Explore the vast range of titles available.

This study focuses on a novel parameterized Wigner distribution, which is an organic integration of the free metaplectic Wigner distribution and the K-Wigner distribution. We style this as the free metaplectic K-Wigner distribution (FMKWD) and investigate its uncertainty principles and related applications. We establish a crucial equivalence relation between the uncertainty product in time-FMKWD and free metaplectic transformation (FMT)-FMKWD domains and those in two FMT domains, from which we derive two types of orthogonality conditions: an orthonormality condition; and two sub-types of minimum or maximum eigenvalue commutativity conditions on the FMKWD. Finally we separately formulate an uncertainty inequality in FMKWD domains for real-valued functions, three kinds of uncertainty inequalities in orthogonal FMKWD domains, an uncertainty inequality in orthonormal FMKWD domains, and four kinds of uncertainty inequalities in the minimum or maximum eigenvalue commutative FMKWD domains for complex-valued functions. The time-frequency resolution of the FMKWD is compared with those of the free metaplectic Wigner distribution, K-Wigner distribution, and N-dimensional Wigner distribution to demonstrate its superiority in super-resolution analysis. For applications, the uncertainty inequalities derived are used to estimate the bandwidth in FMKWD domains, and the FMKWD is applied to detect noisy linear frequency-modulated signals.

This study examines the phase-space representation of the von Neumann equation of motion for the density operator associated with a particle with one-half spin moving in a two-dimensional layer. The general form of this equation is derived from the Stratonovich–Weyl scheme, which allows for the simultaneous consideration of continuous and discrete degrees of freedom. It is also demonstrated that the equations of motion for the marginals of the Wigner distribution function can be expressed as the Moyal equation, framed within the mean-field approximation. Taking into account the Hamiltonian in the Weyl form and using the Markovian approximation, it is shown that the considered equation of motion can be reduced to the diffusion equation with the time-dependent anisotropic diffusion coefficient for the probability density in real space. This equation is, then, solved with the initial condition set as a rescaled Gaussian, miming particle spread within the anomalous diffusion process. The characteristics of these processes are then analyzed using the dynamic overlap measure and the Shannon entropy approach. The advection process is selected as a reference process, as it naturally arises due to the mean-field approximation.

Silicene is a two-dimensional silicon monolayer with a band gap caused by relatively strong spin–orbit coupling. This band gap can be steered using a vertical electric field. In turn, the change in this electric field value leads to a transition from a topological insulator to a bulk insulator regime. This study aims to develop a phase-space approach to detecting the topological phase transitions in silicene induced by the presence of parallel magnetic and electric fields with the aid of the concept of topological quantum number based on the Wigner–Rényi entropy. A reinterpreted definition of the Wigner distribution function is employed to determine this indicator. The topological phase transition in silicene as a function of the electric field in the presence of the magnetic field is confirmed through the use of the topological quantum number determined for the one-half, Shannon and collision entropies.

The traditional scaled Wigner distribution (SWD) is extended to a novel one inspired by merits of fractional instantaneous autocorrelation present in the definition of fractional bi-spectrum and the fractional Fourier transform (FrFT). We begin by examining the basic characteristics of the novel fractional scaled Wigner distribution (Fr-SWD), such as its nonlinearity, marginality, shifting, conjugate symmetry, and antiderivative nature. Following that, a thorough analysis of Moyal’s formula is also conducted. The proposed distribution is used to detect both single-component and multi-component linear frequency-modulated signals in order to demonstrate its effectiveness. The results of the simulation clearly show that the novel fractional scaled Wigner distribution performs exceptionally well in comparison with the conventional Wigner distribution and its scaled version.

The concept of the phase space plays a key role in the analysis of oscillating signals. For a 1-D signal, the coordinates of the 2-D phase space are the observation time and the instant frequency. For measurements of propagating wave fields, the time and instant frequency are linked to the spatial location and wave normal, defining a ray. In this case, the phase space is also termed the ray space. Distributions in the ray space find important applications in the analysis of radio occultation (RO) data because they allow the separation of interfering rays in multipath zones. Examples of such distributions are the spectrogram, Wigner distribution function (WDF), and Kirkwood distribution function (KDF). In this study, we analyze the application of the fractional Fourier transform (FrFT) to the construction of distributions in the ray space. The FrFT implements the phase space rotation. We consider the KDF averaged over the rotation group and demonstrate that it equals the WDF convolved with a smoothing kernel. We give examples of processing simple test signals, for which we evaluate the FrFT, KDF, WDF, and smoothed WDF (SWDF). We analyze the advantages of the SWDF and show examples of its application to the analysis of real RO observations.

