Related papers: Disordered Lieb-Robinson bounds in one dimension
We study the thick points of branching Brownian motion and branching random walk with a critical branching mechanism, focusing on the critical dimension $d = 4$. We determine the exponent governing the probability to hit a small ball with…
Motivated by a class of orbit problems in astrophysics, this paper considers solutions to Hill's equation with forcing strength parameters that vary from cycle to cycle. The results are generalized to include period variations from cycle to…
Robin boundary conditions are a natural consequence of employing Nitsche's method for imposing the kinematic velocity constraint at the fluid-solid interface. Loosely-coupled FSI schemes based on Dirichlet-Robin or Robin-Robin coupling have…
We study transport of interacting particles in weakly disordered media. Our one-dimensional system includes (i) disorder: the hopping rate governing the movement of a particle between two neighboring lattice sites is inhomogeneous, and (ii)…
Power corrections to exclusive processes are usually calculated using models for twist-four distribution amplitudes (DA) which are based on the leading-order terms in the conformal expansion. In this work we develop a different approach…
Statistical description of stochastic dynamics in highly unstable potentials is strongly affected by properties of divergent trajectories, that quickly leave meta-stable regions of the potential landscape and never return. Using ideas from…
The Lieb-Robinson bound (LRB) states that the range and strength of interactions between the constituents of a complex many-body system impose upper limits to how fast the signal can propagate. It manifests in a light cone-like growth of…
This article deals with the uniqueness and stability issues in the inverse problem of determining the unbounded potential of the Schr\"odinger operator in a bounded domain of dimension 3 or greater, endowed with Robin boundary condition,…
Recently, domain-uniform stabilizability and detectability has been the central assumption %in order robustness results on the to ensure robustness in the sense of exponential decay of spatially localized perturbations in optimally…
The propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance $r$ as a power law,…
Systems with local dynamics are characterized by a finite velocity of propagation of perturbations, known as the Lieb-Robinson velocity. On the other hand, irreducible stochastic processes drive states towards some unique fixed point.…
We present an application of the standard Langevin dynamics to the problem of weak coupling perturbative expansions for Lattice QCD. This method can be applied to the computation of the most general observables. In this preliminary work we…
We prove a Lieb-Robinson bound for lattice fermion models with polynomially decaying interactions, which can be used to show the locality of the quasi-local inverse Liouvillian. This allows us to prove automorphic equivalence and the local…
We study the delocalization dynamics of interacting disordered hard-core bosons for quasi-1D and 2D geometries, with system sizes and time scales comparable to state-of-the-art experiments. The results are strikingly similar to the 1D case,…
We study disordered XXZ spin chains in the Ising phase exhibiting droplet localization, a single cluster localization property we previously proved for random XXZ spin chains. It holds in an energy interval $I$ near the bottom of the…
We consider a Neumann problem for strictly convex variational functionals of linear growth. We establish the existence of minimisers among $\operatorname{W}^{1,1}$-functions provided that the domain under consideration is simply connected.…
We study the dynamics of bond-disordered Ising spin systems on random graphs with finite connectivity, using generating functional analysis. Rather than disorder-averaged correlation and response functions (as for fully connected systems),…
We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…
We present a theory of weak localization (WL) in the presence of generic spin-dependent fields, including any type of spin-orbit coupling, Zeeman fields, and non-homogeneous magnetic textures. We go beyond the usual diffusive approximation,…
We investigate population dynamics in N-level systems driven beyond the linear regime by a strong external field, which couples to the system through an operator with nonzero diagonal elements. As concrete example we consider the case of…