Speed limits and locality in many-body quantum dynamics

CFA Chen, A Lucas, C Yin - Reports on Progress in Physics, 2023 - iopscience.iop.org
We review the mathematical speed limits on quantum information processing in many-body
systems. After the proof of the Lieb–Robinson Theorem in 1972, the past two decades have …

The quantum -body problem

W Hunziker, IM Sigal - Journal of Mathematical Physics, 2000 - pubs.aip.org
This selective review is written as an introduction to the mathematical theory of the
Schrödinger equation for N particles. Characteristic for these systems are the cluster …

Resonances, radiation dam** and instabilitym in Hamiltonian nonlinear wave equations

A Soffer, MI Weinstein - Inventiones mathematicae, 1999 - Springer
We consider a class of nonlinear Klein-Gordon equations which are Hamiltonian and are
perturbations of linear dispersive equations. The unperturbed dynamical system has a …

Maximal speed for macroscopic particle transport in the Bose-Hubbard model

J Faupin, M Lemm, IM Sigal - Physical Review Letters, 2022 - APS
The Lieb-Robinson bound asserts the existence of a maximal propagation speed for the
quantum dynamics of lattice spin systems. Such general bounds are not available for most …

On modified scattering for 1D quadratic Klein–Gordon equations with non-generic potentials

H Lindblad, J Lührmann, W Schlag… - International …, 2023 - academic.oup.com
We consider the asymptotic behavior of small global-in-time solutions to a 1D Klein–Gordon
equation with a spatially localized, variable coefficient quadratic nonlinearity and a non …

Linear inviscid dam** and enhanced viscous dissipation of shear flows by using the conjugate operator method

E Grenier, TT Nguyen, F Rousset, A Soffer - Journal of Functional Analysis, 2020 - Elsevier
We study the large time behavior of solutions to two-dimensional Euler and Navier-Stokes
equations linearized about shear flows of the mixing layer type in the unbounded channel …

Asymptotics for 1D Klein-Gordon equations with variable coefficient quadratic nonlinearities

H Lindblad, J Lührmann, A Soffer - Archive for Rational Mechanics and …, 2021 - Springer
We initiate the study of the asymptotic behavior of small solutions to one-dimensional Klein-
Gordon equations with variable coefficient quadratic nonlinearities. The main discovery in …

On pointwise decay of linear waves on a Schwarzschild black hole background

R Donninger, W Schlag, A Soffer - Communications in Mathematical …, 2012 - Springer
We prove sharp pointwise t− 3 decay for scalar linear perturbations of a Schwarzschild black
hole without symmetry assumptions on the data. We also consider electromagnetic and …

Decay and Asymptotics for the One-Dimensional Klein--Gordon Equation with Variable Coefficient Cubic Nonlinearities

H Lindblad, J Luhrmann, A Soffer - SIAM Journal on Mathematical Analysis, 2020 - SIAM
We obtain sharp decay estimates and asymptotics for small solutions to the one-dimensional
Klein--Gordon equation with constant coefficient cubic and spatially localized, variable …

Light cones for open quantum systems

S Breteaux, J Faupin, M Lemm, DHO Yang… - arxiv preprint arxiv …, 2023 - arxiv.org
We consider Markovian open quantum dynamics (MOQD). We show that, up to small-
probability tails, the supports of quantum states evolving under such dynamics propagate …