Pub Date : 2024-08-11DOI: 10.1088/1751-8121/ad6aaf
Rakesh Kumar and Kirankumar R Hiremath
This work investigates a mathematical model of the propagation of lightwaves in bent optical waveguides. This modeling leads to a non-self-adjoint eigenvalue problem for differential operator defined on the unbounded domain. Through detailed analysis, a relationship between the real and imaginary parts of the complex-valued propagation constants was constructed. Using this relation, it is found that the real and imaginary parts of the propagation constants are bounded, meaning they are limited within certain region in the complex plane. The orthogonality of these bent modes is also proved. By the asymptotic analysis of these modes, it is proved that as the behavior of the eigenfunctions is proportional to
{"title":"Mathematical analysis of bent optical waveguide eigenvalue problem","authors":"Rakesh Kumar and Kirankumar R Hiremath","doi":"10.1088/1751-8121/ad6aaf","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6aaf","url":null,"abstract":"This work investigates a mathematical model of the propagation of lightwaves in bent optical waveguides. This modeling leads to a non-self-adjoint eigenvalue problem for differential operator defined on the unbounded domain. Through detailed analysis, a relationship between the real and imaginary parts of the complex-valued propagation constants was constructed. Using this relation, it is found that the real and imaginary parts of the propagation constants are bounded, meaning they are limited within certain region in the complex plane. The orthogonality of these bent modes is also proved. By the asymptotic analysis of these modes, it is proved that as the behavior of the eigenfunctions is proportional to","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943369","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 : 2024-08-09DOI: 10.1088/1751-8121/ad6db0
Mark Aleksiejuk, David A Burton
A relativistic non-linear scalar field theory is developed from a 2+2-dimensional decomposition of the cold plasma field equations, and the theory is used to investigate a 1+1-dimensional description of a laser wakefield accelerator. The relationship between the properties of a compact laser pulse and its wake is explored. Non-linear solutions are sought describing a regular (i.e. unbroken) wake driven by a prescribed circularly-polarised laser pulse. An upper bound on the dimensionless amplitude $a_0$ of the laser pulse is determined as a function of the phase speed $v$ of the wake. The asymptotic behaviour of the upper bound on $a_0$ as $vrightarrow c$ is shown to agree with well-established, but approximate, results obtained using the conventional encoding of the plasma degrees of freedom. Our approach leads to a closed-form expression for the upper bound on $a_0$ which is exact for all values of the phase speed of the wake, unlike conventional results that are applicable only when $v$ is sufficiently close to $c$.
{"title":"A scalar field theory of 1+1-dimensional laser wakefield accelerators","authors":"Mark Aleksiejuk, David A Burton","doi":"10.1088/1751-8121/ad6db0","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6db0","url":null,"abstract":"\u0000 A relativistic non-linear scalar field theory is developed from a 2+2-dimensional decomposition of the cold plasma field equations, and the theory is used to investigate a 1+1-dimensional description of a laser wakefield accelerator. The relationship between the properties of a compact laser pulse and its wake is explored. Non-linear solutions are sought describing a regular (i.e. unbroken) wake driven by a prescribed circularly-polarised laser pulse. An upper bound on the dimensionless amplitude $a_0$ of the laser pulse is determined as a function of the phase speed $v$ of the wake. The asymptotic behaviour of the upper bound on $a_0$ as $vrightarrow c$ is shown to agree with well-established, but approximate, results obtained using the conventional encoding of the plasma degrees of freedom. Our approach leads to a closed-form expression for the upper bound on $a_0$ which is exact for all values of the phase speed of the wake, unlike conventional results that are applicable only when $v$ is sufficiently close to $c$.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141924289","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 : 2024-08-09DOI: 10.1088/1751-8121/ad6db1
Hua Li, Yong Xu, Ralf Metzler, Jianwei Shen
Transitions between long-lived states are rare but important. The statistic of successful transitions is considered in transition path theory. We here consider the transition path properties of a generalized Langevin equation with built-in memory. The general form of the approximate theoretical solutions to the transition path time distribution, mean transition path time, and coefficient of variation are obtained from the generalized Smoluchowski equation. Then, the accuracy of our theoretical results is verified by the Forward Fluxing Sampling scheme. Finally, two examples are worked out in detail. We quantify how the potential function and the memory parameters affect the transition path properties. The short time limit of transition path time distribution always has an exponential decay. For the parabolic potential case, the memory strongly affects the long-time behavior of the transition path time distribution. Our results show that the behavior of the mean transition path time is dominated by the smaller of the two memory times when both memory times exceed the intrinsic diffusion time. Interestingly, the results also show that the memory can effect a coefficient of variation of transition path times exceeding unity, in contrast to Markovian case.
