Dmitri Finkelshtein, Yuri Kondratiev, Peter Kuchling, Eugene Lytvynov, Maria Joao Oliveira
We study analysis on the cone of discrete Radon measures over a locally compact Polish space $X$. We discuss probability measures on the cone and the corresponding correlation measures and correlation functions on the sub-cone of finite discrete Radon measures over $X$. For this, we consider on the cone an analogue of the harmonic analysis on the configuration space developed in [12]. We also study elements of the difference calculus on the cone: we introduce discrete birth-and-death gradients and study the corresponding Dirichlet forms; finally, we discuss a system of polynomial functions on the cone which satisfy the binomial identity.
{"title":"Analysis on the cone of discrete Radon measures","authors":"Dmitri Finkelshtein, Yuri Kondratiev, Peter Kuchling, Eugene Lytvynov, Maria Joao Oliveira","doi":"arxiv-2312.03537","DOIUrl":"https://doi.org/arxiv-2312.03537","url":null,"abstract":"We study analysis on the cone of discrete Radon measures over a locally\u0000compact Polish space $X$. We discuss probability measures on the cone and the\u0000corresponding correlation measures and correlation functions on the sub-cone of\u0000finite discrete Radon measures over $X$. For this, we consider on the cone an\u0000analogue of the harmonic analysis on the configuration space developed in [12].\u0000We also study elements of the difference calculus on the cone: we introduce\u0000discrete birth-and-death gradients and study the corresponding Dirichlet forms;\u0000finally, we discuss a system of polynomial functions on the cone which satisfy\u0000the binomial identity.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545969","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}
Abhijit Chakraborty, Carlos R. Ordóñez, Gustavo Valdivia-Mera
In this article, we follow the framework given in the article Physica A, 158, pg 58-63 (1989) by R. Laflamme to derive the thermofield double state for a causal diamond using the Euclidean path integral formalism, and subsequently derive the causal diamond temperature. The interpretation of the physical and fictitious system in the thermofield double state arises naturally from the boundary conditions of the fields defined on the Euclidean sections of the cylindrical background geometry $S^{1}_{beta}times mathbb{R}$, where $beta$ defines the periodicity of the Euclidean time coordinate and $S^{1}_{beta}$ is the one-dimensional sphere (circle). The temperature detected by a static diamond observer at $x=0$ matches with the thermofield double temperature derived via this path integral procedure.
{"title":"Path integral derivation of the thermofield double state in causal diamonds","authors":"Abhijit Chakraborty, Carlos R. Ordóñez, Gustavo Valdivia-Mera","doi":"arxiv-2312.03541","DOIUrl":"https://doi.org/arxiv-2312.03541","url":null,"abstract":"In this article, we follow the framework given in the article Physica A, 158,\u0000pg 58-63 (1989) by R. Laflamme to derive the thermofield double state for a\u0000causal diamond using the Euclidean path integral formalism, and subsequently\u0000derive the causal diamond temperature. The interpretation of the physical and\u0000fictitious system in the thermofield double state arises naturally from the\u0000boundary conditions of the fields defined on the Euclidean sections of the\u0000cylindrical background geometry $S^{1}_{beta}times mathbb{R}$, where $beta$\u0000defines the periodicity of the Euclidean time coordinate and $S^{1}_{beta}$ is\u0000the one-dimensional sphere (circle). The temperature detected by a static\u0000diamond observer at $x=0$ matches with the thermofield double temperature\u0000derived via this path integral procedure.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545815","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}
Georgios Fotopoulos, Nikos I. Karachalios, Vassilis Koukouloyannis, Paris Kyriazopoulos, Kostas Vetas
The study of nonlinear Schr"odinger-type equations with nonzero boundary conditions define challenging problems both for the continuous (partial differential equation) or the discrete (lattice) counterparts. They are associated with fascinating dynamics emerging by the ubiquitous phenomenon of modulation instability. In this work, we consider the discrete nonlinear Schr"odinger equation with linear gain and nonlinear loss. For the infinite lattice supplemented with nonzero boundary conditions which describe solutions decaying on the top of a finite background, we give a rigorous proof that for the corresponding initial-boundary value problem, solutions exist for any initial condition, if and only if, the amplitude of the background has a precise value $A_*$ defined by the gain-loss parameters. We argue that this essential property of this infinite lattice can't be captured by finite lattice approximations of the problem. Commonly, such approximations are defined by lattices with periodic boundary conditions or as it is shown herein, by a modified problem closed with Dirichlet boundary conditions. For the finite dimensional dynamical system defined by the periodic lattice, the dynamics for all initial conditions are captured by a global attractor. Analytical arguments corroborated by numerical simulations show that the global attractor is trivial, defined by a plane wave of amplitude $A_*$. Thus, any instability effects or localized phenomena simulated by the finite system can be only transient prior the convergence to this trivial attractor. Aiming to simulate the dynamics of the infinite lattice as accurately as possible, we study the dynamics of localized initial conditions on the constant background and investigate the potential impact of the global asymptotic stability of the background with amplitude $A_*$ in the long-time evolution of the system.
