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Showing papers in "Journal of Mathematical Physics in 2021"


Journal ArticleDOI
TL;DR: This article reformulated known exotic theories (including theories of fractons) on a Euclidean spacetime lattice, using the Villain approach, and then modified them to a convenient range of parameters.
Abstract: We reformulate known exotic theories (including theories of fractons) on a Euclidean spacetime lattice. We write them using the Villain approach, and then we modify them to a convenient range of parameters. The new lattice models are closer to the continuum limit than the original lattice versions. In particular, they exhibit many of the recently found properties of the continuum theories, including emergent global symmetries and surprising dualities. In addition, these new models provide a clear and rigorous formulation to the continuum models and their singularities. In Appendixes A–C, we use this approach to review the well-studied lattice models and their continuum limits. These include the XY-model, the ZN clock-model, and various gauge theories in diverse dimensions. This paper clarifies the relation between the condensed-matter and the high-energy views of these systems. It emphasizes the role of symmetries associated with the topology of field space, duality, and various anomalies.

53 citations


Journal ArticleDOI
TL;DR: In this paper, the authors derived the positivity of the modified logarithmic Sobolev constant associated with the dynamics of certain quantum systems from some clustering conditions on the Gibbs state of a local, commuting Hamiltonian.
Abstract: The mixing time of Markovian dissipative evolutions of open quantum many-body systems can be bounded using optimal constants of certain quantum functional inequalities, such as the modified logarithmic Sobolev constant. For classical spin systems, the positivity of such constants follows from a mixing condition for the Gibbs measure via quasi-factorization results for the entropy. Inspired by the classical case, we present a strategy to derive the positivity of the modified logarithmic Sobolev constant associated with the dynamics of certain quantum systems from some clustering conditions on the Gibbs state of a local, commuting Hamiltonian. In particular, we show that for the heat-bath dynamics of 1D systems, the modified logarithmic Sobolev constant is positive under the assumptions of a mixing condition on the Gibbs state and a strong quasi-factorization of the relative entropy.

28 citations


Journal ArticleDOI
TL;DR: In this paper, the authors define the operation of particle-hole conjugation as the tautological algebra automorphism that simply swaps single-fermion creation and annihilation operators, and construct its invariant lift to the Fock space.
Abstract: The term “particle–hole symmetry” is beset with conflicting meanings in contemporary physics. Conceived and written from a condensed-matter standpoint, the present paper aims to clarify and sharpen the terminology. In that vein, we propose to define the operation of “particle–hole conjugation” as the tautological algebra automorphism that simply swaps single-fermion creation and annihilation operators, and we construct its invariant lift to the Fock space. Particle–hole symmetries then arise for gapful or gapless free-fermion systems at half filling, as the concatenation of particle–hole conjugation with one or another involution that reverses the sign of the first-quantized Hamiltonian. We illustrate that construction principle with a series of examples including the Su–Schrieffer–Heeger model and the Kitaev–Majorana chain. For an enhanced perspective, we contrast particle–hole symmetries with the charge-conjugation symmetry of relativistic Dirac fermions. We go on to present two major applications in the realm of interacting electrons. For one, we offer a heuristic argument that the celebrated Haldane phase of antiferromagnetic quantum spin chains is adiabatically connected to a free-fermion topological phase protected by a particle–hole symmetry. For another, we review the recent proposal by Son [Phys. Rev. X 5, 031027 (2015)] for a particle–hole conjugation symmetric effective field theory of the half-filled lowest Landau level, and we comment on the emerging microscopic picture of the composite fermion.

28 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the Weyl tensor is divergence-free and the potential function of the concircular vector field is pointwise collinear with the velocity vector field of perfect fluid spacetime.
Abstract: This paper deals with the study of perfect fluid spacetimes. It is proven that a perfect fluid spacetime is Ricci recurrent if and only if the velocity vector field of perfect fluid spacetime is parallel and α = β. In addition, in a stiff matter perfect fluid Yang pure space with p + σ ≠ 0, the integral curves generated by the velocity vector field are geodesics. Moreover, it is shown that in a generalized Robertson–Walker perfect fluid spacetime, the Weyl tensor is divergence-free and the gradient of the potential function of the concircular vector field is pointwise collinear with the velocity vector field of perfect fluid spacetime. We also characterize the perfect fluid spacetimes whose Lorentzian metrics are Yamabe and gradient Yamabe solitons, respectively.

