相关论文: Time-dependent topological systems: A study of the…

In 1956, Bott in his celebrated paper on closed geodesics and Sturm intersection theory, proved an Index Iteration Formula for closed geodesics on Riemannian manifolds. Some years later, Ekeland improved this formula in the case of convex…

We use Bott periodicity to relate previously defined quantum classes to certain "exotic Chern classes" on $BU$. This provides an interesting computational and theoretical framework for some Gromov-Witten invariants connected with…

We study one-dimensional insulators obeying a chiral symmetry in the single-particle picture. The Fermi level is assumed to lie in a mobility gap. Topological indices are defined for infinite (bulk) or half-infinite (edge) systems, and it…

The quantum theory of indirect measurements in physical systems is studied. The example of an indirect measurement of an observable represented by a self-adjoint operator $\mathcal{N}$ with finite spectrum is analysed in detail. The…

We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…

For time series with long-range temporal dependence, inference for covariance and precision matrices is non-trivial. We propose a Berry-Esseen type Gaussian approximation result that gives a finite-sample bound for the Kolmogorov distance…

We study the nodes of the wavefunction overlap between ground states of a parameter-dependent Hamiltonian. These nodes are topological, and we can use them to analyze in a unifying way both equilibrium and dynamical quantum phase…

We present a general recipe to describe topological phase transitions in condensed matter systems with interactions. We show that topological invariants in the presence of interactions can be efficiently calculated by means of a…

In this paper, we extend the Hartman-Grobman theorem to systems perturbed with white noises. Let's recall that, in deterministic systems, the Hartman-Grobman theorem establishes the "topological equivalence" of the local phase portrait…

The Conley index of an isolated invariant set is a fundamental object in the study of dynamical systems. Here we consider smooth functions on closed submanifolds of Euclidean space and describe a framework for inferring the Conley index of…

In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully…

In this contribution we present an intrinsic description of time-variant Port Hamiltonian systems as they appear in modeling and control theory. This formulation is based on the splitting of the state bundle and the use of appropriate…

We develop a formalism to extend, simultaneously, the usual definition of bulk and edge indices from topological insulators to the case of a finite sample with open boundary conditions, and provide a physical interpretation of these…

Realizing topological insulators is of great current interest because of their remarkable properties and possible future applications. There are recent proposals, based on Floquet analyses, that one can generate topologically nontrivial…

In this paper, we present an algorithm for learning time-correlated measurement covariances for application in batch state estimation. We parameterize the inverse measurement covariance matrix to be block-banded, which conveniently…

Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define…

Quantum sensors based on matter-wave interferometry are promising candidates for high-precision gravimetry and inertial sensing in space. The favorable source for the coherent matter waves in these devices are Bose-Einstein condensates. A…

The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…

Topological invariants are global properties of the ground-state wave function, typically defined as winding numbers in reciprocal space. Over the years, a number of topological markers in real space have been introduced, allowing to map…

Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the possibility of measuring them in systems…