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Field theory equivalences as spans of L ∞-algebras 作为 L ∞-代数跨度的场论等价性
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-06-06 DOI: 10.1088/1751-8121/ad5521
Mehran Jalali Farahani, Christian Saemann, Martin Wolf
{"title":"Field theory equivalences as spans of L\u0000 ∞-algebras","authors":"Mehran Jalali Farahani, Christian Saemann, Martin Wolf","doi":"10.1088/1751-8121/ad5521","DOIUrl":"https://doi.org/10.1088/1751-8121/ad5521","url":null,"abstract":"\u0000 Semi-classically equivalent field theories are related by a quasi-isomorphism between their underlying L∞-algebras, but such a quasi-isomorphism is not necessarily a homotopy transfer. We demonstrate that all quasi-isomorphisms can be lifted to spans of L∞-algebras in which the quasi-isomorphic L∞-algebras are obtained from a correspondence L∞-algebra by a homotopy transfer. Our construction is very useful: homotopy transfer is computationally tractable, and physically, it amounts to integrating out fields in a Feynman diagram expansion. Spans of L∞-algebras allow for a clean definition of quasi-isomorphisms of cyclic L∞-algebras. Furthermore, they appear naturally in many contexts within physics. As examples, we first consider scalar field theory with interaction vertices blown up in different ways. We then show that (non-Abelian) T-duality can be seen as a span of L∞-algebras, and we provide full details in the case of the principal chiral model. We also present the relevant span of L∞-algebras for the Penrose-Ward transform in the context of self-dual Yang-Mills theory and Bogomolny monopoles.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141379317","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}
引用次数: 2
Reply to Comment on ‘Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley–Lieb algebras’ 对 "从周期性 Temperley-Lieb 对象中的特征值同值看 Potts 和 O(N) 模型的临界点 "评论的回复
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-06-06 DOI: 10.1088/1751-8121/ad4d33
Jesper Lykke Jacobsen
{"title":"Reply to Comment on ‘Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley–Lieb algebras’","authors":"Jesper Lykke Jacobsen","doi":"10.1088/1751-8121/ad4d33","DOIUrl":"https://doi.org/10.1088/1751-8121/ad4d33","url":null,"abstract":"The authors replies to the comment made by Yang and Zhou (2024 J. Phys. A: Math. Theor.) on his 2015 paper entitled ‘Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley–Lieb algebras’ (Jacobsen 2015 J. Phys. A: Math. Theor. 48 454003).","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"358 15","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141380928","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}
引用次数: 0
Comment on ‘Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley–Lieb algebras’ 关于 "从周期性 Temperley-Lieb 对象中的特征值特性看 Potts 和 O(N) 模型的临界点 "的评论
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-06-06 DOI: 10.1088/1751-8121/ad4d2c
Yi Yang, Shuigeng Zhou
{"title":"Comment on ‘Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley–Lieb algebras’","authors":"Yi Yang, Shuigeng Zhou","doi":"10.1088/1751-8121/ad4d2c","DOIUrl":"https://doi.org/10.1088/1751-8121/ad4d2c","url":null,"abstract":"We present an algorithm to compute the exact critical probability h(n) for an n×∞ helical square lattice with random and independent site occupancy. The algorithm has time complexity O(n2cn) and space complexity O(cn) with c = 2.7459... and allows us to compute h(n) up to n = 24. Since the extrapolation result of h(n) is inconsistent with the current best estimation of pc , we also compute and extend the exact critical probability pc(n) for an n×∞ cylindrical square lattice to n = 24. Our calculation shows that the current best result of pc=0.59274605079210(2) by Jacobsen (2015 J. Phys. A: Math. Theor. 48 454003) is incorrect and the corrected value should be 0.5927460507896(1) .","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"26 2‐3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141376714","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}
引用次数: 0
Complex dynamics and chaos control of a quantum Stackelberg game with heterogeneous players 具有异质参与者的量子斯塔克尔伯格博弈的复杂动力学与混沌控制
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-06-06 DOI: 10.1088/1751-8121/ad5522
Ji Chen
{"title":"Complex dynamics and chaos control of a quantum Stackelberg game with heterogeneous players","authors":"Ji Chen","doi":"10.1088/1751-8121/ad5522","DOIUrl":"https://doi.org/10.1088/1751-8121/ad5522","url":null,"abstract":"\u0000 In this research article, we explore the complex dynamics of a quantum Stackelberg game and its chaos control involving players with heterogeneous expectations. We utilize the Iqbal & Toor scheme to quantize the classical Stackelberg game and observe that the first mover advantage is diminished in the quantum version of the game. By examining the game from an evolutionary perspective, where the leader firm employs bounded rational expectations and the follower firm adopts adaptive expectations, we discover that the quantum Stackelberg game exhibits complex behaviors, such as cyclic and chaotic states. The local stability of the quantum game depends on the initial state of the game. Additionally, the occurrence of chaos is delayed in the quantum game. To further investigate, we implement the time-delayed feedback method to control the chaos in the quantum game and demonstrate that the techniques used for controlling the classical game are still effective in the quantum game.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"19 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141380015","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}
