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}
Pub Date : 2024-09-09DOI: 10.1088/1751-8121/ad72bc
Alberto Dinelli, Jérémy O’Byrne and Julien Tailleur
In this article we derive and test the fluctuating hydrodynamic description of active particles interacting via taxis and quorum sensing, both for mono-disperse systems and for mixtures of co-existing species of active particles. We compute the average steady-state density profile in the presence of spatial motility regulation, as well as the structure factor and intermediate scattering function for interacting systems. By comparing our predictions to microscopic numerical simulations, we show that our fluctuating hydrodynamics correctly predicts the large-scale static and dynamical properties of the system. We also discuss how the theory breaks down when structures emerge at scales smaller or comparable to the persistence length of the particles. When the density field is the unique hydrodynamic mode of the system, we show that active Brownian particles, run-and-tumble particles and active Ornstein–Uhlenbeck particles, interacting via quorum-sensing or chemotactic interactions, display undistinguishable large-scale properties. This form of universality implies an interesting robustness of the predicted physics but also that large-scale observations of patterns are insufficient to assess their microscopic origins. In particular, our results predict that chemotaxis-induced and motility-induced phase separation should share strong qualitative similarities at the macroscopic scale.
{"title":"Fluctuating hydrodynamics of active particles interacting via taxis and quorum sensing: static and dynamics","authors":"Alberto Dinelli, Jérémy O’Byrne and Julien Tailleur","doi":"10.1088/1751-8121/ad72bc","DOIUrl":"https://doi.org/10.1088/1751-8121/ad72bc","url":null,"abstract":"In this article we derive and test the fluctuating hydrodynamic description of active particles interacting via taxis and quorum sensing, both for mono-disperse systems and for mixtures of co-existing species of active particles. We compute the average steady-state density profile in the presence of spatial motility regulation, as well as the structure factor and intermediate scattering function for interacting systems. By comparing our predictions to microscopic numerical simulations, we show that our fluctuating hydrodynamics correctly predicts the large-scale static and dynamical properties of the system. We also discuss how the theory breaks down when structures emerge at scales smaller or comparable to the persistence length of the particles. When the density field is the unique hydrodynamic mode of the system, we show that active Brownian particles, run-and-tumble particles and active Ornstein–Uhlenbeck particles, interacting via quorum-sensing or chemotactic interactions, display undistinguishable large-scale properties. This form of universality implies an interesting robustness of the predicted physics but also that large-scale observations of patterns are insufficient to assess their microscopic origins. In particular, our results predict that chemotaxis-induced and motility-induced phase separation should share strong qualitative similarities at the macroscopic scale.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"64 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185975","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/ad74be
L M Farrell, D Eaton, P Chitnelawong, K Bencheikh, B P van Zyl
The one-body density matrix (ODM) for a zero temperature non-interacting Fermi gas can be approximately obtained in the semiclassical regime through different ℏ-expansion techniques. One would expect that each method of approximating the ODM should yield equivalent density matrices which are both Hermitian and idempotent to any order in ℏ. However, the Kirzhnits and Wigner–Kirkwood methods do not yield these properties, while the Grammaticos–Voros method does. Here we show explicitly, for arbitrary d-dimensions through an appropriate change into symmetric coordinates, that each method is indeed identical, Hermitian, and idempotent. This change of variables resolves the inconsistencies between the various methods, showing that the non-Hermitian and non-idempotent behavior of the Kirzhnits and Wigner–Kirkwood methods is an artifact of performing a non-symmetric truncation to the semiclassical ℏ-expansions. Our work also provides the first explicit derivation of the d-dimensional Grammaticos–Voros ODM, originally proposed by Redjati et al (2019 J. Phys. Chem. Solids134 313–8) based on their d=1,2,3,4 expressions.
