Pub Date : 2024-09-11DOI: 10.1088/1751-8121/ad7212
D B Milošević, A S Jašarević, D Habibović, E Hasović, A Čerkić and W Becker
The quantum-mechanical transition amplitudes for atomic and molecular processes in strong laser fields are expressed in the form of multidimensional integrals of highly oscillatory functions. Such integrals are ideally suited for the evaluation by asymptotic methods for integrals. Furthermore, using these methods it is possible to identify, in the sense of Feynman’s path-integral formalism, the partial contributions of quantum orbits, which are related to particular solutions of the saddle-point equations. This affords insight into the physics of the problem, which would not have been possible by only solving these integrals numerically. We apply the saddle-point method to various quantum processes that are important in strong-field physics and attoscience. The special case of coalescing or near-coalescing saddle points requires application of the uniform approximation. We also present two modifications of the saddle-point method, for the cases where a singular point of the subintegral function exactly overlaps with a saddle point or is located in its close vicinity. Particular emphasis is on the classification of the saddle-point solutions. This problem is solved for the one-dimensional integral over the ionization time, relevant for above-threshold ionization (ATI), while for two-dimensional integrals a classification by the multi-index is introduced, which is particularly useful for the medium- and high-energy spectrum of high-order harmonic generation (HHG) and backward-scattered electrons (for high-order ATI). For the low-energy structures a classification using the multi-index is introduced for the forward-scattering quantum orbits. In addition to laser-induced processes such as ATI, HHG and high-order ATI, we consider laser-assisted scattering as an example of laser-assisted processes for which real solutions of the saddle-point equation exist. Particular attention is devoted to the quantum orbits that describe and visualize these processes. We also consider finite laser pulses, the semiclassical approximation, the role of the Coulomb field and the case of laser fields intense enough to lead into the relativistic regime.
原子和分子过程在强激光场中的量子力学转变幅度是以高度振荡函数的多维积分形式表示的。这种积分非常适合用渐近积分法进行评估。此外，利用这些方法还可以从费曼路径积分形式主义的意义上识别量子轨道的部分贡献，这些贡献与鞍点方程的特定解有关。这有助于深入了解问题的物理原理，而仅仅通过数值求解这些积分是无法做到这一点的。我们将鞍点方法应用于强场物理学和原子科学中重要的各种量子过程。凝聚或接近凝聚鞍点的特殊情况需要应用均匀近似。我们还介绍了鞍点法的两种修正方法，适用于子积分函数奇异点与鞍点完全重叠或位于其附近的情况。重点是鞍点解的分类。对于电离时间的一维积分，这个问题得到了解决，这与阈值以上电离（ATI）有关；而对于二维积分，则引入了多指数分类法，这对于高阶谐波发生（HHG）和后向散射电子（高阶 ATI）的中高能谱特别有用。对于低能结构，则采用多指数对前向散射量子轨道进行分类。除了 ATI、HHG 和高阶 ATI 等激光诱导过程之外，我们还将激光辅助散射作为激光辅助过程的一个例子进行了考虑，对于这些过程，鞍点方程的实解是存在的。我们特别关注描述这些过程的量子轨道，并将其可视化。我们还考虑了有限激光脉冲、半经典近似、库仑场的作用以及激光场强度足以导致进入相对论机制的情况。
{"title":"Asymptotic methods applied to integrals occurring in strong-laser-field processes","authors":"D B Milošević, A S Jašarević, D Habibović, E Hasović, A Čerkić and W Becker","doi":"10.1088/1751-8121/ad7212","DOIUrl":"https://doi.org/10.1088/1751-8121/ad7212","url":null,"abstract":"The quantum-mechanical transition amplitudes for atomic and molecular processes in strong laser fields are expressed in the form of multidimensional integrals of highly oscillatory functions. Such integrals are ideally suited for the evaluation by asymptotic methods for integrals. Furthermore, using these methods it is possible to identify, in the sense of Feynman’s path-integral formalism, the partial contributions of quantum orbits, which are related to particular solutions of the saddle-point equations. This affords insight into the physics of the problem, which would not have been possible by only solving these integrals numerically. We apply the saddle-point method to various quantum processes that are important in strong-field physics and attoscience. The special case of coalescing or near-coalescing saddle points requires application of the uniform approximation. We also present two modifications of the saddle-point method, for the cases where a singular point of the subintegral function exactly overlaps with a saddle point or is located in its close vicinity. Particular emphasis is on the classification of the saddle-point solutions. This problem is solved for the one-dimensional integral over the ionization time, relevant for above-threshold ionization (ATI), while for two-dimensional integrals a classification by the multi-index is introduced, which is particularly useful for the medium- and high-energy spectrum of high-order harmonic generation (HHG) and backward-scattered electrons (for high-order ATI). For the low-energy structures a classification using the multi-index is introduced for the forward-scattering quantum orbits. In addition to laser-induced processes such as ATI, HHG and high-order ATI, we consider laser-assisted scattering as an example of laser-assisted processes for which real solutions of the saddle-point equation exist. Particular attention is devoted to the quantum orbits that describe and visualize these processes. We also consider finite laser pulses, the semiclassical approximation, the role of the Coulomb field and the case of laser fields intense enough to lead into the relativistic regime.