{"title":"The discrete nonlinear Schrödinger equation with linear gain and nonlinear loss: the infinite lattice with nonzero boundary conditions and its finite dimensional approximations","authors":"Georgios Fotopoulos, Nikos I. Karachalios, Vassilis Koukouloyannis, Paris Kyriazopoulos, Kostas Vetas","doi":"arxiv-2312.03683","DOIUrl":"https://doi.org/arxiv-2312.03683","url":null,"abstract":"The study of nonlinear Schr\"odinger-type equations with nonzero boundary\u0000conditions define challenging problems both for the continuous (partial\u0000differential equation) or the discrete (lattice) counterparts. They are\u0000associated with fascinating dynamics emerging by the ubiquitous phenomenon of\u0000modulation instability. In this work, we consider the discrete nonlinear\u0000Schr\"odinger equation with linear gain and nonlinear loss. For the infinite\u0000lattice supplemented with nonzero boundary conditions which describe solutions\u0000decaying on the top of a finite background, we give a rigorous proof that for\u0000the corresponding initial-boundary value problem, solutions exist for any\u0000initial condition, if and only if, the amplitude of the background has a\u0000precise value $A_*$ defined by the gain-loss parameters. We argue that this\u0000essential property of this infinite lattice can't be captured by finite lattice\u0000approximations of the problem. Commonly, such approximations are defined by\u0000lattices with periodic boundary conditions or as it is shown herein, by a\u0000modified problem closed with Dirichlet boundary conditions. For the finite\u0000dimensional dynamical system defined by the periodic lattice, the dynamics for\u0000all initial conditions are captured by a global attractor. Analytical arguments\u0000corroborated by numerical simulations show that the global attractor is\u0000trivial, defined by a plane wave of amplitude $A_*$. Thus, any instability\u0000effects or localized phenomena simulated by the finite system can be only\u0000transient prior the convergence to this trivial attractor. Aiming to simulate\u0000the dynamics of the infinite lattice as accurately as possible, we study the\u0000dynamics of localized initial conditions on the constant background and\u0000investigate the potential impact of the global asymptotic stability of the\u0000background with amplitude $A_*$ in the long-time evolution of the system.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545816","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}
Vladimir Al. Osipov, Niclas Krieger, Thomas Guhr, Boris Gutkin
We consider the problem of local correlations in the kicked, dual-unitary coupled maps on D-dimensional lattices. We demonstrate that for D>=2, fully dual-unitary systems exhibit ultra-local correlations: the correlations between any pair of operators with local support vanish in a finite number of time steps. In addition, for $D=2$, we consider the partially dual-unitary regime of the model, where the dual-unitarity applies to only one of the two spatial directions. For this case, we show that correlations generically decay exponentially and provide an explicit formula for the correlation function between the operators supported on two and four neighbouring sites.