零温非相互作用费米气体的单体密度矩阵（ODM）可以通过不同的ℏ展开技术在半经典体系中近似得到。我们期望每种近似 ODM 的方法都能得到等效密度矩阵，这些矩阵在ℏ 的任何阶都是赫米特和幂等的。然而，基尔日尼茨法和维格纳-柯克伍德法并不具备这些特性，而格拉马蒂奥斯-沃罗斯法却具备这些特性。在这里，我们通过对对称坐标的适当改变，明确地证明了对于任意的 d 维，每种方法确实是相同的、赫米特的和幂等的。这种变量变化解决了各种方法之间的不一致性，表明基尔日尼茨法和维格纳-柯克伍德法的非赫米提性和非等幂性行为是对半经典ℏ展开进行非对称截断的产物。我们的工作还首次明确推导了 d 维 Grammaticos-Voros ODM，它最初是由 Redjati 等人（2019 J. Phys. Chem. Solids 134 313-8）根据其 d=1,2,3,4 表达式提出的。
{"title":"Preserving the Hermiticity of the one-body density matrix for a non-interacting Fermi gas","authors":"L M Farrell, D Eaton, P Chitnelawong, K Bencheikh, B P van Zyl","doi":"10.1088/1751-8121/ad74be","DOIUrl":"https://doi.org/10.1088/1751-8121/ad74be","url":null,"abstract":"The one-body density matrix (ODM) for a zero temperature non-interacting Fermi gas can be approximately obtained in the semiclassical regime through different <inline-formula>\u0000<tex-math><?CDATA $hbar$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>ℏ</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"aad74beieqn1.gif\"></inline-graphic></inline-formula>-expansion techniques. One would expect that each method of approximating the ODM should yield equivalent density matrices which are both Hermitian and idempotent to any order in <inline-formula>\u0000<tex-math><?CDATA $hbar$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>ℏ</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"aad74beieqn2.gif\"></inline-graphic></inline-formula>. However, the Kirzhnits and Wigner–Kirkwood methods do not yield these properties, while the Grammaticos–Voros method does. Here we show explicitly, for arbitrary <italic toggle=\"yes\">d</italic>-dimensions through an appropriate change into symmetric coordinates, that each method is indeed identical, Hermitian, and idempotent. This change of variables resolves the inconsistencies between the various methods, showing that the non-Hermitian and non-idempotent behavior of the Kirzhnits and Wigner–Kirkwood methods is an artifact of performing a non-symmetric truncation to the semiclassical <inline-formula>\u0000<tex-math><?CDATA $hbar$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>ℏ</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"aad74beieqn3.gif\"></inline-graphic></inline-formula>-expansions. Our work also provides the first explicit derivation of the <italic toggle=\"yes\">d</italic>-dimensional Grammaticos–Voros ODM, originally proposed by Redjati <italic toggle=\"yes\">et al</italic> (2019 <italic toggle=\"yes\">J. Phys. Chem. Solids</italic> <bold>134</bold> 313–8) based on their <inline-formula>\u0000<tex-math><?CDATA $d = 1,2,3,4$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"aad74beieqn4.gif\"></inline-graphic></inline-formula> expressions.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"32 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185978","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 : 2024-09-06DOI: 10.1088/1751-8121/ad742c
Markus A G Amano, Sven Bjarke Gudnason
The instanton in the Sakai-Sugimoto model corresponds to the Skyrmion on the holographic boundary—which is asymptotically flat—and is fundamentally different from the flat Minkowski space Yang–Mills instanton. We use the Atiyah–Patodi–Singer index theorem and a series of transformations to show that there are 6k zeromodes—or moduli—in the limit of infinite ‘t Hooft coupling of the Sakai-Sugimoto model. The implications for the low-energy baryons—the Skyrmions—on the holographic boundary, is a scale separation between 2k ‘heavy’ massive modes and 6k−9 ‘light’ massive modes for k > 1; the 9 global transformations that correspond to translations, rotations and isorotations remain as zeromodes. For k = 1 there are 2 ‘heavy’ modes and 6 zeromodes due to degeneracy between rotations and isorotations.