22 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that any polynomial tau function of the s-component KP and the BKP hierarchies can be interpreted as a zero-mode of an appropriate combinatorial generating function.
Abstract: We show that any polynomial tau-function of the s-component KP and the BKP hierarchies can be interpreted as a zero-mode of an appropriate combinatorial generating function As an application, we obtain explicit formulas for all polynomial tau-functions of these hierarchies in terms of Schur polynomials and Q-Schur polynomials, respectively We also obtain formulas for polynomial tau-functions of the reductions of the s-component KP hierarchy associated with partitions in s parts

22 citations


Journal ArticleDOI
TL;DR: Deng et al. as discussed by the authors considered the defocusing Hartree nonlinear Schrodinger equations on T3 with real-valued and even potential V and Fourier multiplier decaying such as |k|−β by relying on the method of random averaging operators.
Abstract: In this paper, we consider the defocusing Hartree nonlinear Schrodinger equations on T3 with real-valued and even potential V and Fourier multiplier decaying such as |k|−β By relying on the method of random averaging operators [Deng et al, arXiv:191008492 (2019)], we show that there exists β0, which is less than but close to 1, such that for β > β0, we have invariance of the associated Gibbs measure and global existence of strong solutions in its statistical ensemble In this way, we extend Bourgain’s seminal result [J Bourgain, J Math Pures Appl 76, 649–702 (1997)], which requires β > 2 in this case

21 citations


Journal ArticleDOI
TL;DR: In this paper, the ∂-dressing method is developed to study the three-component coupled Hirota (tcCH) equations, and the one-, two-, and three-soliton solutions are analyzed to discuss the dynamic phenomena of the tcCH equations.
Abstract: The ∂-dressing method is developed to study the three-component coupled Hirota (tcCH) equations. We first start from a ∂-problem and construct a new spectral problem. Based on the recursive operator, we successfully derive the tcCH hierarchy associated with the given spectral problem. In addition, the soliton solutions of the tcCH equations are first obtained via determining the spectral transform matrix in the ∂-problem. Finally, one-, two-, and three-soliton solutions are analyzed to discuss the dynamic phenomena of the tcCH equations. It is remarked that the interaction between solitons depends on whether the characteristic lines intersect.

20 citations


Journal ArticleDOI
TL;DR: In this article, the Friedrichs-Lee model of a two-level atom interacting with a structured boson field is generalized to singular atom-field couplings, and a characterization of its spectrum and resonances is provided.
Abstract: We show that the Friedrichs–Lee model, which describes the one-excitation sector of a two-level atom interacting with a structured boson field, can be generalized to singular atom–field couplings. We provide a characterization of its spectrum and resonances and discuss the inverse spectral problem.

20 citations


Journal ArticleDOI
TL;DR: In this article, a fresh look at the methods introduced by Boccato, Brennecke, Cenatiempo, and Schlein concerning the trapped Bose gas was presented, and a conceptually simple and concise proof of Bose-Einstein condensation in the Gross-Pitaevskii limit for small interaction potentials was given.
Abstract: We present a fresh look at the methods introduced by Boccato, Brennecke, Cenatiempo, and Schlein [Commun. Math. Phys. 359(3), 975–1026 (2018); Acta Math. 222(2), 219–335 (2019); Commun. Math. Phys. 376, 1311 (2020)] concerning the trapped Bose gas and give a conceptually very simple and concise proof of Bose–Einstein condensation in the Gross–Pitaevskii limit for small interaction potentials.

20 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the Fermi velocity vanishes for at least one α between 0.57 and 0.61 by rigorously justifying Tarnopolsky, Kruchkov, and Vishwanath (TKV)'s formal expansion of the velocity over a sufficiently large interval of α values.
Abstract: We consider the chiral model of twisted bilayer graphene introduced by Tarnopolsky, Kruchkov, and Vishwanath (TKV). TKV proved that for inverse twist angles α such that the effective Fermi velocity at the moire K point vanishes, the chiral model has a perfectly flat band at zero energy over the whole Brillouin zone. By a formal expansion, TKV found that the Fermi velocity vanishes at α ≈ 0.586. In this work, we give a proof that the Fermi velocity vanishes for at least one α between 0.57 and 0.61 by rigorously justifying TKV’s formal expansion of the Fermi velocity over a sufficiently large interval of α values. The idea of the proof is to project the TKV Hamiltonian onto a finite-dimensional subspace and then expand the Fermi velocity in terms of explicitly computable linear combinations of modes in the subspace while controlling the error. The proof relies on two propositions whose proofs are computer-assisted, i.e., numerical computation together with worst-case estimates on the accumulation of round-off error, which show that round-off error cannot possibly change the conclusion of computation. The propositions give a bound below on the spectral gap of the projected Hamiltonian, an Hermitian 80 × 80 matrix whose spectrum is symmetric about 0, and verify that two real 18-th order polynomials, which approximate the numerator of the Fermi velocity, take values with a definite sign when evaluated at specific values of α. Together with TKV’s work, our result proves the existence of at least one perfectly flat band of the chiral model.

