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Linear Canonical Transformations (LCTs) are known in signal processing and optics as the generalization of certain useful integral transforms. In quantum theory, they can be identified as the linear transformations which keep invariant the…
Audio signal processing frequently requires time-frequency representations and in many applications, a non-linear spacing of frequency-bands is preferable. This paper introduces a framework for efficient implementation of invertible signal…
Quantum computers, with parallel computing and entanglement effects, excel in cryptography analysis and big data processing. However, they are not fully developed yet, and their performance needs further evaluation. Traditional computer…
In this work, we analyze the effect of transmission line dynamics on grid-forming control for inverter-based AC power systems. In particular, we investigate a dispatchable virtual oscillator control (dVOC) strategy that was recently…
A classical linear oscillator is treated in the small amplitude limit so that it will be approximately relativistic. The oscillator involves a charge particle in a linear potential in classical zero-point radiation. It is found that the…
Power-electronics-based converters are being considerably employed through the power system to interconnect multiple heterogeneous electrical layers. Furthermore, the intrinsic versatility to play with the converter network topology is…
Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work…
Power transforms, such as the Box-Cox transform and Tukey's ladder of powers, are a fundamental tool in mathematics and statistics. These transforms are primarily used for normalizing and standardizing datasets, effectively by raising…
This \textquoteleft research-survey' is meant for beginners in the studies of integrable systems. Here we outline some analytical methods for dealing with a class of nonlinear partial differential equations. We pay special attention to…
We investigate the relationship between two kinds of ground-state local convertibility and quantum phase transitions in XY model. The local operations and classical communications (LOCC) convertibility is examined by the majorization…
Recently the general linear transformation for point rotation coordinate frames was considered. A distinguishing feature of the frame, in contrast to the Cartesian one, is the existence of the rotation axis at every point. The frame…
We consider generic pure $n$-qubit states and a general class of pure states of arbitrary dimensions and arbitrarily many subsystems. We characterize those states which can be reached from some other state via Local Operations assisted by…
The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…
The main challenge in visible light communications (VLC) is the low modulation bandwidth of light-emitting diodes (LEDs). This forms a barrier towards achieving high data rates. Moreover, the implementation of high order modulation schemes…
We discuss here phase transitions in quantum field theory in the context of vacuum realignment through an explicit construction. Vacuum destabilisation may occur through a scalar attaining a nonzero expectation value, or through a…
We consider the constrained zero modes found in the application of discrete light-cone quantization (DLCQ) to the nonperturbative solution of quantum field theories. These modes are usually neglected for simplicity, but we show that their…
Continuous phase transitions in equilibrium statistical mechanics were successfully described 50 years ago with the development of the renormalization group framework. This framework was initially developed in the context of phase…
Integral transformations are useful mathematical tool to work out signals and wave-packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory, in particular from quantum…
We study phase coherent transport in a single channel system using the scattering matrix approach. It is shown that identical vanishing of the transmission amplitude occurs generically in quasi-1D systems if the time-reversal is a good…
In the present paper we extend the multiparameter coupling constant metamorphosis, also known as the generalized St\"ackel transform, from Hamiltonian dynamical systems to general finite-dimensional dynamical systems and ODEs. This…