我们考虑了 D 维晶格上被踢的双单元耦合映射中的局部相关性问题。我们证明，对于 D>=2，完全双单元系统表现出超局域相关性：具有局域支持的任何一对算子之间的相关性在有限的时间步数内消失。此外，对于 $D=2$，我们考虑了模型的部分双统一体系，即双统一性只适用于两个空间方向中的一个。对于这种情况，我们证明了相关性一般呈指数衰减，并提供了两个和四个相邻位点上支持的算子之间的相关函数的明确公式。
{"title":"Local correlations in partially dual-unitary lattice models","authors":"Vladimir Al. Osipov, Niclas Krieger, Thomas Guhr, Boris Gutkin","doi":"arxiv-2312.03445","DOIUrl":"https://doi.org/arxiv-2312.03445","url":null,"abstract":"We consider the problem of local correlations in the kicked, dual-unitary\u0000coupled maps on D-dimensional lattices. We demonstrate that for D>=2, fully\u0000dual-unitary systems exhibit ultra-local correlations: the correlations between\u0000any pair of operators with local support vanish in a finite number of time\u0000steps. In addition, for $D=2$, we consider the partially dual-unitary regime of\u0000the model, where the dual-unitarity applies to only one of the two spatial\u0000directions. For this case, we show that correlations generically decay\u0000exponentially and provide an explicit formula for the correlation function\u0000between the operators supported on two and four neighbouring sites.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545810","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}
We present a framework that enables to write a family of convex approximations of complex contact models. Within this framework, we show that we can incorporate well established and experimentally validated contact models such as the Hunt & Crossley model. Moreover, we show how to incorporate Coulomb's law and the principle of maximum dissipation using a regularized model of friction. Contrary to common wisdom that favors the use of rigid contact models, our convex formulation is robust and performant even at high stiffness values far beyond that of materials such as steel. Therefore, the same formulation enables the modeling of compliant surfaces such as rubber gripper pads or robot feet as well as hard objects. We characterize and evaluate our approximations in a number of tests cases. We report their properties and highlight limitations. Finally, we demonstrate robust simulation of robotic tasks at interactive rates, with accurately resolved stiction and contact transitions, as required for meaningful sim-to-real transfer. Our method is implemented in the open source robotics toolkit Drake.
{"title":"A Theory of Irrotational Contact Fields","authors":"Alejandro Castro, Xuchen Han, Joseph Masterjohn","doi":"arxiv-2312.03908","DOIUrl":"https://doi.org/arxiv-2312.03908","url":null,"abstract":"We present a framework that enables to write a family of convex\u0000approximations of complex contact models. Within this framework, we show that\u0000we can incorporate well established and experimentally validated contact models\u0000such as the Hunt & Crossley model. Moreover, we show how to incorporate\u0000Coulomb's law and the principle of maximum dissipation using a regularized\u0000model of friction. Contrary to common wisdom that favors the use of rigid\u0000contact models, our convex formulation is robust and performant even at high\u0000stiffness values far beyond that of materials such as steel. Therefore, the\u0000same formulation enables the modeling of compliant surfaces such as rubber\u0000gripper pads or robot feet as well as hard objects. We characterize and\u0000evaluate our approximations in a number of tests cases. We report their\u0000properties and highlight limitations. Finally, we demonstrate robust simulation of robotic tasks at interactive\u0000rates, with accurately resolved stiction and contact transitions, as required\u0000for meaningful sim-to-real transfer. Our method is implemented in the open\u0000source robotics toolkit Drake.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138555558","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}
Baran Bayraktaroglu, Konstantin Izyurov, Tuomas Virtanen, Christian Webb
We prove bosonization identities for the scaling limits of the critical Ising correlations in finitely-connected planar domains, expressing those in terms of correlations of the compactified Gaussian free field. This, in particular, yields explicit expressions for the Ising correlations in terms of domain's period matrix, Green's function, harmonic measures of boundary components and arcs, or alternatively, Abelian differentials on the Schottky double. Our proof is based on a limiting version of a classical identity due to D.~Hejhal and J.~Fay relating SzegH{o} kernels and Abelian differentials on Riemann surfaces, and a systematic use of operator product expansions both for the Ising and the bosonic correlations.
{"title":"Bosonization of primary fields for the critical Ising model on multiply connected planar domains","authors":"Baran Bayraktaroglu, Konstantin Izyurov, Tuomas Virtanen, Christian Webb","doi":"arxiv-2312.02960","DOIUrl":"https://doi.org/arxiv-2312.02960","url":null,"abstract":"We prove bosonization identities for the scaling limits of the critical Ising\u0000correlations in finitely-connected planar domains, expressing those in terms of\u0000correlations of the compactified Gaussian free field. This, in particular,\u0000yields explicit expressions for the Ising correlations in terms of domain's\u0000period matrix, Green's function, harmonic measures of boundary components and\u0000arcs, or alternatively, Abelian differentials on the Schottky double. Our proof is based on a limiting version of a classical identity due to\u0000D.~Hejhal and J.~Fay relating SzegH{o} kernels and Abelian differentials on\u0000Riemann surfaces, and a systematic use of operator product expansions both for\u0000the Ising and the bosonic correlations.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525270","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}
We clarify the structure obtained in H'elein and Vey's proposition for a variational principle for the Einstein-Cartan gravitation formulated on a frame bundle starting from a structure-less differentiable 10-manifold. The obtained structure is locally equivalent to a frame bundle which we term "generalised frame bundle". In the same time, we enrich the model with a Dirac spinor coupled to the Einstein-Cartan spacetime. The obtained variational equations generalise the usual Einstein-Cartan-Dirac field equations in that they are shown to imply the usualy field equations when the generalised frame bundle is a standard frame bundle.
