Publications related to Insight into the eigenmodes of plasmonic nanoclusters based on the Green's tensor method

Rank-Adaptive Time Integration Of Tree Tensor Networks

A rank-adaptive integrator for the approximate solution of high-order tensor differential equations by tree tensor networks is proposed and analyzed. In a recursion from the leaves to the root, the integrator updates bases and then evolves connection tenso ...

SIAM PUBLICATIONS2023

Low-Rank Tensor Methods for High-Dimensional Problems

Christoph Max Strössner

In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

EPFL2023

Mutual information for low-rank even-order symmetric tensor estimation

Nicolas Macris, Jean François Emmanuel Barbier, Clément Dominique Luneau

We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method orig ...

OXFORD UNIV PRESS2021

Continuous dissipative phase transitions with or without symmetry breaking

Fabrizio Minganti

The paradigm of second-order phase transitions (PTs) induced by spontaneous symmetry breaking (SSB) in thermal and quantum systems is a pillar of modern physics that has been fruitfully applied to out-of-equilibrium open quantum systems. Dissipative phase ...

IOP Publishing Ltd2021

Complements to Mugge and Friedel's Theory of Twinning

Cyril Cayron

The crystallography of twinning is based on the concepts of simple shear and obliquity introduced by Mugge, Mallard and Friedel at the turn of the last century, with tensor mathematics later developed by Bilby, Bevis and Crocker in the 1960s. We propose a ...

2020

Mutual Information for Low-Rank Even-Order Symmetric Tensor Factorization

Nicolas Macris, Jean François Emmanuel Barbier, Clément Dominique Luneau

We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its mutual information when the tensor is of even order. The proof uses the adaptive interpolation method, for which rank-on ...

IEEE2019

Tensor Robust Pca On Graphs

Pierre Vandergheynst, Nauman Shahid, Francesco Grassi

We propose a graph signal processing framework to overcome the computational burden of Tensor Robust PCA (TRPCA). Our framework also serves as a convex alternative to graph regularized tensor factorization methods. Our method is based on projecting a tenso ...

IEEE2019

Multilinear Low-Rank Tensors on Graphs & Applications

Pierre Vandergheynst, Nauman Shahid, Francesco Grassi

We propose a new framework for the analysis of low- rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the classical low-rank S ...

2016

Preconditioned Low-Rank Riemannian Optimization For Linear Systems With Tensor Product Structure

Daniel Kressner, Michael Maximilian Steinlechner

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number ...

Siam Publications2016

Topological Aspects of Symmetry Breaking in Triangular-Lattice Ising Antiferromagnets

Frédéric Mila, Andrew James Smerald

Using a specially designed Monte Carlo algorithm with directed loops, we investigate the triangular lattice Ising antiferromagnet with coupling beyond the nearest neighbors. We show that the first-order transition from the stripe state to the paramagnet ca ...

2016

Charge transport in superionic and melted AgI under a magnetic field studied via molecular dynamics

Sara Bonella, Luca Gagliardi

Charge transport in AgI subject to an external magnetic field is studied via computer simulations. We demonstrate that a recently developed algorithm can effectively complement problematic experiments to detect the ionic Hall effect, and identify previousl ...

Amer Physical Soc2016

Direct Comparison of Second Harmonic Generation and Two-Photon Photoluminescence from Single Connected Gold Nanodimers

Olivier Martin, Jérémy Butet

In this article we compare the two-photon photoluminescence and second harmonic generation from single connected gold nanodimers. Analyzing the particle size-dependent nonlinear optical spectra and performing excitation polarization resolved measurements u ...

American Chemical Society2016

Zoology of condensed matter: framids, ordinary stuff, extra-ordinary stuff

Riccardo Rattazzi

We classify condensed matter systems in terms of the spacetime symmetries they spontaneously break. In particular, we characterize condensed matter itself as any state in a Poincare-invariant theory that spontaneously breaks Lorentz boosts while preserving ...

Springer Nature2015

Spectral signatures of high-symmetry quantum dots and effects of symmetry breaking

Marc-André Dupertuis, Elyahou Kapon, Daniel Oberli, Alok Rudra, Valentina Troncale

High symmetry epitaxial quantum dots (QDs) with three or more symmetry planes provide a very promising route for the generation of entangled photons for quantum information applications. The great challenge to fabricate nanoscopic high symmetry QDs is furt ...

Iop Publishing Ltd2015

Dynamical Approximation By Hierarchical Tucker And Tensor-Train Tensors

We extend results on the dynamical low-rank approximation for the treatment of time-dependent matrices and tensors (Koch and Lubich; see [SIAM J. Matrix Anal. Appl., 29 (2007), pp. 434-454], [SIAM J. Matrix Anal. Appl., 31 (2010), pp. 2360-2375]) to the re ...

Society for Industrial and Applied Mathematics2013

Symmetry Elevation and Symmetry Breaking: Keys to Describe and Explain Excitonic Complexes in Semiconductor Quantum Dots

Marc-André Dupertuis, Elyahou Kapon, Daniel Oberli, Alok Rudra

The results of a group theoretical analysis of the excitonic fine structure are presented and compared with spectroscopic data on single quantum dots. The spectral features reveal the signatures of a symmetry higher than the crystal symmetry (C-3v). A cons ...

Amer Inst Physics, 2 Huntington Quadrangle, Ste 1No1 D, Melville, Ny 11747-4501 Usa2011

Low-rank tensor Krylov subspace methods for parametrized linear systems

Christine Tobler, Daniel Kressner

We consider linear systems A(alpha)x(alpha) - b(alpha) depending on possibly many parameters alpha = (alpha(1), ... , alpha(p)). Solving these systems simultaneously for a standard discretization of the parameter range would require a computational effort ...

Society for Industrial and Applied Mathematics2011

Simultaneous Dimerization and SU(4) Symmetry Breaking of 4-Color Fermions on the Square Lattice

Frédéric Mila, Karlo Penc

Using infinite projected entangled-pair states, exact diagonalization, and flavor-wave theory, we show that the SU(4) Heisenberg model undergoes a spontaneous dimerization on the square lattice, in contrast with its SU(2) and SU(3) counterparts, which deve ...

2011

Anharmonic order-parameter oscillations and lattice coupling in strongly driven 1T-TaS2 and TbTe3 charge-density-wave compounds: A multiple-pulse femtosecond laser spectroscopy study

Helmuth Berger, László Forró

The anharmonic response of charge-density wave (CDW) order to strong laser-pulse perturbations in 1T-TaS2 and TbTe3 is investigated by means of multiple-pump-pulse time-resolved femtosecond optical spectroscopy. We observe remarkable anharmonic effects hit ...

2011

Reduction theory for symmetry breaking with applications to nematic systems

François Gay-Balmaz, Cesare Tronci

We formulate Euler-Poincare and Lagrange-Poincare equations for systems with broken symmetry. We specialize the general theory to present explicit equations of motion for nematic systems, ranging from single nematic molecules to biaxial liquid crystals. Th ...

2010