The tussling interplay between the thermal photons and the squeezed photons is discussed. Thermal and squeezed photons are chosen to represent the ‘classical’ and ‘quantum’ noises respectively, and, they are pitted against each other in a coherent background radiation field (represented by coherent photons). The squeezed coherent thermal states (SCTS) and their photon counting distributions (PCD) are employed for this purpose. It is observed that the addition of thermal photons and squeezed photons have counterbalancing effects, by delocalizing and localizing the PCD, respectively. Various aspects of the atom-field interaction, like the atomic inversion, and entanglement dynamics in the Jaynes-Cummings model have been investigated. Particular attention is given to the study of atomic inversion and entanglement dynamics due to the addition of thermal and squeezed photons to the coherent state. The interplay of thermal photons and squeezed photons have drastic effects on the PCD, atomic inversion, and entanglement dynamics of the atom-field interaction. The thermal photons display supremacy over the squeezed photons at the level of PCD and atomic inversion. The entanglement dynamics vary from that of a coherent state to a Glauber-Lachs state. We have also studied the mixing of thermal photons and squeezed photons using coherent squeezed thermal states, for which the behaviour of PCD, atomic inversion, and entanglement dynamics are contrasting to those of squeezed coherent thermal states. The parameter ranges for these states for which the zero Hanbury Brown and Twiss correlation is exhibited are also obtained. The associated Wigner distribution functions are also discussed.

Linear canonical transform (LCT) is a powerful tool for improving the detection accuracy of the conventional Wigner distribution (WD). However, the LCT free parameters embedded increase computational complexity. Recently, the instantaneous cross-correlation function type of WD (ICFWD), a specific WD relevant to the LCT, has shown to be an outcome of the tradeoff between detection accuracy and computational complexity. In this paper, the ICFWD is applied to detect noisy single component and bi-component linear frequency-modulated (LFM) signals through the output signal-to-noise ratio (SNR) inequality modeling and solving with respect to the ICFWD and WD. The expectation-based output SNR inequality model between the ICFWD and WD on a pure deterministic signal added with a zero-mean random noise is proposed. The solutions of the inequality model in regard to single component and bi-component LFM signals corrupted with additive zero-mean stationary noise are obtained respectively. The detection accuracy of ICFWD with that of the closed-form ICFWD (CICFWD), the affine characteristic Wigner distribution (ACWD), the kernel function Wigner distribution (KFWD), the convolution representation Wigner distribution (CRWD) and the classical WD is compared. It also compares the computing speed of ICFWD with that of CICFWD, ACWD, KFWD and CRWD.

Two-dimensional Wigner distribution (2D WD) and ambiguity function (2D AF) are important tools for time–frequency analysis and signal processing, especially in the analysis of 2D chirp signals. In this paper, based on the classical 2D WD and 2D AF, a new kind of 2D WD and 2D AF associated with 2D nonseparable linear canonical transform (2D NSLCT) are proposed, namely NSLCWD and NSLCAF. The definition obtained by this method not only has the advantages of 2D NSLCT, but also has the good characteristics of 2D WD (2D AF). The emergence of the new definition also broadens the development of 2D theory to a certain extent. Then, we derive a series of important properties related to the new definition and present theoretical proof. Moreover, we find that the original 2D WD and 2D AF exist as special cases of two new definitions. In addition, the relationship between the new definition and 2D NSLCT is also the focus of our discussion. Finally, the NSLCWD and NSLCAF are applied to detect different forms of 2D chirp signals. The results confirm that our new definitions, NSLCWD and NSLCAF, are useful and effective.

Designing a transmission line (TL) for a widely tunable, broadband terahertz radiation source presents substantial challenges due to the complexity of beam dynamics and spectral characteristics. Here, we investigate the propagation of the most significant radiation modes expected to traverse the TL, intended for integration with an advanced particle accelerator currently under construction at the Schlesinger Family Center for Compact Accelerators, Radiation Sources and Applications. The total electromagnetic field at the source output is expressed in the frequency domain via cavity eigenmodes and transformed into an optical field representation using the Wigner distribution function (WDF). This formulation enables physically consistent modeling within the constraints of geometric optics and Wigner formalism of the spatiotemporal evolution of the radiation during propagation. The initial TL design is developed and optimized based on this representation. A 3D space–frequency analysis tool for pulsed radiation, based on the WDF, was implemented to characterize field behavior and guide system development. Complementary ray tracing simulations were conducted using the Zemax Optic Studio platform, supporting the assessment of optical feasibility through simulation and system feasibility.

In order to achieve time–frequency superresolution in comparison to the conventional Wigner distribution (WD), this study generalizes the well-known τ-Wigner distribution (τ-WD) with only one parameter τ to the multiple-parameter matrix-Wigner distribution (M-WD) with the parameter matrix M. According to operator theory, we construct Heisenberg’s inequalities on the uncertainty product in M-WD domains and formulate two kinds of attainable lower bounds dependent on M. We solve the problem of lower bound minimization and obtain the optimality condition of M, under which the M-WD achieves superior time–frequency resolution. It turns out that the M-WD breaks through the limitation of the τ-WD and gives birth to some novel distributions other than the WD that could generate the highest time–frequency resolution. As an example, the two-dimensional linear frequency-modulated signal is carried out to demonstrate the time–frequency concentration superiority of the M-WD over the short-time Fourier transform and wavelet transform.