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"1960 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185945","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 : 2024-09-11DOI: 10.1088/1751-8121/ad7710
Lingxuan Feng and Shunlong Luo
Stabilizer states serve as ‘classical objects’ in the stabilizer formalism of quantum theory, and play an important role in quantum error correction, fault-tolerant quantum computation, and quantum communication. They provide an efficient description of many basic features of quantum theory and exhibit a rich structure. For prime dimensional systems, they may be defined by two quite different yet equivalent ways: The first is via stabilizer groups (maximal Abelian subgroups of the discrete Heisenberg–Weyl group). The second is via the orbits of the Clifford group acting on any computational basis state. However, in a general dimensional system, this equivalence breaks down, and consequently, it is desirable to clarify the difference and relation between the above two approaches to stabilizer states. In this work, we show that these two approaches are equivalent if and only if the system dimension is square-free (i.e. has no square factor). Furthermore, we completely reveal the relation between the Clifford orbits and stabilizer states in an arbitrary dimensional system, derive the explicit expressions of the Clifford orbits and determine their cardinalities.
{"title":"Clifford orbits and stabilizer states","authors":"Lingxuan Feng and Shunlong Luo","doi":"10.1088/1751-8121/ad7710","DOIUrl":"https://doi.org/10.1088/1751-8121/ad7710","url":null,"abstract":"Stabilizer states serve as ‘classical objects’ in the stabilizer formalism of quantum theory, and play an important role in quantum error correction, fault-tolerant quantum computation, and quantum communication. They provide an efficient description of many basic features of quantum theory and exhibit a rich structure. For prime dimensional systems, they may be defined by two quite different yet equivalent ways: The first is via stabilizer groups (maximal Abelian subgroups of the discrete Heisenberg–Weyl group). The second is via the orbits of the Clifford group acting on any computational basis state. However, in a general dimensional system, this equivalence breaks down, and consequently, it is desirable to clarify the difference and relation between the above two approaches to stabilizer states. In this work, we show that these two approaches are equivalent if and only if the system dimension is square-free (i.e. has no square factor). Furthermore, we completely reveal the relation between the Clifford orbits and stabilizer states in an arbitrary dimensional system, derive the explicit expressions of the Clifford orbits and determine their cardinalities.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185972","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 : 2024-09-11DOI: 10.1088/1751-8121/ad74bb
Yundu Zhao, Shan Huang and Shengjun Wu
Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information theory. In this article, we investigate entropic uncertainty relations and entanglement detection with an emphasis on quantum measurements with design structures. On the one hand, we derive improved Rényi entropic uncertainty relations for design-structured measurements, exploiting the property that the sum of powered (e.g. squared) probabilities of obtaining different measurement outcomes is now invariant under unitary transformations of the measured system and can be easily computed. On the other hand, the above property essentially imposes a state-independent upper bound, which is achieved at all pure states, on one’s ability to predict local outcomes when performing a set of design-structured measurements on quantum systems. Realizing this, we also obtain criteria for detecting multipartite entanglement with design-structured measurements.
