Related papers: Lieb-Robinson bounds in classical oscillating latt…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
We show that excitations of interacting quantum particles in lattice models always propagate with a finite speed of sound. Our argument is simple yet general and shows that by focusing on the physically relevant observables one can…
We prove global existence and uniqueness of dynamics on the quasi-local algebra $\mathcal{A}$ of a quantum lattice system for spatially growing derivations $\mathcal{L}_\Phi = \sum_x [ \Phi_x , \cdot ]$. Existing results assume that the…
This paper extends the tools of C*-algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories. We introduce the approach first in the simple case of finite systems. Then we apply this…
Classical integrable Hamiltonian systems generated by elements of the Poisson commuting ring of spectral invariants on rational coadjoint orbits of the loop algebra $\wt{\gr{gl}}^{+*}(2,{\bf R})$ are integrated by separation of variables in…
Rotating waves are a fascinating feature of a wide array of complex systems, particularly those arising in the study of many chemical and biological processes. With many rigorous mathematical investigations of rotating waves relying on the…
We consider a collisionless ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove local-in-time existence…
Based on the assumption that time evolves only in one direction and mechanical systems can be described by Lagrangeans, a dynamical C*-algebra is presented for non-relativistic particles at atomic scales. Without presupposing any…
The resolvent algebra is a new C*-algebra of the canonical commutation relations of a boson field given by Buchholz-Grundling. We study analytic properties of quasi-free dynamics on the resolvent algebra. Subsequently we consider a…
A physical system is said to satisfy a thermal area law if the mutual information between two adjacent regions in the Gibbs state is controlled by the area of their boundary. Thermal area laws have been derived for systems with bounded…
Global existence and boundedness of classical solutions are shown for a parabolic-elliptic chemotaxis system with local sensing when the motility function is assumed to be unbounded at infinity. The cornerstone of the proof is the…
Strongly long-range interacting quantum systems---those with interactions decaying as a power-law $1/r^{\alpha}$ in the distance $r$ on a $D$-dimensional lattice for $\alpha\le D$---have received significant interest in recent years. They…
In this work, we investigate how quickly local perturbations propagate in interacting boson systems with Bose-Hubbard-type Hamiltonians. In general, these systems have unbounded local energies, and arbitrarily fast information propagation…
The relational framework of canonical quantum gravity with non-ultralocal constraints is explored. After demonstrating the absence of anomalies, a spatially discretized version of the relational framework is introduced. This allows the…
We review various bounds concerning out-of-equilibrium dynamics in few-level and many-body quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical…
In non-relativistic quantum theories the Lieb-Robinson bound defines an effective light cone with exponentially small tails outside of it. In this work we use it to derive a bound for the time evolution of the correlation function of two…
We give a general existence result for interacting particle systems with local interactions and bounded jump rates but noncompact state space at each site. We allow for jump events at a site that affect the state of its neighbours. We give…
Unitary dynamics with a strict causal cone (or "light cone") have been studied extensively, under the name of quantum cellular automata (QCAs). In particular, QCAs in one dimension have been completely classified by an index theory.…
We start presenting an $L^{\infty}$-gradient bound for solutions to non-homogeneous $p$-Laplacean type systems and equations, via suitable non-linear potentials of the right hand side. Such a bound implies a Lorentz space characterization…
In this paper we discuss mechanical systems with inequality constraints. We demonstrate how such constraints can be taken into account by proper modification of the action which describes the original unconstrained dynamics. To illustrate…