{"title":"Modes of the Sakai-Sugimoto soliton","authors":"Markus A G Amano, Sven Bjarke Gudnason","doi":"10.1088/1751-8121/ad742c","DOIUrl":"https://doi.org/10.1088/1751-8121/ad742c","url":null,"abstract":"The instanton in the Sakai-Sugimoto model corresponds to the Skyrmion on the holographic boundary—which is asymptotically flat—and is fundamentally different from the flat Minkowski space Yang–Mills instanton. We use the Atiyah–Patodi–Singer index theorem and a series of transformations to show that there are 6<italic toggle=\"yes\">k</italic> zeromodes—or moduli—in the limit of infinite ‘t Hooft coupling of the Sakai-Sugimoto model. The implications for the low-energy baryons—the Skyrmions—on the holographic boundary, is a scale separation between 2<italic toggle=\"yes\">k</italic> ‘heavy’ massive modes and <inline-formula>\u0000<tex-math><?CDATA $6k-9$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mn>6</mml:mn><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mn>9</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"aad742cieqn1.gif\"></inline-graphic></inline-formula> ‘light’ massive modes for <italic toggle=\"yes\">k</italic> > 1; the 9 global transformations that correspond to translations, rotations and isorotations remain as zeromodes. For <italic toggle=\"yes\">k</italic> = 1 there are 2 ‘heavy’ modes and 6 zeromodes due to degeneracy between rotations and isorotations.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"26 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185984","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 : 2024-09-06DOI: 10.1088/1751-8121/ad74bc
Emel Altas, Bayram Tekin
We give a detailed canonical analysis of the n-dimensional f(Riemann) gravity, correcting the earlier results in the literature. We also write the field equations in the Fischer–Marsden form which is amenable to identifying the non-stationary energy on a spacelike hypersurface. We give pure R2 and RμνRμν theories as examples.
我们对 n 维 f(黎曼)引力进行了详细的规范分析，修正了文献中的早期结果。我们还以费舍尔-马斯登形式写出了场方程，这有利于识别空间似超曲面上的非稳态能量。我们给出了纯 R2 和 RμνRμν 理论作为例子。
{"title":"Constraints and time evolution in generic f(Riemann) gravity","authors":"Emel Altas, Bayram Tekin","doi":"10.1088/1751-8121/ad74bc","DOIUrl":"https://doi.org/10.1088/1751-8121/ad74bc","url":null,"abstract":"We give a detailed canonical analysis of the <italic toggle=\"yes\">n</italic>-dimensional <italic toggle=\"yes\">f</italic>(Riemann) gravity, correcting the earlier results in the literature. We also write the field equations in the Fischer–Marsden form which is amenable to identifying the non-stationary energy on a spacelike hypersurface. We give pure <italic toggle=\"yes\">R</italic><sup>2</sup> and <inline-formula>\u0000<tex-math><?CDATA $R_{munu}R^{munu}$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>μ</mml:mi><mml:mi>ν</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>μ</mml:mi><mml:mi>ν</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math><inline-graphic xlink:href=\"aad74bcieqn1.gif\"></inline-graphic></inline-formula> theories as examples.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"17 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185979","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 : 2024-09-06DOI: 10.1088/1751-8121/ad6410
Mohammed Ahrami, Zakaria El Allali, Evans M Harrell II, James B Kennedy
We study the problem of minimizing or maximizing the fundamental spectral gap of Schrödinger operators on metric graphs with either a convex potential or a ‘single-well’ potential on an appropriate specified subset. (In the case of metric trees, such a subset can be the entire graph.) In the convex case we find that the minimizing and maximizing potentials are piecewise linear with only a finite number of points of non-smoothness, but give examples showing that the optimal potentials need not be constant. This is a significant departure from the usual scenarios on intervals and domains where the constant potential is typically minimizing. In the single-well case we show that the optimal potentials are piecewise constant with a finite number of jumps, and in both cases give an explicit estimate on the number of points of non-smoothness, respectively jumps, the minimizing potential can have. Furthermore, we show that, unlike on domains, it is not generally possible to find nontrivial bounds on the fundamental gap in terms of the diameter of the graph alone, within the given classes.