{"title":"Entropic uncertainty relations and entanglement detection from quantum designs","authors":"Yundu Zhao, Shan Huang and Shengjun Wu","doi":"10.1088/1751-8121/ad74bb","DOIUrl":"https://doi.org/10.1088/1751-8121/ad74bb","url":null,"abstract":"Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information theory. In this article, we investigate entropic uncertainty relations and entanglement detection with an emphasis on quantum measurements with design structures. On the one hand, we derive improved Rényi entropic uncertainty relations for design-structured measurements, exploiting the property that the sum of powered (e.g. squared) probabilities of obtaining different measurement outcomes is now invariant under unitary transformations of the measured system and can be easily computed. On the other hand, the above property essentially imposes a state-independent upper bound, which is achieved at all pure states, on one’s ability to predict local outcomes when performing a set of design-structured measurements on quantum systems. Realizing this, we also obtain criteria for detecting multipartite entanglement with design-structured measurements.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"25 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185946","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 : 2024-09-10DOI: 10.1088/1751-8121/ad72bd
Dagne Wordofa Tola and Mulugeta Bekele
The study of nonequilibrium steady-state (NESS) in the Ising model offers rich insights into the properties of complex systems far from equilibrium. This paper explores the nature of NESS phase transitions (PTs) in a two-dimensional (2D) ferromagnetic Ising model on a square lattice under effective interactions using Monte Carlo (MC) algorithms. It requires extensive MC simulations using the modified Metropolis and Glauber update rules. Using an appropriate definition of an effective parameter h helps to qualify the modified update rules. For , the analytical solution shows that the nature of the PT (including the critical temperature) is independent of h. Furthermore, for , we study the steady-state properties of PTs using numerical methods. Therefore, we performed simulations for different lattice sizes and measured relevant physical quantities. From the data, we determined the numerical results of the transition temperature and relevant critical exponents for various values of h by applying finite-size scaling (FSS). We found that the FSS analysis of the exponents is consistent with the analytical values of the equilibrium 2D Ising model.
伊辛模型中的非平衡稳态（NESS）研究为了解远离平衡的复杂系统的特性提供了丰富的见解。本文利用蒙特卡罗（Monte Carlo，MC）算法，探索了有效相互作用下方形晶格上的二维（2D）铁磁伊辛模型中的非平衡稳态相变（PTs）的性质。它需要使用修改后的 Metropolis 和 Glauber 更新规则进行大量 MC 模拟。使用有效参数 h 的适当定义有助于修正更新规则。此外，对于Ⅳ，我们使用数值方法研究了Ⅳ的稳态特性。因此，我们对不同晶格尺寸进行了模拟，并测量了相关物理量。根据这些数据，我们采用有限尺寸缩放（FSS）方法确定了不同 h 值的转变温度和相关临界指数的数值结果。我们发现，指数的 FSS 分析与平衡二维伊辛模型的分析值一致。
{"title":"Nonequilibrium phase transitions in a 2D ferromagnetic spins with effective interactions","authors":"Dagne Wordofa Tola and Mulugeta Bekele","doi":"10.1088/1751-8121/ad72bd","DOIUrl":"https://doi.org/10.1088/1751-8121/ad72bd","url":null,"abstract":"The study of nonequilibrium steady-state (NESS) in the Ising model offers rich insights into the properties of complex systems far from equilibrium. This paper explores the nature of NESS phase transitions (PTs) in a two-dimensional (2D) ferromagnetic Ising model on a square lattice under effective interactions using Monte Carlo (MC) algorithms. It requires extensive MC simulations using the modified Metropolis and Glauber update rules. Using an appropriate definition of an effective parameter h helps to qualify the modified update rules. For , the analytical solution shows that the nature of the PT (including the critical temperature) is independent of h. Furthermore, for , we study the steady-state properties of PTs using numerical methods. Therefore, we performed simulations for different lattice sizes and measured relevant physical quantities. From the data, we determined the numerical results of the transition temperature and relevant critical exponents for various values of h by applying finite-size scaling (FSS). We found that the FSS analysis of the exponents is consistent with the analytical values of the equilibrium 2D Ising model.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"67 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185948","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 : 2024-09-10DOI: 10.1088/1751-8121/ad75d8
Katarzyna Grabowska, Janusz Grabowski, Marek Kuś and Giuseppe Marmo
If η is a contact form on a manifold M such that the orbits of the Reeb vector field form a simple foliation on M, then the presymplectic 2-form on M induces a symplectic structure ω on the quotient manifold . We call a contactification of the symplectic manifold . First, we present an explicit geometric construction of contactifications of some coadjoint orbits of connected Lie groups. Our construction is a far going generalization of the well-known contactification of the complex projective space , being the unit sphere in , and equipped with the restriction of the Liouville 1-form on . Second, we describe a constructive procedure for obtaining contactification in the process of the Marsden–Weinstein–Meyer symplectic reduction and indicate geometric obstructions for the existence of compact contactifications. Third, we show that contactifications provide a nice geometrical tool for a Lagrangian description of Hamiltonian systems on compact symplectic manifolds , on which symplectic forms never admit a ‘vector potential’.