{"title":"Physics and Geometry from a Lagrangian: Dirac Spinors on a Generalised Frame Bundle","authors":"Jérémie Pierard de Maujouy","doi":"arxiv-2312.03163","DOIUrl":"https://doi.org/arxiv-2312.03163","url":null,"abstract":"We clarify the structure obtained in H'elein and Vey's proposition for a\u0000variational principle for the Einstein-Cartan gravitation formulated on a frame\u0000bundle starting from a structure-less differentiable 10-manifold. The obtained\u0000structure is locally equivalent to a frame bundle which we term \"generalised\u0000frame bundle\". In the same time, we enrich the model with a Dirac spinor\u0000coupled to the Einstein-Cartan spacetime. The obtained variational equations\u0000generalise the usual Einstein-Cartan-Dirac field equations in that they are\u0000shown to imply the usualy field equations when the generalised frame bundle is\u0000a standard frame bundle.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545812","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}
Simran Singh, Massimo Cipressi, Francesco Di Renzo
We present a numerical calculation of the Lee-Yang and Fisher zeros of the 2D Ising model using multi-point Pad'{e} approximants. We perform simulations for the 2D Ising model with ferromagnetic couplings both in the absence and in the presence of a magnetic field using a cluster spin-flip algorithm. We show that it is possible to extract genuine signature of Lee Yang and Fisher zeros of the theory through the poles of magnetization and specific heat, using multi-point Pad'{e} method. We extract the poles of magnetization using Pad'{e} approximants and compare their scaling with known results. We verify the circle theorem associated to the well known behaviour of Lee Yang zeros. We present our finite volume scaling analysis of the zeros done at $T=T_c$ for a few lattice sizes, extracting to a very good precision the (combination of) critical exponents $beta delta$. The computation at the critical temperature is performed after the latter has been determined via the study of Fisher zeros, thus extracting both $beta_c$ and the critical exponent $nu$. Results already exist for extracting the critical exponents for the Ising model in 2 and 3 dimensions making use of Fisher and Lee Yang zeros. In this work, multi-point Pad'{e} is shown to be competitive with this respect and thus a powerful tool to study phase transitions.
{"title":"Exploring Lee-Yang and Fisher Zeros in the 2D Ising Model through Multi-Point Padé Approximants","authors":"Simran Singh, Massimo Cipressi, Francesco Di Renzo","doi":"arxiv-2312.03178","DOIUrl":"https://doi.org/arxiv-2312.03178","url":null,"abstract":"We present a numerical calculation of the Lee-Yang and Fisher zeros of the 2D\u0000Ising model using multi-point Pad'{e} approximants. We perform simulations for\u0000the 2D Ising model with ferromagnetic couplings both in the absence and in the\u0000presence of a magnetic field using a cluster spin-flip algorithm. We show that\u0000it is possible to extract genuine signature of Lee Yang and Fisher zeros of the\u0000theory through the poles of magnetization and specific heat, using multi-point\u0000Pad'{e} method. We extract the poles of magnetization using Pad'{e}\u0000approximants and compare their scaling with known results. We verify the circle\u0000theorem associated to the well known behaviour of Lee Yang zeros. We present\u0000our finite volume scaling analysis of the zeros done at $T=T_c$ for a few\u0000lattice sizes, extracting to a very good precision the (combination of)\u0000critical exponents $beta delta$. The computation at the critical temperature\u0000is performed after the latter has been determined via the study of Fisher\u0000zeros, thus extracting both $beta_c$ and the critical exponent $nu$. Results\u0000already exist for extracting the critical exponents for the Ising model in 2\u0000and 3 dimensions making use of Fisher and Lee Yang zeros. In this work,\u0000multi-point Pad'{e} is shown to be competitive with this respect and thus a\u0000powerful tool to study phase transitions.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545813","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}
Zi-Jian Li, Gabriel Cardoso, Emil J. Bergholtz, Qing-Dong Jiang
We show that the perturbation of the Su-Schrieffer-Heeger chain by a localized lossy defect leads to higher-order exceptional points (HOEPs). Depending on the location of the defect, third- and fourth-order exceptional points (EP3s & EP4s) appear in the space of Hamiltonian parameters. On the one hand, they arise due to the non-Abelian braiding properties of exceptional lines (ELs) in parameter space. Namely, the HOEPs lie at intersections of mutually non-commuting ELs. On the other hand, we show that such special intersections happen due to the fact that the delocalization of edge states, induced by the non-Hermitian defect, hybridizes them with defect states. These can then coalesce together into an EP3. When the defect lies at the midpoint of the chain, a special symmetry of the full spectrum can lead to an EP4. In this way, our model illustrates the emergence of interesting non-Abelian topological properties in the multiband structure of non-Hermitian perturbations of topological phases.