18 citations


Journal ArticleDOI
TL;DR: It is proposed to study the Hessian metric of given functional in the space of probability space embedded with $L^2$--Wasserstein (optimal transport) metric, which contains and extends the classical Wasserstein metric.
Abstract: We propose to study the Hessian metric of a functional on the space of probability measures endowed with the Wasserstein-2 metric. We name it transport Hessian metric, which contains and extends the classical Wasserstein-2 metric. We formulate several dynamical systems associated with transport Hessian metrics. Several connections between transport Hessian metrics and mathematical physics equations are discovered. For example, the transport Hessian gradient flow, including Newton’s flow, formulates a mean-field kernel Stein variational gradient flow; the transport Hessian Hamiltonian flow of Boltzmann–Shannon entropy forms the shallow water equation; and the transport Hessian gradient flow of Fisher information leads to the heat equation. Several examples and closed-form solutions for transport Hessian distances are presented.

Journal ArticleDOI
TL;DR: In this paper, the authors construct global solutions to the incompressible Oldroyd-B model without damping on the stress tensor in Rn(n=2,3) without dampening the initial velocities.
Abstract: The present work is dedicated to the global solutions to the incompressible Oldroyd-B model without damping on the stress tensor in Rn(n=2,3) This result allows us to construct global solutions for a class of highly oscillating initial velocities The proof uses the special structure of the system Moreover, our theorem extends the previous result of Zhu [J Funct Anal 274, 2039–2060 (2018)] and covers the recent result of Chen and Hao [J Math Fluid Mech 21, 42 (2019)]

Journal ArticleDOI
TL;DR: In this article, the authors consider charge transport for interacting many-body systems with a gapped ground state subspace that is finitely degenerate and topologically ordered, and prove that the index is additive under composition of unitaries.
Abstract: We consider charge transport for interacting many-body systems with a gapped ground state subspace that is finitely degenerate and topologically ordered. To any locality-preserving, charge-conserving unitary that preserves the ground state space, we associate an index that is an integer multiple of 1/p, where p is the ground state degeneracy. We prove that the index is additive under composition of unitaries. This formalism gives rise to several applications: fractional quantum Hall conductance, a fractional Lieb–Schultz–Mattis (LSM) theorem that generalizes the standard LSM to systems where the translation-invariance is broken, and the interacting generalization of the Avron–Dana–Zak relation between the Hall conductance and the filling factor.

Journal ArticleDOI
TL;DR: Several techniques of generating random quantum channels, which act on the set of d-dimensional quantum states, are investigated in this article, and three approaches to the problem of sampling of quantum channels and show that they are mathematically equivalent.
Abstract: Several techniques of generating random quantum channels, which act on the set of d-dimensional quantum states, are investigated. We present three approaches to the problem of sampling of quantum channels and show that they are mathematically equivalent. We discuss under which conditions they give the uniform Lebesgue measure on the convex set of quantum operations and compare their advantages and computational complexity and demonstrate which of them is particularly suitable for numerical investigations. Additional results focus on the spectral gap and other spectral properties of random quantum channels and their invariant states. We compute the mean values of several quantities characterizing a given quantum channel, including its unitarity, the average output purity, and the 2-norm coherence of a channel, averaged over the entire set of the quantum channels with respect to the uniform measure. An ensemble of classical stochastic matrices obtained due to super-decoherence of random quantum stochastic maps is analyzed, and their spectral properties are studied using the Bloch representation of a classical probability vector.