如果 η 是流形 M 上的接触形式，使得里布向量场的轨道在 M 上形成简单折射，那么 M 上的前折射 2 形式会在商流形上诱导出交映结构 ω 。我们称之为交映流形的接触化。首先，我们提出了连通李群某些共轭轨道接触化的明确几何构造。我们的构造是对众所周知的复投影空间Ⅳ的接触化的进一步概括，Ⅳ是Ⅳ中的单位球，并在Ⅳ上配备了Liouville 1-form的限制。其次，我们描述了在 Marsden-Weinstein-Meyer 对称还原过程中获得接触化的构造过程，并指出了紧凑接触化存在的几何障碍。第三，我们证明了接触化为紧凑交映流形上哈密尔顿系统的拉格朗日描述提供了一个很好的几何工具，而在紧凑交映流形上交映形式永远不承认 "矢量势"。
{"title":"Contactifications: a Lagrangian description of compact Hamiltonian systems *","authors":"Katarzyna Grabowska, Janusz Grabowski, Marek Kuś and Giuseppe Marmo","doi":"10.1088/1751-8121/ad75d8","DOIUrl":"https://doi.org/10.1088/1751-8121/ad75d8","url":null,"abstract":"If η is a contact form on a manifold M such that the orbits of the Reeb vector field form a simple foliation on M, then the presymplectic 2-form on M induces a symplectic structure ω on the quotient manifold . We call a contactification of the symplectic manifold . First, we present an explicit geometric construction of contactifications of some coadjoint orbits of connected Lie groups. Our construction is a far going generalization of the well-known contactification of the complex projective space , being the unit sphere in , and equipped with the restriction of the Liouville 1-form on . Second, we describe a constructive procedure for obtaining contactification in the process of the Marsden–Weinstein–Meyer symplectic reduction and indicate geometric obstructions for the existence of compact contactifications. Third, we show that contactifications provide a nice geometrical tool for a Lagrangian description of Hamiltonian systems on compact symplectic manifolds , on which symplectic forms never admit a ‘vector potential’.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"25 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185973","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 : 2024-09-10DOI: 10.1088/1751-8121/ad6f7d
Marian Stengl, Patrick Gelß, Stefan Klus and Sebastian Pokutta
The Koopman–von Neumann equation describes the evolution of a complex-valued wavefunction corresponding to the probability distribution given by an associated classical Liouville equation. Typically, it is defined on the whole Euclidean space. The investigation of bounded domains, particularly in practical scenarios involving quantum-based simulations of dynamical systems, has received little attention so far. We consider the Koopman–von Neumann equation associated with an ordinary differential equation on a bounded domain whose trajectories are contained in the set’s closure. Our main results are the construction of a strongly continuous semigroup together with the existence and uniqueness of solutions of the associated initial value problem. To this end, a functional-analytic framework connected to Sobolev spaces is proposed and analyzed. Moreover, the connection of the Koopman–von Neumann framework to transport equations is highlighted.