我们的研究表明，局部有损缺陷对苏-施里弗-希格链的扰动会导致高阶异常点（HOEPs）。根据缺陷的位置，哈密顿参数空间会出现三阶和四阶异常点（EP3s & EP4s）。一方面，它们是由于参数空间中例外线（EL）的非阿贝尔编织特性而产生的。也就是说，HOEPs 位于互不换向的 EL 的交点上。另一方面，我们证明了这种特殊交集的发生是由于非赫米提缺陷引起的边缘态的非局域化，使它们与缺陷态杂交。然后，这些态会凝聚成一个 EP3。当缺陷位于链的中点时，全谱的特殊对称性会导致 EP4。通过这种方式，我们的模型说明了在拓扑相的非ermitian扰动的多带结构中出现了有趣的非阿贝尔拓扑特性。
{"title":"Braids and Higher-order Exceptional Points from the Interplay Between Lossy Defects and Topological Boundary States","authors":"Zi-Jian Li, Gabriel Cardoso, Emil J. Bergholtz, Qing-Dong Jiang","doi":"arxiv-2312.03054","DOIUrl":"https://doi.org/arxiv-2312.03054","url":null,"abstract":"We show that the perturbation of the Su-Schrieffer-Heeger chain by a\u0000localized lossy defect leads to higher-order exceptional points (HOEPs).\u0000Depending on the location of the defect, third- and fourth-order exceptional\u0000points (EP3s & EP4s) appear in the space of Hamiltonian parameters. On the one\u0000hand, they arise due to the non-Abelian braiding properties of exceptional\u0000lines (ELs) in parameter space. Namely, the HOEPs lie at intersections of\u0000mutually non-commuting ELs. On the other hand, we show that such special\u0000intersections happen due to the fact that the delocalization of edge states,\u0000induced by the non-Hermitian defect, hybridizes them with defect states. These\u0000can then coalesce together into an EP3. When the defect lies at the midpoint of\u0000the chain, a special symmetry of the full spectrum can lead to an EP4. In this\u0000way, our model illustrates the emergence of interesting non-Abelian topological\u0000properties in the multiband structure of non-Hermitian perturbations of\u0000topological phases.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545817","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}
Trace-free Einstein gravity is a theory of gravity that is an alternative to general relativity, wherein the cosmological constant arises as an integration constant. However, there are no fully diffeomorphism-invariant action principles available that lead to the equations of motion of this theory. Unimodular gravity comes close to this idea, but it relies on action principles that are invariant only under volume-preserving diffeomorphisms. We present a real $BF$-type action principle for trace-free Einstein gravity that is fully diffeomorphism-invariant and does not require any unimodular condition or nondynamical fields. We generalize this action principle by giving another one involving a free parameter.
{"title":"Diffeomorphism-invariant action principles for trace-free Einstein gravity","authors":"Merced Montesinos, Diego Gonzalez","doi":"arxiv-2312.03062","DOIUrl":"https://doi.org/arxiv-2312.03062","url":null,"abstract":"Trace-free Einstein gravity is a theory of gravity that is an alternative to\u0000general relativity, wherein the cosmological constant arises as an integration\u0000constant. However, there are no fully diffeomorphism-invariant action\u0000principles available that lead to the equations of motion of this theory.\u0000Unimodular gravity comes close to this idea, but it relies on action principles\u0000that are invariant only under volume-preserving diffeomorphisms. We present a\u0000real $BF$-type action principle for trace-free Einstein gravity that is fully\u0000diffeomorphism-invariant and does not require any unimodular condition or\u0000nondynamical fields. We generalize this action principle by giving another one\u0000involving a free parameter.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545971","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}
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