相关论文: Generalization of spectral bulk-boundary correspon…
We study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle $ \Omega \subset \mathbb{R}^3 $. From the Stratton-Chu integral representation, we derive a new representation formula when constant…
We propose new dipole and quadrupole indices for interacting insulators with point group symmetries. The proposed indices are defined in terms of many-body quantum multipole operators combined with the generator of the point group symmetry.…
We show that bulk quantities localized on a minimal surface homologous to a boundary region correspond in the CFT to operators that commute with the modular Hamiltonian associated with the boundary region. If two such minimal surfaces…
The Spin-Boson model describes a two-level quantum system that interacts with a second-quantized boson scalar field. Recently the relation between the integral kernel of the scattering matrix and the resonance in this model has been…
The bulk-boundary correspondence is a key concept in topological quantum materials. For instance, a quantum spin Hall insulator features a bulk insulating gap with gapless helical boundary states protected by the underlying Z2 topology.…
How to properly describe continuum thermodynamics of binary mixtures where each constituent has its own momentum? The Symmetric Hyperbolic Thermodynamically Consistent (SHTC) framework and Hamiltonian mechanics in the form of the General…
We present a linear coordinate transform to expand the solution of scattering and emission problems into a basis of forward and backward directional vector harmonics. The transform provides intuitive algebraic and geometric interpretations…
A bound state in the continuum (BIC) is an unusual localized state that is embedded in a continuum of extended states. Here, we present the general condition for BICs to arise from wave equation separability and show that the directionality…
This article surveys the research presented by the author at the MATRIX Institute workshop "Hyperbolic Differential Equations in Geometry and Physics" in April 2022. The work is centered about establishing rigorous mathematical statements…
We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative…
The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for…
Calogero-Sutherland models of type $BC_N$ are known to be relevant to the physics of one-dimensional quantum impurity effects. Here we represent certain correlation functions of these models in terms of generalized hypergeometric functions.…
We develop a general mathematical framework to study mixtures of different physical systems brought together on a discrete interface. Adapting work by M\u{a}ntoiu et al., we use an operator algebraic framework such that the bulk systems at…
In contrast to eigenvalue-based approaches, we formulate the bulk-boundary correspondence for two-dimensional non-Hermitian quadratic lattice Hamiltonians in terms of Toeplitz operators and singular values, which correctly capture the…
We establish a quantitative bulk-boundary correspondence in interacting topological insulators by relating many-body topological invariants to characteristic degeneracy structures in the entanglement spectrum. Focusing on generalized…
In this paper, we contribute to the mathematical foundations of the recently established theory of Spectrum Broadcast Structures (SBS). These are multipartite quantum states, encoding an operational notion of objectivity and exhibiting a…
The strong form of the AdS/CFT correspondence implies that the leading $N$ expressions for the connected correlation functions of the gauge invariant operators in the free ${\cal N}=4$ supersymmetric Yang-Mills theory with the gauge group…
We propose a new approach for constructing the late-time conformal boundary of quantum field theory in de Sitter spacetime. A boundary theory which consists of a continuous family of primary operators residing on unitary irreducible…
This paper is concerned with the physics of parametrized gapped quantum many-body systems, which can be viewed as a generalization of conventional topological phases of matter. In such systems, rather than considering a single Hamiltonian,…
Non-Hermitian systems characterized by suitable spatial distributions of gain and loss can exhibit "spectral singularities" in the form of zero-width resonances associated to real-frequency poles in the scattering operator. Here, we study…