引用次数: 0
Quantum Fisher information power of quantum evolutions 量子演变的量子费舍尔信息力量
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-06-06 DOI: 10.1088/1751-8121/ad5524
Jun-Long Zhao, Yan-Hui Zhou, Dong Chen, Qiping Su, Xiao-Lan Zong, Qi-Cheng Wu, Ming Yang, Chuiping Yang
{"title":"Quantum Fisher information power of quantum evolutions","authors":"Jun-Long Zhao, Yan-Hui Zhou, Dong Chen, Qiping Su, Xiao-Lan Zong, Qi-Cheng Wu, Ming Yang, Chuiping Yang","doi":"10.1088/1751-8121/ad5524","DOIUrl":"https://doi.org/10.1088/1751-8121/ad5524","url":null,"abstract":"\u0000 Quantum metrology is an important field in quantum information and plays a crucial role in quantum parameter estimation. Quantum Fisher information (QFI) is widely used to characterize the precision of quantum parameter estimation. However, a full understanding of the precision for different parameterization processes and the role of quantum evolutions in quantum parameter estimations, remains a crucial area of research. In this paper, we introduce a new concept, named as quantum Fisher information power (QFI power), to characterize the QFI-creating capability of quantum evolutions. At the same time, we take both unitary and non-unitary evolutions as examples and study QFI power. The results show that: (i) For unitary evolutions described by spin angular momentum operators, the dynamic of QFI power is dependent on the z component of the Bloch vector, and the rotating angle; (ii) For non-unitary evolutions under decoherence channels, QFI cannot be enhanced when the initial probe state belongs to zero QFI set, and the QFI power is negative when the initial probe state has maximal QFI; (iii) For the PT - and APT -symmetric non-unitary evolutions, the dynamics of QFI power exhibit oscillations in symmetry unbroken regime, while the phenomenon of stable value (SV) occurs in broken regimes with the SV=1.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"139 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141376872","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}
引用次数: 0
Exact minimal effective amounts of three 1D continuous functions and their use in Anderson transitions 三个一维连续函数的精确最小有效量及其在安德森转换中的应用
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-06-05 DOI: 10.1088/1751-8121/ad54a7
Longyan Gong
{"title":"Exact minimal effective amounts of three 1D continuous functions and their use in Anderson transitions","authors":"Longyan Gong","doi":"10.1088/1751-8121/ad54a7","DOIUrl":"https://doi.org/10.1088/1751-8121/ad54a7","url":null,"abstract":"A conceptual quantity—the minimal effective amount of a quantum state ϕ(rj) in d-dimensional systems, defined by N∗=∑j=1Nmin{N|ϕ(rj)|2,1} , is newly proposed, where system sizes N=Ld . The effective dimension d IR can be calculated by N∗=h∗(L)LdIR , where h∗(L) does not change faster than any nonzero power. However, the nature of h∗(L) is unknown priori in any given model, but is at the same time very important for its numerical analysis. Hence, analytical results can provide insights on h∗(L) in more complex situations. In this paper, we get exact results of 1D continuous sine functions, exponential decay functions and power-law decay functions. They are used to distinguish extended and localized phases in the 1D uniform potential model, Anderson model and HMP (hopping rates modulated by a power-law function) model.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"19 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141383207","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}
引用次数: 0
Analytical description of the ionic relaxation in the presence of surface adsorption 存在表面吸附时离子弛豫的分析描述
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-06-05 DOI: 10.1088/1751-8121/ad54a6
Giovanni Barbero, Y. Aliyev, A. M. Scarfone
{"title":"Analytical description of the ionic relaxation in the presence of surface adsorption","authors":"Giovanni Barbero, Y. Aliyev, A. M. Scarfone","doi":"10.1088/1751-8121/ad54a6","DOIUrl":"https://doi.org/10.1088/1751-8121/ad54a6","url":null,"abstract":"\u0000 The temporal evolution of the surface electric field in a cell in the presence of ionic adsorption is investigated. The analysis is performed in the framework of the Poisson-Nernst-Planck model, based on the conservation of particles and the equation of Poisson for the actual electric potential across the cell, assuming that only the ions of a given sign are mobile. The adsorption is described using a kinetic equation of Langmuir's type. The simple case of small adsorption is considered, in which the saturation effect can be neglected, and the fundamental equations of the model can be linearized. In this framework, the effective relaxation time describing the dynamics of the system is evaluated, as well as the profiles of the ions and the electric field. The case in which the sample is a half-space is first considered. A more realistic situation where the sample is a slab of thickness $d$, limited by two identical or different electrodes, is analyzed too. The difference in electric potential due to the adsorption phenomenon between the electrodes is determined. Our analysis shows that its time dependence, when the electrodes have different adsorption properties, is not monotonic.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"284 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141386681","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}