{"title":"Existence and uniqueness of solutions of the Koopman–von Neumann equation on bounded domains","authors":"Marian Stengl, Patrick Gelß, Stefan Klus and Sebastian Pokutta","doi":"10.1088/1751-8121/ad6f7d","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6f7d","url":null,"abstract":"The Koopman–von Neumann equation describes the evolution of a complex-valued wavefunction corresponding to the probability distribution given by an associated classical Liouville equation. Typically, it is defined on the whole Euclidean space. The investigation of bounded domains, particularly in practical scenarios involving quantum-based simulations of dynamical systems, has received little attention so far. We consider the Koopman–von Neumann equation associated with an ordinary differential equation on a bounded domain whose trajectories are contained in the set’s closure. Our main results are the construction of a strongly continuous semigroup together with the existence and uniqueness of solutions of the associated initial value problem. To this end, a functional-analytic framework connected to Sobolev spaces is proposed and analyzed. Moreover, the connection of the Koopman–von Neumann framework to transport equations is highlighted.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"6 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185971","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 : 2024-09-10DOI: 10.1088/1751-8121/ad7655
Felix Finster, Johannes Kleiner and Claudio F Paganini
It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schrödinger equation are derived from the causal action principle. The dynamics of the statistical operator is described by a deterministic equation of Kossakowski–Lindblad form. Moreover, the quantum state undergoes a dynamical collapse compatible with the Born rule. The effective model has similarities with the continuous spontaneous localization model, but differs from it by a conservation law for the probability integral as well as a non-locality in time on a microscopic length scale .
{"title":"Causal fermion systems as an effective collapse theory","authors":"Felix Finster, Johannes Kleiner and Claudio F Paganini","doi":"10.1088/1751-8121/ad7655","DOIUrl":"https://doi.org/10.1088/1751-8121/ad7655","url":null,"abstract":"It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schrödinger equation are derived from the causal action principle. The dynamics of the statistical operator is described by a deterministic equation of Kossakowski–Lindblad form. Moreover, the quantum state undergoes a dynamical collapse compatible with the Born rule. The effective model has similarities with the continuous spontaneous localization model, but differs from it by a conservation law for the probability integral as well as a non-locality in time on a microscopic length scale .","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"1961 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185974","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 : 2024-09-10DOI: 10.1088/1751-8121/ad75d7
Q Q Zheng, X Li, J W Shen, V Pandey and L N Guan
Investigating Turing patterns in complex networks presents a significant challenge, particularly in understanding the transition from simple to complex systems. We examine the network-organized SIR model, incorporating the Matthew effect and double delays, to demonstrate how network structures directly impact critical delay values, providing insights into historical patterns of disease spread. The study reveals that both susceptible and infected individuals experience a latent period due to interactions between the Matthew effect and incubation, mirroring historical patterns observed in seasonal flu outbreaks. The emergence of chaotic states is observed when two delays intersect critical curves, highlighting the complex dynamics that can arise in historical epidemic models. A novel approach is introduced, utilizing eigenvalue ratios from minimum/maximum Laplacian matrices (excluding 0) and critical delay values, to identify stable regions within network-organized systems, providing a new tool for historical epidemiological analysis. The paper further explores dynamic and biological mechanisms, discussing how these findings can inform historical and contemporary strategies for managing infectious disease outbreaks.