{"title":"Transition path properties for one-dimensional non-Markovian models","authors":"Hua Li, Yong Xu, Ralf Metzler, Jianwei Shen","doi":"10.1088/1751-8121/ad6db1","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6db1","url":null,"abstract":"\u0000 Transitions between long-lived states are rare but important. The statistic of successful transitions is considered in transition path theory. We here consider the transition path properties of a generalized Langevin equation with built-in memory. The general form of the approximate theoretical solutions to the transition path time distribution, mean transition path time, and coefficient of variation are obtained from the generalized Smoluchowski equation. Then, the accuracy of our theoretical results is verified by the Forward Fluxing Sampling scheme. Finally, two examples are worked out in detail. We quantify how the potential function and the memory parameters affect the transition path properties. The short time limit of transition path time distribution always has an exponential decay. For the parabolic potential case, the memory strongly affects the long-time behavior of the transition path time distribution. Our results show that the behavior of the mean transition path time is dominated by the smaller of the two memory times when both memory times exceed the intrinsic diffusion time. Interestingly, the results also show that the memory can effect a coefficient of variation of transition path times exceeding unity, in contrast to Markovian case.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141923224","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 : 2024-08-08DOI: 10.1088/1751-8121/ad695e
Fernando S Filho, C E Fernández Noa, Carlos E Fiore, B Wijns and B Cleuren
Sequential (or collisional) engines have been put forward as an alternative candidate for the realisation of reliable engine setups. Despite this, the role of the different stages and the influence of the intermediate reservoirs is not well understood. We introduce the idea of conveniently adjusting/choosing intermediate reservoirs at engine devices as a strategy for optimizing its performance. This is done by considering a minimal model composed of a quantum-dot machine sequentially exposed to various reservoirs at each stage, and for which thermodynamic quantities (including power and efficiency) can be obtained exactly from the framework of stochastic thermodynamics, irrespective the number of stages. Results show that a significant gain can be obtained by increasing the number of stages and conveniently choosing their parameters.
{"title":"Thermodynamics of a collisional quantum-dot machine: the role of stages","authors":"Fernando S Filho, C E Fernández Noa, Carlos E Fiore, B Wijns and B Cleuren","doi":"10.1088/1751-8121/ad695e","DOIUrl":"https://doi.org/10.1088/1751-8121/ad695e","url":null,"abstract":"Sequential (or collisional) engines have been put forward as an alternative candidate for the realisation of reliable engine setups. Despite this, the role of the different stages and the influence of the intermediate reservoirs is not well understood. We introduce the idea of conveniently adjusting/choosing intermediate reservoirs at engine devices as a strategy for optimizing its performance. This is done by considering a minimal model composed of a quantum-dot machine sequentially exposed to various reservoirs at each stage, and for which thermodynamic quantities (including power and efficiency) can be obtained exactly from the framework of stochastic thermodynamics, irrespective the number of stages. Results show that a significant gain can be obtained by increasing the number of stages and conveniently choosing their parameters.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943442","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 : 2024-08-08DOI: 10.1088/1751-8121/ad653e
Luis Pedro Lara, Ricardo Weder and Luis Octavio Castaños-Cervantes
We consider a one-dimensional membrane-in-the-middle model for a cavity that consists of two fixed, perfect mirrors and a mobile dielectric membrane between them that has a constant electric susceptibility. We present a sequence of exact cavity angular frequencies that we call structural angular frequencies and that have the remarkable property that they are independent of the position of the membrane inside the cavity. Furthermore, the case of a thin membrane is considered and simple, approximate formulae for the angular frequencies and for the modes of the cavity are obtained. Finally, the cavity electromagnetic potential is numerically calculated and it is found that the potential is accurately described by a multiple scales solution.