Journal ArticleDOI
TL;DR: In this article, the authors investigate the most general form of the one-dimensional Dirac Hamiltonian HD in the presence of scalar and pseudoscalar potentials, and construct a quasi-Hamiltonian K, defined as the square of HD, to explore the consequences.
Abstract: We investigate the most general form of the one-dimensional Dirac Hamiltonian HD in the presence of scalar and pseudoscalar potentials. To seek embedding of supersymmetry (SUSY) in it, as an alternative procedure to directly employing the intertwining relations, we construct a quasi-Hamiltonian K, defined as the square of HD, to explore the consequences. We show that the diagonal elements of K under a suitable approximation reflect the presence of a superpotential, thus proving a useful guide in unveiling the role of SUSY. For illustrative purposes, we apply our scheme to the transformed one-dimensional version of the planar electron Hamiltonian under the influence of a magnetic field. We generate spectral solutions for a class of isochronous potentials.

Journal ArticleDOI
TL;DR: In this article, the Gauss hypergeometric differential equation determining the Stieltjes transform of the limiting density in the Jacobi case is identified, and the moments and covariances of monomial linear statistics are characterized through recurrence relations.
Abstract: In the classical β-ensembles of random matrix theory, setting β = 2α/N and taking the N → ∞ limit gives a statistical state depending on α. Using the loop equations for the classical β-ensembles, we study the corresponding eigenvalue density, its moments, covariances of monomial linear statistics, and the moments of the leading 1/N correction to the density. From earlier literature, the limiting eigenvalue density is known to be related to classical functions. Our study gives a unifying mechanism underlying this fact, identifying, in particular, the Gauss hypergeometric differential equation determining the Stieltjes transform of the limiting density in the Jacobi case. Our characterization of the moments and covariances of monomial linear statistics is through recurrence relations. We also extend recent work, which begins with the β-ensembles in the high-temperature limit and constructs a family of tridiagonal matrices referred to as α-ensembles, obtaining a random anti-symmetric tridiagonal matrix with i.i.d. (Independent Identically Distributed) gamma distributed random variables. From this, we can supplement analytic results obtained by Dyson in the study of the so-called type I disordered chain.

Journal ArticleDOI
TL;DR: In this article, the general structure of (2n + 1)-gon and 2n-simplex equations in direct sums of vector spaces is examined, and a construction for their solutions, parameterized by elements of the Grassmannian Gr(n+ 1, 2n+1).
Abstract: We consider polygon and simplex equations, of which the simplest nontrivial examples are pentagon (5-gon) and Yang–Baxter (2-simplex), respectively. We examine the general structure of (2n + 1)-gon and 2n-simplex equations in direct sums of vector spaces. Then, we provide a construction for their solutions, parameterized by elements of the Grassmannian Gr(n + 1, 2n + 1).

Journal ArticleDOI
TL;DR: In this paper, the reachability of linear and non-linear systems in the sense of the ψ-Hilfer pseudo-fractional derivative in g-calculus by means of the Mittag-Leffler functions (one and two parameters) was investigated.
Abstract: In this paper, we investigate the reachability of linear and non-linear systems in the sense of the ψ-Hilfer pseudo-fractional derivative in g-calculus by means of the Mittag–Leffler functions (one and two parameters). In this sense, two numerical examples are discussed in order to elucidate the investigated results.

Journal ArticleDOI
TL;DR: In this paper, the Cartan map is used to embed the Grassmannian GrV0(V+V*) of maximal isotropic subspaces of V + V*, with respect to the natural scalar product, into the projectivization of the exterior space Λ(V), and the Plucker map is shown to be equivalent to an identity of Cauchy-Binet type, expressing the determinants of square submatrices of a skew symmetric N × N matrix as bilinear sums over the Pfaffians of their principal minors.
Abstract: This work is motivated by the relation between the KP and BKP integrable hierarchies, whose τ-functions may be viewed as flows of sections of dual determinantal and Pfaffian line bundles over infinite dimensional Grassmannians. In finite dimensions, we show how to relate the Cartan map, which, for a vector space V of dimension N, embeds the Grassmannian GrV0(V+V*) of maximal isotropic subspaces of V + V*, with respect to the natural scalar product, into the projectivization of the exterior space Λ(V), and the Plucker map, which embeds the Grassmannian GrV(V + V*) of all N-planes in V + V* into the projectivization of ΛN(V + V*). The Plucker coordinates on GrV0(V+V*) are expressed bilinearly in terms of the Cartan coordinates, which are holomorphic sections of the dual Pfaffian line bundle Pf*→GrV0(V+V*,Q). In terms of affine coordinates on the big cell, this is equivalent to an identity of Cauchy–Binet type, expressing the determinants of square submatrices of a skew symmetric N × N matrix as bilinear sums over the Pfaffians of their principal minors.

