onset of an oscillating phase. In addition, we show that the overlap distribution also provides evidence for the presence of oscillations, without explicit knowledge of the disorder.
{"title":"Hidden collective oscillations in a disordered mean-field spin model with non-reciprocal interactions","authors":"Laura Guislain, Eric Bertin","doi":"10.1088/1751-8121/ad6ab4","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6ab4","url":null,"abstract":"We study the effect of introducing separable quenched disorder on a non-equilibrium mean-field spin model exhibiting a phase transition to an oscillating state in the absence of disorder, due to non-reciprocal interactions. In the disordered model, the magnetisation and its time derivative no longer carry the signature of the phase transition to an oscillating state. However, thanks to the separable (Mattis-type) form of the disorder, the presence of oscillations can be revealed by introducing a specific, disorder-dependent observable. We also introduce generalised linear and non-linear susceptibilities associated either with the magnetisation or with its time derivative. While linear susceptibilities show no sign of a phase transition, the third-order susceptibilities present a clear signature of the onset of an oscillating phase. In addition, we show that the overlap distribution also provides evidence for the presence of oscillations, without explicit knowledge of the disorder.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"7 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1088/1751-8121/ad7108
Prabuddha Roy, A K Pan
The parity-oblivious random-access-code (PORAC) is a class of communication games involving a sender (Alice) and a receiver (Bob). In such games, Alice’s amount of communication to Bob is constraint by the parity-oblivious (PO) conditions, so that the parity information of her inputs remains oblivious to Bob. The PO condition in an operational theory is equivalently represented in an ontological model that satisfies the preparation noncontextuality. In this paper, we provide a nontrivial generalization of the existing two-level PORAC and derive the winning probability of the game in the preparation noncontextual ontological model. We demonstrate that the quantum theory outperforms the preparation noncontextual model by predicting higher winning probability in our generalized PORAC.
{"title":"Generalized parity-oblivious communication games powered by quantum preparation contextuality","authors":"Prabuddha Roy, A K Pan","doi":"10.1088/1751-8121/ad7108","DOIUrl":"https://doi.org/10.1088/1751-8121/ad7108","url":null,"abstract":"The parity-oblivious random-access-code (PORAC) is a class of communication games involving a sender (Alice) and a receiver (Bob). In such games, Alice’s amount of communication to Bob is constraint by the parity-oblivious (PO) conditions, so that the parity information of her inputs remains oblivious to Bob. The PO condition in an operational theory is equivalently represented in an ontological model that satisfies the preparation noncontextuality. In this paper, we provide a nontrivial generalization of the existing two-level PORAC and derive the winning probability of the game in the preparation noncontextual ontological model. We demonstrate that the quantum theory outperforms the preparation noncontextual model by predicting higher winning probability in our generalized PORAC.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"5 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-27DOI: 10.1088/1751-8121/ad6f81
Suvendu Barik, Alexander S Garkun, Vladimir Gritsev
We explore the algebraic structure of a particular ansatz of the Yang-Baxter equation (YBE), which is inspired by the Bethe Ansatz treatment of the asymmetric simple exclusion process spin-model. Various classes of Hamiltonian density arriving from the two types of R-matrices are found, which also appear as solutions of the constant YBE. We identify the idempotent and nilpotent categories of such constant R-matrices and perform a rank-1 numerical search for the lowest dimension. A summary of the final results reveals general non-Hermitian spin-1/2 chain models.
我们探索了杨-巴克斯特方程（Yang-Baxter equation，YBE）的一种特殊解析的代数结构，这种解析受到非对称简单排除过程自旋模型的贝特解析处理的启发。我们发现了从两类 R 矩得出的各类哈密顿密度，它们也作为恒定 YBE 的解出现。我们确定了这类恒定 R 矩的幂等和零等类别，并对最低维度进行了秩-1 数值搜索。对最终结果的总结揭示了一般的非赫米提自旋-1/2 链模型。
{"title":"Novel ASEP-inspired solutions of the Yang-Baxter equation","authors":"Suvendu Barik, Alexander S Garkun, Vladimir Gritsev","doi":"10.1088/1751-8121/ad6f81","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6f81","url":null,"abstract":"We explore the algebraic structure of a particular ansatz of the Yang-Baxter equation (YBE), which is inspired by the Bethe Ansatz treatment of the asymmetric simple exclusion process spin-model. Various classes of Hamiltonian density arriving from the two types of R-matrices are found, which also appear as solutions of the constant YBE. We identify the idempotent and nilpotent categories of such constant R-matrices and perform a rank-1 numerical search for the lowest dimension. A summary of the final results reveals general non-Hermitian spin-1/2 chain models.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"6 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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