Concept
Rigged Hilbert space
Related publications (49)
Quantum circuits for solving local fermion-to-qubit map- pings
Giuseppe Carleo, Jannes Willy E. Nys
Local Hamiltonians of fermionic systems on a lattice can be mapped onto local qubit Hamiltonians. Maintaining the lo-cality of the operators comes at the ex-pense of increasing the Hilbert space with auxiliary degrees of freedom. In order to retrieve the l ...
VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF2023TimeEvolver: A program for time evolution with improved error bound
We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...
ELSEVIER2022Spectral analysis for transmission eigenvalue problems with and without the complementing conditions
The interior transmission eigenvalue problem is a system of partial differential equations equipped with Cauchy data on the boundary: the transmission conditions. This problem appears in the inverse scattering theory for inhomogeneous media when, for some ...
EPFL2022Adaptive Approximation of Shapes
We consider scalar-valued shape functionals on sets of shapes which are small perturbations of a reference shape. The shapes are described by parameterizations and their closeness is induced by a Hilbert space structure on the parameter domain. We justify ...
TAYLOR & FRANCIS INC2021Many-body localization in a fragmented Hilbert space
We study many-body localization (MBL) in a pair-hopping model exhibiting strong fragmentation of the Hilbert space. We show that several Krylov subspaces have both ergodic statistics in the thermodynamic limit and a dimension that scales much slower than t ...
2021A kernel‐based change detection method to map shifts in phytoplankton communities measured by flow cytometry
Automated, ship-board flow cytometers provide high-resolution maps of phytoplankton composition over large swaths of the world's oceans. They therefore pave the way for understanding how environmental conditions shape community structure. Identification o ...
2021The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations
Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod
Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreten ess of the set of eigenvalues of the transmission problem and studied their locations. In this paper, we establish ...
2021Gelfand pairs admit an Iwasawa decomposition
Every Gelfand pair (G, K) admits a decomposition G = K P, where P < G is an amenable subgroup. In particular, the Furstenberg boundary of G is homogeneous. Applications include the complete classification of non-positively curved Gelfand pairs, relying on ...
SPRINGER HEIDELBERG2020Convergences of Regularized Algorithms and Stochastic Gradient Methods with Random Projections
We study the least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space as a special case. We rst investigate regularized algorithms adapted to a projection operator on a closed subspace ...
2020A reflected forward-backward splitting method for monotone inclusions involving Lipschitzian operators
In this paper, we propose a novel splitting method for finding a zero point of the sum of two monotone operators where one of them is Lipschizian. The weak convergence the method is proved in real Hilbert spaces. Applying the proposed method to composite m ...
2020