{"title":"Optimizing the fundamental eigenvalue gap of quantum graphs","authors":"Mohammed Ahrami, Zakaria El Allali, Evans M Harrell II, James B Kennedy","doi":"10.1088/1751-8121/ad6410","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6410","url":null,"abstract":"We study the problem of minimizing or maximizing the fundamental spectral gap of Schrödinger operators on metric graphs with either a convex potential or a ‘single-well’ potential on an appropriate specified subset. (In the case of metric trees, such a subset can be the entire graph.) In the convex case we find that the minimizing and maximizing potentials are piecewise linear with only a finite number of points of non-smoothness, but give examples showing that the optimal potentials need not be constant. This is a significant departure from the usual scenarios on intervals and domains where the constant potential is typically minimizing. In the single-well case we show that the optimal potentials are piecewise constant with a finite number of jumps, and in both cases give an explicit estimate on the number of points of non-smoothness, respectively jumps, the minimizing potential can have. Furthermore, we show that, unlike on domains, it is not generally possible to find nontrivial bounds on the fundamental gap in terms of the diameter of the graph alone, within the given classes.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"25 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185981","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 : 2024-09-05DOI: 10.1088/1751-8121/ad7429
Wentao Ye, Jiaju Zhang
We investigate the Shannon entropy of the total system and its subsystems, as well as the subsystem Shannon mutual information, in quasiparticle excited states of free bosonic and fermionic chains and the ferromagnetic phase of the spin-1/2 XXX chain. For single-particle and double-particle states, we derive various analytical formulas for free bosonic and fermionic chains in the scaling limit. These formulas are also applicable to certain magnon excited states in the XXX chain in the scaling limit. We also calculate numerically the Shannon entropy and mutual information for triple-particle and quadruple-particle states in bosonic, fermionic, and XXX chains. We discover that Shannon entropy, unlike entanglement entropy, typically does not separate for quasiparticles with large momentum differences. Moreover, in the limit of large momentum difference, we obtain universal quantum bosonic and fermionic results that are generally distinct and cannot be explained by a semiclassical picture.
{"title":"Shannon entropy in quasiparticle states of quantum chains","authors":"Wentao Ye, Jiaju Zhang","doi":"10.1088/1751-8121/ad7429","DOIUrl":"https://doi.org/10.1088/1751-8121/ad7429","url":null,"abstract":"We investigate the Shannon entropy of the total system and its subsystems, as well as the subsystem Shannon mutual information, in quasiparticle excited states of free bosonic and fermionic chains and the ferromagnetic phase of the spin-1/2 XXX chain. For single-particle and double-particle states, we derive various analytical formulas for free bosonic and fermionic chains in the scaling limit. These formulas are also applicable to certain magnon excited states in the XXX chain in the scaling limit. We also calculate numerically the Shannon entropy and mutual information for triple-particle and quadruple-particle states in bosonic, fermionic, and XXX chains. We discover that Shannon entropy, unlike entanglement entropy, typically does not separate for quasiparticles with large momentum differences. Moreover, in the limit of large momentum difference, we obtain universal quantum bosonic and fermionic results that are generally distinct and cannot be explained by a semiclassical picture.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"12 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185980","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 : 2024-09-05DOI: 10.1088/1751-8121/ad742a
Sourav Paul, Anant Vijay Varma, Sourin Das
A pure state of a qubit can be geometrically represented as a point on the extended complex plane through stereographic projection. By employing successive conformal maps on the extended complex plane, we can generate an effective discrete-time evolution of the pure states of the qubit. This work focuses on a subset of analytic maps known as fractional linear conformal maps. We show that these maps serve as a unifying framework for a diverse range of quantum-inspired conceivable dynamics, including (i) unitary dynamics,(ii) non-unitary but linear dynamics and (iii) non-unitary and non-linear dynamics where linearity (non-linearity) refers to the action of the discrete time evolution operator on the Hilbert space. We provide a characterization of these maps in terms of Leggett–Garg inequality complemented with no-signaling in time and arrow of time conditions.