Journal ArticleDOI
TL;DR: In this article, the authors give the definition of a double field theory algebroid as a curved L∞-algebra and show how implementation of the strong constraint of DFT theory can be formulated as an L ∞ algebra morphism.
Abstract: A double field theory algebroid (DFT algebroid) is a special case of the metric (or Vaisman) algebroid, shown to be relevant in understanding the symmetries of double field theory. In particular, a DFT algebroid is a structure defined on a vector bundle over doubled spacetime equipped with the C-bracket of double field theory. In this paper, we give the definition of a DFT algebroid as a curved L∞-algebra and show how implementation of the strong constraint of double field theory can be formulated as an L∞-algebra morphism. Our results provide a useful step toward coordinate invariant descriptions of double field theory and the construction of the corresponding sigma-model.

Journal ArticleDOI
TL;DR: In this paper, the integration problem of a C-bracket and a Vaisman (metric, pre-DFT) algebroid that are geometric structures of double field theory is analyzed.
Abstract: The integration problem of a C-bracket and a Vaisman (metric, pre-DFT) algebroid that are geometric structures of double field theory (DFT) is analyzed. We introduce a notion of a pre-rackoid as a global group-like object for an infinitesimal algebroid structure. We propose several realizations of pre-rackoid structures: One realization is that elements of a pre-rackoid are defined by cotangent paths along doubled foliations in a para-Hermitian manifold. Another realization is proposed as a formal exponential map of the algebroid of DFT. We show that the pre-rackoid reduces to a rackoid that is the integration of the Courant algebroid when the strong constraint of DFT is imposed. Finally, for a physical application, we show an implementation of the (pre-)rackoid in a three-dimensional topological sigma model.

Journal ArticleDOI
TL;DR: In this paper, the authors considered the swelling problem in porous elastic soils with fluid saturation and showed that the energy associated with the system is dissipative, and established the stability of the system in the exponential way.
Abstract: In this article, we consider the swelling problem in porous elastic soils with fluid saturation. We study the well-posedness of the problem based on the semigroup theory, show that the energy associated with the system is dissipative, and establish the stability of the system in the exponential way. To guarantee the stability of the systems, we consider both viscous damping and the time delay term acting on the first equation of the system.

Journal ArticleDOI
TL;DR: In this paper, a theory for the reduction in Lagrangian systems subjected to external forces, which are invariant under the action of a Lie group, is presented. But this theory is restricted to Rayleigh dissipation functions, i.e., external forces derived from a dissipation function.
Abstract: This paper is devoted to the study of mechanical systems subjected to external forces in the framework of symplectic geometry. We obtain Noether’s theorem for Lagrangian systems with external forces, among other results regarding symmetries and conserved quantities. We particularize our results for the so-called Rayleigh dissipation, i.e., external forces that are derived from a dissipation function, and illustrate them with some examples. Moreover, we present a theory for the reduction in Lagrangian systems subjected to external forces, which are invariant under the action of a Lie group.

Journal ArticleDOI
TL;DR: In this article, an invariant difference scheme for equations in Eulerian coordinates with arbitrary bottom topography is constructed and the developed invariant conservative difference schemes are verified numerically using examples of flow with various bottom topographies.
Abstract: The one-dimensional shallow water equations in Eulerian coordinates are considered. Relations between symmetries and conservation laws for the potential form of the equations and symmetries and conservation laws in Eulerian coordinates are shown. An invariant difference scheme for equations in Eulerian coordinates with arbitrary bottom topography is constructed. It possesses all the finite-difference analogs of the conservation laws. Some bottom topographies require moving meshes in Eulerian coordinates, which are stationary meshes in mass Lagrangian coordinates. The developed invariant conservative difference schemes are verified numerically using examples of flow with various bottom topographies.

Journal ArticleDOI
TL;DR: In this paper, the authors considered the longitudinal dynamical two-point function of the XXZ quantum spin chain in the antiferromagnetic massive regime and derived a series representation based on the form factors of the quantum transfer matrix of the model.
Abstract: We consider the longitudinal dynamical two-point function of the XXZ quantum spin chain in the antiferromagnetic massive regime. It has a series representation based on the form factors of the quantum transfer matrix of the model. The nth summand of the series is a multiple integral accounting for all n-particle–n-hole excitations of the quantum transfer matrix. In previous works, the expressions for the form factor amplitudes appearing under the integrals were either again represented as multiple integrals or in terms of Fredholm determinants. Here, we obtain a representation which reduces, in the zero-temperature limit, essentially to a product of two determinants of finite matrices whose entries are known special functions. This will facilitate the further analysis of the correlation function.