{"title":"Membrane-in-the-middle optomechanical system and structural frequencies","authors":"Luis Pedro Lara, Ricardo Weder and Luis Octavio Castaños-Cervantes","doi":"10.1088/1751-8121/ad653e","DOIUrl":"https://doi.org/10.1088/1751-8121/ad653e","url":null,"abstract":"We consider a one-dimensional membrane-in-the-middle model for a cavity that consists of two fixed, perfect mirrors and a mobile dielectric membrane between them that has a constant electric susceptibility. We present a sequence of exact cavity angular frequencies that we call structural angular frequencies and that have the remarkable property that they are independent of the position of the membrane inside the cavity. Furthermore, the case of a thin membrane is considered and simple, approximate formulae for the angular frequencies and for the modes of the cavity are obtained. Finally, the cavity electromagnetic potential is numerically calculated and it is found that the potential is accurately described by a multiple scales solution.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943440","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 : 2024-08-07DOI: 10.1088/1751-8121/ad653a
Huck Stepanyants, Alan Beardon, Jeremy Paton and Dmitri Krioukov
Riemann surfaces are among the simplest and most basic geometric objects. They appear as key players in many branches of physics, mathematics, and other sciences. Despite their widespread significance, how to compute distances between pairs of points on compact Riemann surfaces is surprisingly unknown, unless the surface is a sphere or a torus. This is because on higher-genus surfaces, the distance formula involves an infimum over infinitely many terms, so it cannot be evaluated in practice. Here we derive a computable distance formula for a broad class of Riemann surfaces. The formula reduces the infimum to a minimum over an explicit set consisting of finitely many terms. We also develop a distance computation algorithm, which cannot be expressed as a formula, but which is more computationally efficient on surfaces with high genuses. We illustrate both the formula and the algorithm in application to generalized Bolza surfaces, which are a particular class of highly symmetric compact Riemann surfaces of any genus greater than 1.
{"title":"Computing distances on Riemann surfaces","authors":"Huck Stepanyants, Alan Beardon, Jeremy Paton and Dmitri Krioukov","doi":"10.1088/1751-8121/ad653a","DOIUrl":"https://doi.org/10.1088/1751-8121/ad653a","url":null,"abstract":"Riemann surfaces are among the simplest and most basic geometric objects. They appear as key players in many branches of physics, mathematics, and other sciences. Despite their widespread significance, how to compute distances between pairs of points on compact Riemann surfaces is surprisingly unknown, unless the surface is a sphere or a torus. This is because on higher-genus surfaces, the distance formula involves an infimum over infinitely many terms, so it cannot be evaluated in practice. Here we derive a computable distance formula for a broad class of Riemann surfaces. The formula reduces the infimum to a minimum over an explicit set consisting of finitely many terms. We also develop a distance computation algorithm, which cannot be expressed as a formula, but which is more computationally efficient on surfaces with high genuses. We illustrate both the formula and the algorithm in application to generalized Bolza surfaces, which are a particular class of highly symmetric compact Riemann surfaces of any genus greater than 1.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943441","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 : 2024-08-07DOI: 10.1088/1751-8121/ad5fd0
Zvi Bern, John Joseph Carrasco, Marco Chiodaroli, Henrik Johansson and Radu Roiban
This review describes the duality between color and kinematics and its applications, with the aim of gaining a deeper understanding of the perturbative structure of gauge and gravity theories. We emphasize, in particular, applications to loop-level calculations, the broad web of theories linked by the duality and the associated double-copy structure, and the issue of extending the duality and double copy beyond scattering amplitudes. The review is aimed at doctoral students and junior researchers both inside and outside the field of amplitudes and is accompanied by various exercises.
