Related papers: Time-frequency shift invariance of Gabor spaces ge…

We consider stochastic dynamics of lattice systems with finite local state space, possibly at low temperature, and possibly non-reversible. We assume the additional regularity properties on the dynamics: a) There is at least one stationary…

We examine the diffraction properties of lattice dynamical systems of algebraic origin. It is well-known that diverse dynamical properties occur within this class. These include different orders of mixing (or higher-order correlations), the…

In this paper, we obtain a sharp Garliardo-Nirenberg inequality on integer lattices and characterize its rigidity. Moreover, as a consequence of the sharp Garliardo-Nirenberg inequality, we obtain sharp logarithmic Sobolev inequalities on…

An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…

In time series classification and regression, signals are typically mapped into some intermediate representation used for constructing models. Since the underlying task is often insensitive to time shifts, these representations are required…

We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the coincidence site lattices of a shifted square lattice by…

We consider irreversible translation-invariant interacting particle systems on the $d$-dimensional cubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy…

In this paper we connect the well established discrete frame theory of generalized shift invariant systems to a continuous frame theory. To do so, we let $\Gamma_j$, $j \in J$, be a countable family of closed, co-compact subgroups of a…

This paper focuses on the invariance control problem for discrete-time switched nonlinear systems. The proposed approach computes controlled invariant sets in a finite number of iterations and directly yields a partition-based invariance…

We show that a sufficient density condition for Gabor systems with Hermite functions over lattices is not sufficient in general. This follows from a result on how zeros of the Zak transform determine the frame property of integer…

It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as…

Graviton loop corrections to observables in de Sitter space often lead to infrared divergences. We show that these infrared divergences are resolved by the spontaneous breaking of de Sitter invariance.

The space rotation invariance hypothesis is examined. The basic space-time properties and the physical object description from this point of view are considered. An $\omega$-invariance as an approximation of the space rotation invariance…

Lattice gauge theories (LGTs) are one of the most fundamental subjects in many-body physics, and has recently attracted considerable research interests in quantum simulations. Here we experimentally investigate the emergent $\mathbb{Z}_2$…

Diffeomorphism invariance is a feature that gets sometimes highlighted as something with profound implications in the physics of spacetime. Moreover, it is often wrongly associated exclusively with General Relativity. The fact that…

In this paper we consider invariant Matsumoto metrics which are induced by invariant Riemannian metrics and invariant vector fields on homogeneous spaces then we give the flag curvature formula of them. Also we study the special cases of…

I review recent work on massive higher (s>1) spins in constant curvature (deSitter) spaces. Some of the novel properties that emerge are: partial masslessness and new local gauge invariances, unitarily forbidden ranges of mass, correlation…

Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with…

Model sets (also called cut and project sets) are generalizations of lattices. Here we show how the self-similarities of model sets are a natural replacement for the group of translations of a lattice. This leads us to the concept of…

Using a \emph{gedanken} experiment providing presumably a minimal inaccuracy the uncertainty contributions to the space-time measurement are precisely evaluated for clock and mirror respectively. The resulting expression of minimal…