引用次数: 0
Lattice eigenfunction equations of KdV-type KdV 型晶格特征函数方程
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-05-17 DOI: 10.1088/1751-8121/ad4d30
Xiaoyan Wu, Cheng Zhang, Da‐jun Zhang, Haifei Zhang
{"title":"Lattice eigenfunction equations of KdV-type","authors":"Xiaoyan Wu, Cheng Zhang, Da‐jun Zhang, Haifei Zhang","doi":"10.1088/1751-8121/ad4d30","DOIUrl":"https://doi.org/10.1088/1751-8121/ad4d30","url":null,"abstract":"\u0000 We develop lattice eigenfunction equations of the lattice KdV equation, which are equations obeyed by auxiliary functions, or eigenfunctions, of the Lax pair of the lattice KdV equation. These equations are three-dimensionally consistent quad-equations, that are closely related to lattice equations in the Adler-Bobenko-Suris (ABS) classification. The connection between the H3(δ), Q1(δ), Q2 and Q3(δ) equations in the ABS classification and the lattice eigenfunction equations is explicitly showed. In particular, we provide a natural interpretation of the δ term in those equations. This can be understood as “interactions” between the eigenfunctions. Other integrable properties of the eigenfunction equations, such as exact solutions, discrete zero curvature conditions are also provided. We believe that the approach presented in this paper can be used as a means to search for integrable lattice equations.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"3 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140962677","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}
引用次数: 0
Asymptotic analysis of fundamental solution of multi-dimensional distributed-order time-fractional diffusion equation with unit density function 带单位密度函数的多维分布阶时间-分数扩散方程基本解的渐近分析
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-05-16 DOI: 10.1088/1751-8121/ad4ca9
Arman Kalvari Hashemzadeh, Alireza Ansari, Hassan Askari
{"title":"Asymptotic analysis of fundamental solution of multi-dimensional distributed-order time-fractional diffusion equation with unit density function","authors":"Arman Kalvari Hashemzadeh, Alireza Ansari, Hassan Askari","doi":"10.1088/1751-8121/ad4ca9","DOIUrl":"https://doi.org/10.1088/1751-8121/ad4ca9","url":null,"abstract":"\u0000 In this paper, we consider the multi-dimensional distributed-order time-fractional diffusion equation with the unit density function. We introduce the new Volterra-Bessel function and give the integral representations of fundamental solutions of equations in terms of this function in the whole- and half-space. The fractional moments of fundamental solutions are also provided in the higher dimensions using the Mellin transforms. We further apply steepest descent method to find the asymptotic behaviors of solutions using the Schl\"{a}fli integral of the Volterra-Bessel function. In this respect, we study the asymptotic analysis of the Volterra-Bessel function with the large parameters, and subsequently obtain the asymptotic behaviors of fundamental solutions with a discussion on the large space variable, large time variable, higher dimensions and small diffusivity constant.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"53 19","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140969216","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}
引用次数: 0
Crossover in densities of confined particles with finite range of interaction 相互作用范围有限的密闭粒子密度交叉
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-05-15 DOI: 10.1088/1751-8121/ad4c30
Saikat Santra, Anupam Kundu
{"title":"Crossover in densities of confined particles with finite range of interaction","authors":"Saikat Santra, Anupam Kundu","doi":"10.1088/1751-8121/ad4c30","DOIUrl":"https://doi.org/10.1088/1751-8121/ad4c30","url":null,"abstract":"\u0000 We study a one-dimensional classical system of $N$ particles confined within a harmonic trap. Interactions among these particles are dictated by a pairwise potential $V(x)$, where $x$ is the separation between two particles. Each particle can interact with a maximum of $d$ neighbouring particles on either side (left or right), if available. By adjusting the parameter $d$, the system can be made nearest neighbour $(d=1)$ to all-to-all $(d=N-1)$ interacting. As suggested by prior studies, the equilibrium density profile of these particles is expected to undergo shape variations as $d$ is changed. In this paper, we investigate this crossover by tuning the parameter $f(=d/N)$ from $1$ to $0$ in the large $N$ limit for two distinct choices of interaction potentials, $V(x) = - |x|$ and $V(x) =- log(|x|)$ which correspond to 1d one-component plasma and the log-gas model, respectively. For both models, the system size scaling of the density profile for fixed $f$ turns out to be the same as in their respective all-to-all case. However, the scaling function exhibits diverse shapes as $f$ varies. We explicitly compute the average density profile for any $f in (0,1]$ in the 1d plasma model, while for the log-gas model, we provide approximate calculations for large (close to $1$) and small (close to $0$) $f$. Additionally, we present simulation results to numerically demonstrate the crossover and compare these findings with our theoretical results.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"44 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140974081","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}
引用次数: 0
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