{"title":"The duality between color and kinematics and its applications","authors":"Zvi Bern, John Joseph Carrasco, Marco Chiodaroli, Henrik Johansson and Radu Roiban","doi":"10.1088/1751-8121/ad5fd0","DOIUrl":"https://doi.org/10.1088/1751-8121/ad5fd0","url":null,"abstract":"This review describes the duality between color and kinematics and its applications, with the aim of gaining a deeper understanding of the perturbative structure of gauge and gravity theories. We emphasize, in particular, applications to loop-level calculations, the broad web of theories linked by the duality and the associated double-copy structure, and the issue of extending the duality and double copy beyond scattering amplitudes. The review is aimed at doctoral students and junior researchers both inside and outside the field of amplitudes and is accompanied by various exercises.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943444","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 : 2024-08-04DOI: 10.1088/1751-8121/ad6720
Francisco J Sevilla, Guillermo Chacón-Acosta and Trifce Sandev
The transport equation of active motion is generalised to consider time-fractional dynamics to describe the anomalous diffusion of self-propelled particles. In the present study, we consider an arbitrary active motion pattern modelled by a scattering function that defines the dynamics of the change of the self-propulsion direction. The exact probability density of the particle positions at a given time is obtained. From it, the time dependence of the firsts moments, i.e. the mean square displacement and the kurtosis for an arbitrary scattering function, are derived and analysed. Anomalous diffusion is found with a crossover of the scaling exponent from 2α in the short-time regime to α in the long-time one, being the order of the fractional derivative considered. It is shown that the exact solution found satisfies a fractional diffusion equation that accounts for the non-local and retarded effects of the Laplacian of the probability density function through a coupled temporal and spatial memory function. Such a memory function holds the complete information of the active-motion pattern. In the long-time regime, space and time are decoupled in the memory function, and the time fractional telegrapher’s equation is recovered. The theoretical framework presented here can be applied as model of active motion that exhibits anomalous diffusion.
{"title":"Anomalous diffusion of self-propelled particles","authors":"Francisco J Sevilla, Guillermo Chacón-Acosta and Trifce Sandev","doi":"10.1088/1751-8121/ad6720","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6720","url":null,"abstract":"The transport equation of active motion is generalised to consider time-fractional dynamics to describe the anomalous diffusion of self-propelled particles. In the present study, we consider an arbitrary active motion pattern modelled by a scattering function that defines the dynamics of the change of the self-propulsion direction. The exact probability density of the particle positions at a given time is obtained. From it, the time dependence of the firsts moments, i.e. the mean square displacement and the kurtosis for an arbitrary scattering function, are derived and analysed. Anomalous diffusion is found with a crossover of the scaling exponent from 2α in the short-time regime to α in the long-time one, being the order of the fractional derivative considered. It is shown that the exact solution found satisfies a fractional diffusion equation that accounts for the non-local and retarded effects of the Laplacian of the probability density function through a coupled temporal and spatial memory function. Such a memory function holds the complete information of the active-motion pattern. In the long-time regime, space and time are decoupled in the memory function, and the time fractional telegrapher’s equation is recovered. The theoretical framework presented here can be applied as model of active motion that exhibits anomalous diffusion.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943445","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 : 2024-08-04DOI: 10.1088/1751-8121/ad6225
Shin-itiro Goto
The Fokker–Planck equation is one of the fundamental equations in nonequilibrium statistical mechanics, and this equation is known to be derived from the Wasserstein gradient flow equation with a free energy. This gradient flow equation describes relaxation processes and is formulated on a Riemannian manifold. Meanwhile contact Hamiltonian systems are also known to describe relaxation processes. Hence a relation between these two equations is expected to be clarified, which gives a solid foundation in geometric statistical mechanics. In this paper a class of contact Hamiltonian systems is derived from a class of the Fokker–Planck equations on Riemannian manifolds. In the course of the derivation, the Fokker–Planck equation is shown to be written as a diffusion equation with a weighted Laplacian without any approximation, which enables to employ a theory of eigenvalue problems.
