Related papers: Spectral Dimension from Nonlocal Dynamics on Causa…
We study fractal dimension properties of singular Jacobi operators. We prove quantitative lower spectral/quantum dynamical bounds for general operators with strong repetition properties and controlled singularities. For analytic…
We calculate the spectral dimension for a nonperturbative lattice approach to quantum gravity, known as causal dynamical triangulations (CDT), showing that the dimension of spacetime smoothly decreases from approximately 4 on large distance…
The scattering matrix which describes low-energy, non-relativistic scattering of spin-1/2 fermions interacting via finite-range potentials can be obtained from a geometric action principle in which space and time do not appear explicitly…
Pendulum-like dynamics is a universal motif across many areas of physics, underlying systems ranging from classical nonlinear oscillators to superconducting qubits and cold-atom tunneling platforms. Here we present an exact frequency-domain…
We investigate the causal structure of two-sheeted space-times using the tools of Lorentzian spectral triples. We show that the noncommutative geometry of these spaces allows for causal relations between the two sheets. The computation is…
This paper is concerned with the quantum theory of noncommutative scalar fields in two dimensional space time. It is shown that the noncommutativity originates from the the deformation of symplectic structures. The quantization is performed…
In this paper we investigate, through numerical studies, the dynamical evolutions encoded in a linear one-dimensional nonlocal equation arising in peridynamcs. The different propagation regimes ranging from the hyperbolic to the dispersive,…
We report an investigation of the Snyder noncommutative spacetime and of some of its most natural generalizations, also looking at them as a powerful tool for comparing different notions of dimensionality of a quantum spacetime. It is known…
We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum…
Non-relativistic quantum mechanical scattering from an inverse square potential in two spatial dimensions leads to a novel representation of the Bernoulli numbers.
Different approaches to quantum gravity generally predict that the dimension of spacetime at the fundamental level is not 4. The principal tool to measure how the dimension changes between the IR and UV scales of the theory is the spectral…
In this short note, we derive dimension formulas for spaces of Drinfeld cusp forms corresponding to harmonic cocycles invariant under the group $\mathrm{SL}_2(\mathbb{F}_q[t])$ and with values in absolutely irreducible…
We introduce the notion of angular values for deterministic linear difference equations and random linear cocycles. We measure the principal angles between subspaces of fixed dimension as they evolve under nonautonomous or random linear…
We explore the phenomenon of unidirectional invisibility in two dimensions, examine its optical realizations, and discuss its three-dimensional generalization. In particular we construct an infinite class of unidirectionally invisible…
The superselection sectors of two classes of scalar bilocal quantum fields in D>=4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective…
When one applies a type of non-Hermitian effect, constant imaginary vector potential, to disordered systems, delocalization is induced even in two or lower dimension. By using the non-Hermitian induced transition as a probe, We propose a…
Recently, we pointed out that on a class on non exactly decimable fractals two different parameters are required to describe diffusive and vibrational dynamics. This phenomenon we call dynamical dimension splitting is related to the lack of…
We show that the spectral dimension on non-generic branched polymer models with susceptibility exponent $\gamma$ is given by $2/(1+\gamma)$. For those models with negative $\gamma$ we find that the spectral dimension is 2.
We study the multifractal analysis of dimension spectrum for almost additive potential in a class of one dimensional non-uniformly hyperbolic dynamic systems and prove that the irregular set has full Hausdroff dimension.
We study the symmetry of the class of nonlocal models which includes the nonlocal extension of the Pais-Uhlenbeck oscillator. As a consequence, we obtain an infinite dimensional symmetry algebra, containing the Virasoro algebra, which can…