Related papers: A Balian-Low Theorem for Subspaces
This paper is the second in a series of papers considering symmetry properties of a bosonic quantum system over an 2D graph, with continuous spins, in the spirit of the Mermin--Wagner theorem. Here we consider bosonic systems on…
In relativity, there is no absolute notion of simultaneity, because two clocks that are in different places can always be desynchronized by a Lorentz boost. Here, we explore the implications of this effect for the quantum theory of unstable…
We construct consistent brane-world Kaluza-Klein reductions involving the radion mode that measures the separation of the domain-wall branes. In these new examples, we can obtain matter supermultiplets coupled to supergravity on the brane,…
We consider convex monotone $C_0$-semigroups on a Banach lattice, which is assumed to be a Riesz subspace of a $\sigma$-Dedekind complete Banach lattice. Typical examples include the space of all bounded uniformly continuous functions and…
The problem of reconstructing a function from the magnitudes of its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This result also holds for frames that are possibly continuous…
We show that if the Gabor system $\{ g(x-t) e^{2\pi i s x}\}$, $t \in T$, $s \in S$, is an orthonormal basis in $L^2(\mathbb{R})$ and if the window function $g$ is compactly supported, then both the time shift set $T$ and the frequency…
In this work we study the dynamical generation of mass in the Lorentz-violating low-dimensional Super-Yang-Mills theory in the aether superspace coupled to a scalar matter. We also suggest that our studies can be applied for condensed…
We investigate the reproducing properties of Gabor systems within the context of expansible groups. These properties are established in terms of density conditions. The concept of density that we employ mirrors the well-known Beurling…
Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply…
Adiabatic approximations are a powerful tool for simplifying nonlinear quantum dynamics, and are applicable whenever a system exhibits a hierarchy of time scales. Current interest in small nonlinear quantum systems, such as few-mode…
The special theory of relativity teaches us that, although distinct inertial frames perceive the same dynamical laws, space and time intervals differ in value. We revisit the problem of time contraction using the paradigmatic model of a…
We derive the Ward-Takahashi identity and establish the gauge-invariant response theory for open quantum systems described by Lindbladians to show that particle-number conservation is not necessary to satisfy gauge invariance. We construct…
The article is devoted to the generalization of the second Bogolyubov's theorem to non-almost periodic dynamical systems. We prove the analog of the second Bogolyubov's theorem for recurrent or pseudo recurrent dynamical systems in Banach…
Gauge theories formulated in a space-time manifold that includes compact extra dimensions can show a nontrivial gauge structure. Depending on whether the gauge parameters propagate or not in the extra dimensions, two different Kaluza--Klein…
Recently it has been advocated [1] that for describing nature within the minimal symmetry requirement, certain subgroups of Lorentz group may play a fundamental role. One such group is E(2) which induces a Lie algebraic Non-Commutative…
We consider the spatially inhomogeneous Landau equation with soft potentials, including the case of Coulomb interactions. First, we establish the existence of solutions for a short time, assuming the initial data is in a fourth-order…
In the restricted setting of product phase space lattices, we give an alternate proof of P. Linnell's theorem on the finite linear independence of lattice Gabor systems in $L^2(\mathbb R^d)$. Our proof is based on a simple argument from the…
This paper extends the nonlinear ISS small-gain theorem to a large-scale time delay system composed of three or more subsystems. En route to proving this small-gain theorem for systems of differential equations with delays, a small-gain…
Shifted and modulated Gaussian functions play a vital role in the representation of signals. We extend the theory into a quaternionic setting, using two exponential kernels with two complex numbers. As a final result, we show that every…
The classical criterion for compactness in Banach spaces of functions can be reformulated into a simple tightness condition in the time-frequency domain. This description preserves more explicitly the symmetry between time and frequency…