相关论文: Fractional revivals through R\'enyi uncertainty re…

We derive exact relations between the Renyi entanglement entropies and the particle number fluctuations of spatial connected regions in systems of N noninteracting fermions in arbitrary dimension. We prove that the asymptotic large-N…

In a quantum revival, a localized wavepacket re-forms or "revives" into a compact reincarnation of itself long after it has spread in an unruly fashion over a region restricted only by the potential energy. This is a purely quantum…

Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep…

Paraxial wave packets with discrete spatial, temporal, or spatiotemporal spectra are known to undergo periodic axial revivals on propagation in either free space or linear transparent, weakly dispersive media. Such spectacular revivals,…

Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…

In this article, we give characterization for existence of quantum fractional revival in unitary Cayley graph utilizing adjacency matrix Hamiltonian. Unitary Cayley graph $X=( Z_n, S)$ is a special graph as connection set $S \subseteq Z_n$…

A new method for the study of resonant behavior - using wave-packet dynamics - is presented, based on the powerful window operator technique. The method is illustrated and quantified by application to the astrophysically-important example…

Uncertainty relations for a pair of arbitrary measurements and for a single measurement are posed in the form of inequalities using the Renyi entropies. The formulation deals with discrete observables. Both the relations with…

We initiate the study of approximate quantum fractional revival in graphs, a generalization of pretty good quantum state transfer in graphs. We give a complete characterization of approximate fractional revival in a graph in terms of the…

We investigate the large-time asymptotics of nonlinear diffusion equations $u_t = \Delta u^p$ in dimension $n \ge 1$, in the exponent interval $p > n/(n+2)$, when the initial datum $u_0$ is of bounded second moment. Precise rates of…

The long-term dynamical evolution is a crucial point in recent planetary research. Although the amount of observational data is continuously growing and the precision allows us to obtain accurate planetary orbits, the canonical stability…

The interplay of quantum and classical fluctuations in the vicinity of a quantum critical point (QCP) gives rise to various regimes or phases with distinct quantum character. In this work, we show that the R\'enyi entropy is a precious tool…

An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum…

In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…

For a particle in a box, the operator $-i\partial_x$ is not self-adjoint and thus does not qualify as the physical momentum. As a result, in general the Ehrenfest theorem is violated. Based upon a recently developed new concept for a…

Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide…

In this paper, we tackle a critical issue in nonparametric inference for systems of interacting particles on Riemannian manifolds: the identifiability of the interaction functions. Specifically, we define the function spaces on which the…

Non-reciprocal interactions are present in many systems out of equilibrium. The rate of entropy production is a measure that quantifies the time irreversibility of a system, and thus how far it is from equilibrium. In this work, we…

In the course of the last decades entropic uncertainty relations have attracted much attention not only due to their fundamental role as manifestation of non-classicality of quantum mechanics, but also as major tools for applications of…

The dynamics of a single quantum state embedded in one or several (quasi-)continua is one of the most studied phenomena in quantum mechanics. In this work we investigate its discrete analogue and consider short and long time dynamics based…