{"title":"From the Fokker–Planck equation to a contact Hamiltonian system","authors":"Shin-itiro Goto","doi":"10.1088/1751-8121/ad6225","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6225","url":null,"abstract":"The Fokker–Planck equation is one of the fundamental equations in nonequilibrium statistical mechanics, and this equation is known to be derived from the Wasserstein gradient flow equation with a free energy. This gradient flow equation describes relaxation processes and is formulated on a Riemannian manifold. Meanwhile contact Hamiltonian systems are also known to describe relaxation processes. Hence a relation between these two equations is expected to be clarified, which gives a solid foundation in geometric statistical mechanics. In this paper a class of contact Hamiltonian systems is derived from a class of the Fokker–Planck equations on Riemannian manifolds. In the course of the derivation, the Fokker–Planck equation is shown to be written as a diffusion equation with a weighted Laplacian without any approximation, which enables to employ a theory of eigenvalue problems.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943443","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 : 2024-08-01DOI: 10.1088/1751-8121/ad6653
Bikash Bhattacharjya, Hermie Monterde, Hiranmoy Pal
A blow-up of n copies of a graph G is the graph obtained by replacing every vertex of G by an independent set of size n, where the copies of two vertices in G are adjacent in the blow-up if and only if they are adjacent in G. In this work, we characterize strong cospectrality, periodicity, perfect state transfer (PST) and pretty good state transfer (PGST) in blow-up graphs. We prove that if a blow-up admits PST or PGST, then n = 2. In particular, if G has an invertible adjacency matrix, then each vertex in a blow of two copies of G pairs up with a unique vertex to exhibit strong cospectrality. Under mild conditions, we show that periodicity (resp., almost periodicity) of a vertex in G guarantees PST (resp. PGST) between the two copies of the vertex in the blow-up. This allows us to construct new families of graphs with PST from graphs that do not admit PST. We also characterize PST and PGST in the blow-ups of complete graphs, paths, cycles and cones. Finally, while trees in general do not admit PST, we provide infinite families of stars and subdivided stars whose blow-ups admit PST.
一个图 G 的 n 个副本的炸开图是将 G 的每个顶点替换为大小为 n 的独立集合后得到的图，其中 G 中两个顶点的副本在炸开图中相邻，当且仅当它们在 G 中相邻。在这项工作中，我们描述了炸开图中的强共谱性、周期性、完美状态转移（PST）和相当好状态转移（PGST）。我们证明，如果炸开图允许 PST 或 PGST，那么 n = 2。特别是，如果 G 有一个可逆的邻接矩阵，那么两个 G 副本的炸开图中的每个顶点都会与一个唯一的顶点配对，从而表现出强共谱性。在温和的条件下，我们证明了 G 中一个顶点的周期性（或者说，几乎周期性）保证了该顶点的两个副本在炸开时的 PST（或者说 PGST）。这样，我们就能从不带 PST 的图中构造出具有 PST 的新图族。我们还描述了完整图、路径、循环和锥体炸开时的 PST 和 PGST 特性。最后，虽然树一般不包含 PST，但我们提供了星和细分星的无限族，它们的炸开都包含 PST。
{"title":"Quantum walks on blow-up graphs","authors":"Bikash Bhattacharjya, Hermie Monterde, Hiranmoy Pal","doi":"10.1088/1751-8121/ad6653","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6653","url":null,"abstract":"A blow-up of <italic toggle=\"yes\">n</italic> copies of a graph <italic toggle=\"yes\">G</italic> is the graph obtained by replacing every vertex of <italic toggle=\"yes\">G</italic> by an independent set of size <italic toggle=\"yes\">n</italic>, where the copies of two vertices in <italic toggle=\"yes\">G</italic> are adjacent in the blow-up if and only if they are adjacent in <italic toggle=\"yes\">G</italic>. In this work, we characterize strong cospectrality, periodicity, perfect state transfer (PST) and pretty good state transfer (PGST) in blow-up graphs. We prove that if a blow-up admits PST or PGST, then <italic toggle=\"yes\">n</italic> = 2. In particular, if <italic toggle=\"yes\">G</italic> has an invertible adjacency matrix, then each vertex in a blow of two copies of <italic toggle=\"yes\">G</italic> pairs up with a unique vertex to exhibit strong cospectrality. Under mild conditions, we show that periodicity (resp., almost periodicity) of a vertex in <italic toggle=\"yes\">G</italic> guarantees PST (resp. PGST) between the two copies of the vertex in the blow-up. This allows us to construct new families of graphs with PST from graphs that do not admit PST. We also characterize PST and PGST in the blow-ups of complete graphs, paths, cycles and cones. Finally, while trees in general do not admit PST, we provide infinite families of stars and subdivided stars whose blow-ups admit PST.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867968","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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