Journal ArticleDOI
TL;DR: In this article, the authors study the Hamiltonian describing two anyons moving in a plane in the presence of an external magnetic field and identify a one-parameter family of self-adjoint realizations of the corresponding Schrodinger operator.
Abstract: We study the Hamiltonian describing two anyons moving in a plane in the presence of an external magnetic field and identify a one-parameter family of self-adjoint realizations of the corresponding Schrodinger operator. We also discuss the associated model describing a quantum particle immersed in a magnetic field with a local Aharonov–Bohm singularity. For a special class of magnetic potentials, we provide a complete classification of all possible self-adjoint extensions.

Journal ArticleDOI
Wilhelm Schlag1
TL;DR: In this paper, the authors introduced some of the basic mechanisms relating the behavior of the spectral measure of Schrodinger operators near zero energy to the long-term decay and dispersion of the associated Schrodings and wave evolutions.
Abstract: This paper introduces some of the basic mechanisms relating the behavior of the spectral measure of Schrodinger operators near zero energy to the long-term decay and dispersion of the associated Schrodinger and wave evolutions. These principles are illustrated by means of the author’s work on decay of Schrodinger and wave equations under various types of perturbations, including those of the underlying metric. In particular, we consider local decay of solutions to the linear Schrodinger and wave equations on curved backgrounds that exhibit trapping. A particular application is waves on a Schwarzschild black hole spacetime. We elaborate on Price’s law of local decay that accelerates with the angular momentum, which has recently been settled by Hintz, also in the much more difficult Kerr black hole setting. While the author’s work on the same topic was conducted ten years ago, the global semiclassical representation techniques developed there have recently been applied by Krieger, Miao, and the author [“A stability theory beyond the co-rotational setting for critical wave maps blow up,” arXiv:2009.08843 (2020)] to the nonlinear problem of stability of blowup solutions to critical wave maps under non-equivariant perturbations.

Journal ArticleDOI
TL;DR: In this paper, it was shown that chargequantization of the M-theory C-field in J-twisted Cohomotopy implies the emergence of a higher Sp(1)-gauge field on single heterotic M5-branes, which exhibits a world-volume Stringc2-structure.
Abstract: We show that charge-quantization of the M-theory C-field in J-twisted Cohomotopy implies the emergence of a higher Sp(1)-gauge field on single heterotic M5-branes, which exhibits a worldvolume Stringc2-structure.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the min-cut function of any weighted hypergraph can be approximated by the entropies of quantum states known as stabilizer states.
Abstract: The von Neumann entropy of pure quantum states and the min-cut function of weighted hypergraphs are both symmetric submodular functions. In this article, we explain this coincidence by proving that the min-cut function of any weighted hypergraph can be approximated (up to an overall rescaling) by the entropies of quantum states known as stabilizer states. We do so by constructing a novel ensemble of random quantum states, built from tensor networks, whose entanglement structure is determined by a given hypergraph. This implies that the min-cuts of hypergraphs are constrained by quantum entropy inequalities, and it follows that the recently defined hypergraph cones are contained in the quantum stabilizer entropy cones, which confirms a conjecture made in the recent literature.

Journal ArticleDOI
TL;DR: In this paper, it was shown that any static, vacuum, and "asymptotically isotropic" n + 1-dimensional spacetime that possesses what we call an "equipotential" and "outward directed" photon surface is isometric to the Schwarzschild spacetime of the same mass using a uniqueness result obtained by the first author.
Abstract: Photon surfaces are timelike totally umbilic hypersurfaces of Lorentzian spacetimes. In the first part of this paper, we locally characterize all possible photon surfaces in a class of static spherically symmetric spacetimes that includes (exterior) Schwarzschild, Reissner–Nordstrom, and Schwarzschild–anti de Sitter in n + 1 dimensions. In the second part, we prove that any static, vacuum, and “asymptotically isotropic” n + 1-dimensional spacetime that possesses what we call an “equipotential” and “outward directed” photon surface is isometric to the Schwarzschild spacetime of the same (necessarily positive) mass using a uniqueness result obtained by the first author.