研究复杂网络中的图灵模式是一项重大挑战，尤其是在理解从简单系统到复杂系统的过渡方面。我们研究了包含马修效应和双重延迟的网络组织 SIR 模型，以展示网络结构如何直接影响临界延迟值，从而深入了解疾病传播的历史模式。研究发现，由于马太效应和潜伏期之间的相互作用，易感个体和感染个体都会经历一段潜伏期，这与在季节性流感爆发中观察到的历史模式如出一辙。当两个延迟与临界曲线相交时，就会出现混沌状态，这凸显了历史流行病模型中可能出现的复杂动态。本文引入了一种新方法，利用最小/最大拉普拉奇矩阵（不包括 0）的特征值比和临界延迟值来识别网络组织系统中的稳定区域，为历史流行病学分析提供了一种新工具。论文进一步探讨了动态和生物机制，讨论了这些发现如何为管理传染病爆发的历史和当代战略提供信息。
{"title":"Network topology and double delays in turing instability and pattern formation","authors":"Q Q Zheng, X Li, J W Shen, V Pandey and L N Guan","doi":"10.1088/1751-8121/ad75d7","DOIUrl":"https://doi.org/10.1088/1751-8121/ad75d7","url":null,"abstract":"Investigating Turing patterns in complex networks presents a significant challenge, particularly in understanding the transition from simple to complex systems. We examine the network-organized SIR model, incorporating the Matthew effect and double delays, to demonstrate how network structures directly impact critical delay values, providing insights into historical patterns of disease spread. The study reveals that both susceptible and infected individuals experience a latent period due to interactions between the Matthew effect and incubation, mirroring historical patterns observed in seasonal flu outbreaks. The emergence of chaotic states is observed when two delays intersect critical curves, highlighting the complex dynamics that can arise in historical epidemic models. A novel approach is introduced, utilizing eigenvalue ratios from minimum/maximum Laplacian matrices (excluding 0) and critical delay values, to identify stable regions within network-organized systems, providing a new tool for historical epidemiological analysis. The paper further explores dynamic and biological mechanisms, discussing how these findings can inform historical and contemporary strategies for managing infectious disease outbreaks.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"32 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185986","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 : 2024-09-09DOI: 10.1088/1751-8121/ad75d6
Dariusz Chruściński and Bihalan Bhattacharya
A class of unital qubit maps displaying diagonal unitary and orthogonal symmetries is analyzed. Such maps have already found a lot applications in quantum information theory. We provide a complete characterization of this class of maps showing intricate relation between positivity, operator Schwarz inequality, and complete positivity. Finally, it is shown how to generalize the entire picture beyond unital case (so called generalized Schwarz maps). Interestingly, the first example of Schwarz but not completely positive map found by Choi belongs to our class. As a case study we provide a full characterization of Pauli maps. Our analysis leads to generalization of seminal Fujiwara–Algoet conditions for Pauli quantum channels.
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Pub Date : 2024-09-09DOI: 10.1088/1751-8121/ad74bd
Nicolae Cotfas
There exist many attempts to define a Wigner function for quantum systems with finite-dimensional Hilbert space, each of them coming with its advantages and limitations. The existing finite versions have simple definitions, but they are based only on the existence of a formal analogy with the continuous-variable Wigner function and do not allow an intuitive state analysis. The continuous versions have more complicated definitions, but they are closer to the original Wigner function and allow a visualization of the quantum states. The version based on the concept of tight frame we present is finite, but it has certain properties and applications similar to those of continuous versions. It allows us to present a new graphical representation of qubit states, and to define new parameters concerning them. An important advantage of frame representation follows from the use of redundant information. The values taken by the frame version of Wigner function are not independent. They have to satisfy a large number of mathematical relations, useful in error detection and correction.
{"title":"Frame representation of quantum systems with finite-dimensional Hilbert space","authors":"Nicolae Cotfas","doi":"10.1088/1751-8121/ad74bd","DOIUrl":"https://doi.org/10.1088/1751-8121/ad74bd","url":null,"abstract":"There exist many attempts to define a Wigner function for quantum systems with finite-dimensional Hilbert space, each of them coming with its advantages and limitations. The existing finite versions have simple definitions, but they are based only on the existence of a formal analogy with the continuous-variable Wigner function and do not allow an intuitive state analysis. The continuous versions have more complicated definitions, but they are closer to the original Wigner function and allow a visualization of the quantum states. The version based on the concept of tight frame we present is finite, but it has certain properties and applications similar to those of continuous versions. It allows us to present a new graphical representation of qubit states, and to define new parameters concerning them. An important advantage of frame representation follows from the use of redundant information. The values taken by the frame version of Wigner function are not independent. They have to satisfy a large number of mathematical relations, useful in error detection and correction.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"392 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185976","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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