Related papers: A simple position operator for periodic systems
We discuss a general combinatorial framework for operator ordering problems by applying it to the normal ordering of the powers and exponential of the boson number operator. The solution of the problem is given in terms of Bell and Stirling…
This paper reviews recent results on the classification of partial differential operators modeling bulk and interface topological insulators in Euclidean spaces. Our main objective is the mathematical analysis of the unusual,…
We study operator algebras arising from monomial ideals in the ring of polynomials in noncommuting variables, through the apparatus of subproduct systems and C*-correspondences. We provide a full comparison amongst the related operator…
We describe some applications of group- and bundle-theoretic methods in solid state physics, showing how symmetries lead to a proof of the localization of electrons in gapped crystalline solids, as e.g. insulators and semiconductors. We…
The one-dimensional parabolic potential barrier dealt with in an earlier paper is re-examined from the point of view of operator methods, for the purpose of getting generalized Fock spaces.
Using a three-frequency one-dimensional kicked rotor experimentally realized with a cold atomic gas, we study the transport properties at the critical point of the metal-insulator Anderson transition. We accurately measure the…
Topological states of matter were first introduced for non-interacting fermions on an infinite uniform lattice. Since then, substantial effort has been made to generalize these concepts to more complex settings. Recently, local markers have…
In this paper we introduce and study several new Hilbert-type operators acting between the weighted Fock spaces. We provide some sufficient and necessary conditions for the boundedness and compactness of certain Hilbert-type operators from…
Interior-boundary conditions (IBCs) have been suggested as a possibility to circumvent the problem of ultraviolet divergences in quantum field theories. In the IBC approach, particle creation and annihilation is described with the help of…
We study a non-stabilizerness resource theory for operators, which is dual to that describing states. We identify that the stabilizer R\'enyi entropy analog in operator space is a good magic monotone satisfying the usual conditions while…
We conduct the first detailed analysis in quantum information of recently derived operator relations from the study of quantum one-way local operations and classical communications (LOCC). We show how operator structures such as operator…
We prove the complete spectral and the strong dynamical Anderson localization in a two-particle random Schr\"odinger operators with the Poisson potential. The results apply with sufficiently weak interaction between the particle system.
Periodic boundary conditions are commonly applied in molecular dynamics simulations in the microcanonical (NVE), canonical (NVT) and isothermal-isobaric (NpT) ensembles. In their simplest application, a biological system of interest is…
Robotics demands simulation that can reason about the diversity of real-world physical interactions, from rigid to deformable objects and fluids. Current simulators address this by stitching together multiple subsolvers for different…
We exhibit limit-periodic Schr\"odinger operators that are uniformly localized in the strongest sense possible. That is, for these operators there are uniform exponential decay rates such that every element of the hull has a complete set of…
This paper compares Tensor Boundary Conditions (TBCs), which were introduced to model multilayered dielectric structures, with Generalized Sheet Transition Conditions (GSTCs), which have been recently used to model metasurfaces. It shows…
We first consider two types of localizations of singular integral operators of convolution type, and show, under mild decay and smoothness conditions on the auxiliary functions, that their boundedness on the local Hardy space…
We apply the exchange operator formalism in polar coordinates to a one-parameter family of three-body problems in one dimension and prove the integrability of the model both with and without the oscillator potential. We also present exact…
In the earlier unitary-model-operator approach (UMOA), one-body correlations have been taken into account approximately by the diagonalization of unitary-transformed Hamiltonians in the $0p0h$ and $1p1h$ space. With this prescription, the…
We study concircular tensors in spaces of constant curvature and then apply the results obtained to the problem of the orthogonal separation of the Hamilton-Jacobi equation on these spaces. Any coordinates which separate the geodesic…