{"title":"Fractional conformal map, qubit dynamics and the Leggett–Garg inequality","authors":"Sourav Paul, Anant Vijay Varma, Sourin Das","doi":"10.1088/1751-8121/ad742a","DOIUrl":"https://doi.org/10.1088/1751-8121/ad742a","url":null,"abstract":"A pure state of a qubit can be geometrically represented as a point on the extended complex plane through stereographic projection. By employing successive conformal maps on the extended complex plane, we can generate an effective discrete-time evolution of the pure states of the qubit. This work focuses on a subset of analytic maps known as fractional linear conformal maps. We show that these maps serve as a unifying framework for a diverse range of quantum-inspired conceivable dynamics, including (i) unitary dynamics,(ii) non-unitary but linear dynamics and (iii) non-unitary and non-linear dynamics where linearity (non-linearity) refers to the action of the discrete time evolution operator on the Hilbert space. We provide a characterization of these maps in terms of Leggett–Garg inequality complemented with no-signaling in time and arrow of time conditions.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"196 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185983","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 : 2024-09-04DOI: 10.1088/1751-8121/ad7340
Jiazhen Shao, Igor P Ivanov, Mikko Korhonen
We continue classification of finite groups which can be used as symmetry group of the scalar sector of the four-Higgs-doublet model (4HDM). Our objective is to systematically construct non-abelian groups via the group extension procedure, starting from the abelian groups A and their automorphism groups Aut(A). Previously, we considered all cyclic groups A available for the 4HDM scalar sector. Here, we further develop the method and apply it to extensions by the remaining rephasing groups A, namely A=Z2×Z2, Z4×Z2, and Z2×Z2×Z2. As Aut(A) grows, the procedure becomes more laborious, but we prove an isomorphism theorem which helps classify all the options. We also comment on what remains to be done to complete the classification of all finite n
我们继续对可用作四希格斯双重模型（4HDM）标量部门对称群的有限群进行分类。我们的目标是通过群扩展程序，从非阿贝尔群 A 及其自变群 Aut(A) 开始，系统地构造非阿贝尔群。在此之前，我们考虑了 4HDM 标量扇形的所有循环群 A。在这里，我们进一步发展了这一方法，并将其应用于剩余的重合群 A 的扩展，即 A=Z2×Z2、Z4×Z2 和 Z2×Z2×Z2。随着 Aut(A) 的增长，这一过程变得更加费力，但我们证明了一个同构定理，它有助于对所有选项进行分类。我们还评论了要完成所有可在 4HDM 标量扇形中实现的有限非阿贝尔群的分类，而不出现意外的连续对称性，还有哪些工作要做。
{"title":"Symmetries for the 4HDM: II. Extensions by rephasing groups","authors":"Jiazhen Shao, Igor P Ivanov, Mikko Korhonen","doi":"10.1088/1751-8121/ad7340","DOIUrl":"https://doi.org/10.1088/1751-8121/ad7340","url":null,"abstract":"We continue classification of finite groups which can be used as symmetry group of the scalar sector of the four-Higgs-doublet model (4HDM). Our objective is to systematically construct non-abelian groups via the group extension procedure, starting from the abelian groups <italic toggle=\"yes\">A</italic> and their automorphism groups <inline-formula>\u0000<tex-math><?CDATA $mathrm{Aut}(A)$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mi>Aut</mml:mi></mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>A</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"aad7340ieqn1.gif\"></inline-graphic></inline-formula>. Previously, we considered all cyclic groups <italic toggle=\"yes\">A</italic> available for the 4HDM scalar sector. Here, we further develop the method and apply it to extensions by the remaining rephasing groups <italic toggle=\"yes\">A</italic>, namely <inline-formula>\u0000<tex-math><?CDATA $A = mathbb{Z}_2timesmathbb{Z}_2$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"double-struck\">Z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"double-struck\">Z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\"aad7340ieqn2.gif\"></inline-graphic></inline-formula>, <inline-formula>\u0000<tex-math><?CDATA $mathbb{Z}_4times mathbb{Z}_2$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"double-struck\">Z</mml:mi></mml:mrow><mml:mn>4</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"double-struck\">Z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\"aad7340ieqn3.gif\"></inline-graphic></inline-formula>, and <inline-formula>\u0000<tex-math><?CDATA $mathbb{Z}_2times mathbb{Z}_2times mathbb{Z}_2$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"double-struck\">Z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"double-struck\">Z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"double-struck\">Z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\"aad7340ieqn4.gif\"></inline-graphic></inline-formula>. As <inline-formula>\u0000<tex-math><?CDATA $mathrm{Aut}(A)$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mi>Aut</mml:mi></mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>A</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"aad7340ieqn5.gif\"></inline-graphic></inline-formula> grows, the procedure becomes more laborious, but we prove an isomorphism theorem which helps classify all the options. We also comment on what remains to be done to complete the classification of all finite n","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185982","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 : 2024-09-03DOI: 10.1088/1751-8121/ad6f80
Ryan A Palmer, Isaac V Chenchiah, Daniel Robert
Increasing empirical evidence suggests that many terrestrial arthropods, such as bees, spiders, and caterpillars, sense electric fields in their environments. This relatively newly discovered sense may play a unique role within their broader sensory ecology, alongside other fundamental senses such as vision, hearing, olfaction, and aero-acoustic sensing. Deflectable hairs are the primary candidate for the reception of electrical stimuli. From the deflections of individually innervated hairs, the arthropod can transduce environmental and ecological information. However, it is unclear what information an animal can elicit from hair receptors and how it relates to their environment. This paper explores how an arthropod may ascertain geometric and electrical information about its environment. Using two-dimensional models, we explore the possibility of electroreceptive object recognition and reconstruction via multiple observations and several deflecting hairs. We analyse how the number of hairs, the observed shape, and the observation path alter the accuracy of the reconstructed representations. The results herein indicate the formidable possibility that geometric information about the environment can be electro-mechanically measured and acquired at a distance.
{"title":"Sensing electrical environments: mechanical object reconstruction via electrosensors","authors":"Ryan A Palmer, Isaac V Chenchiah, Daniel Robert","doi":"10.1088/1751-8121/ad6f80","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6f80","url":null,"abstract":"Increasing empirical evidence suggests that many terrestrial arthropods, such as bees, spiders, and caterpillars, sense electric fields in their environments. This relatively newly discovered sense may play a unique role within their broader sensory ecology, alongside other fundamental senses such as vision, hearing, olfaction, and aero-acoustic sensing. Deflectable hairs are the primary candidate for the reception of electrical stimuli. From the deflections of individually innervated hairs, the arthropod can transduce environmental and ecological information. However, it is unclear what information an animal can elicit from hair receptors and how it relates to their environment. This paper explores how an arthropod may ascertain geometric and electrical information about its environment. Using two-dimensional models, we explore the possibility of electroreceptive object recognition and reconstruction via multiple observations and several deflecting hairs. We analyse how the number of hairs, the observed shape, and the observation path alter the accuracy of the reconstructed representations. The results herein indicate the formidable possibility that geometric information about the environment can be electro-mechanically measured and acquired at a distance.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"159 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186010","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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