Related papers: Theory of Periodic Sequence: Bridging Time-Domain …
Spherically embedded time series are time series with values naturally residing on or can be equivalently mapped to the sphere. Despite their ubiquity in diverse scientific fields, these data frequently exhibit complex non-stationarity…
Using the time periodic ABCD parameters, an expression for the dispersion relation of space-time modulated structures is obtained. The relation is valid for general structures even when the spatial granularity is comparable to the operating…
Periodic and semi periodic patterns are very common in nature. In this paper we introduce a topological toolbox aiming in detecting and quantifying periodicity. The presented technique is of a general nature and may be employed wherever…
Many new possibilities to observe and use novel physical effects are discovered at so called exceptional points (EPs). This is done by using parity-time (PT) -symmetric non-Hermitian systems and balancing gains and losses. When combined…
Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large…
We study the periodic properties of sequences of quantum channels sampled from an ergodic stochastic process satisfying a natural irreducibility condition. We relate these periodic properties to certain global spectral data defined by the…
Electromagnetic pulses are typically treated as space-time (or space-frequency) separable solutions of Maxwell's equations, where spatial and temporal (spectral) dependence can be treated separately. In contrast to this traditional…
Long-period systems and superlattices, with additional periodicity, have new effects on the energy spectrum and wave functions. Most approaches adjust theories for infinite systems, which is acceptable for large but not small number of unit…
In recent experiments, time-dependent periodic fields are used to create exotic topological phases of matter with potential applications ranging from quantum transport to quantum computing. These nonequilibrium states, at high driving…
This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…
Energy conversion in a physical system requires time-translation invariance breaking according to Noether's theorem. Closely associated with this symmetry-conservation relation, the frequencies of electromagnetic waves are found to be…
Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…
Time series refer to a series of data points indexed in time order, which can be found in various fields, e.g., transportation, healthcare, and finance. Accurate time series forecasting can enhance optimization planning and decision-making…
Terahertz time-domain spectroscopy (THz-TDS) provides a non-invasive and label-free method for probing the internal structure and electromagnetic response of materials. Numerical simulation of THz-TDS can help understanding wave-matter…
A process-theoretic approach to electrodynamics based on persistent Kac-type stochastic processes is developed. Finite-velocity stochastic propagation is taken as primary, while relativistic wave equations arise as emergent descriptions…
Terahertz time-domain spectroscopy (THz-TDS) is a powerful tool for extracting optical and electrical parameters, as well as probing internal structures and surface morphology of materials. However, conventional simulation techniques, such…
In this work we provide a mathematical framework to describe the periodically time variant (PTV) linear systems. We study their frequency-domain features to estimate the output bandwidth, a necessary value to obtain a suitable digital…
This monograph introduces key concepts and problems in the new research area of Periodic Geometry and Topology for materials applications.Periodic structures such as solid crystalline materials or textiles were previously classified in…
Both statistical phase space (SPS), which is $\Gamma = T^*\mathbb R^{3N}$ of $N$-body particle system, and kinetic theory phase space (KTPS), which is the cotangent bundle $T^*\mathcal P(\Gamma)$ of the probability space $\mathcal…
A review of the present state of investigations of the pseudospin-electron model (PEM), which is used in the theory of strongly correlated electron systems, is given. The model is used to describe the systems with the locally anharmonic…