相关论文: Unitarity breaking in self-averaging spectral form…

The short-time Fourier transform (STFT) provides the foundation of binary-mask based audio source separation approaches. In computing a spectrogram, the STFT window size parameterizes the trade-off between time and frequency resolution.…

This paper details the purpose, difficulties, theory, implementation, and results of developing a Fast Fourier Transform (FFT) using the prime factor algorithm on an embedded system. Many applications analyze the frequency content of…

Fourier representations play a central role in operator learning methods for partial differential equations and are increasingly being explored in quantum machine learning architectures. The classical fast Fourier transform (FFT),…

Stochastic dynamics of a quantum system driven by $N$ statistically independent random sudden quenches in a fixed time interval is studied. We reveal that with growing $N$ the system approaches a deterministic limit indicating…

We consider a free quantum particle in one dimension whose mass profile exhibits jump discontinuities. The corresponding Hamiltonian is a self-adjoint realisation of the kinetic-energy operator, with the specific realisation determined by…

The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can…

The functional defined as the squared modulus of the spatial average of the wave function squared, plays the role of an ``order parameter'' for the transition between Hamiltonian ensembles with orthogonal and unitary symmetry. Upon breaking…

The local density of states or its Fourier transform, usually called fidelity amplitude, are important measures of quantum irreversibility due to imperfect evolution. In this Rapid Communication we study both quantities in a paradigmatic…

Coherence is a fundamental characteristic of quantum systems and central to understanding quantum behaviour. It is also important for a variety of applications in quantum information. However, physical systems suffer from decoherence due to…

The apparantly irregular (unpredictable) space-time fluctuations in atmospheric flows ranging from climate (thousands of kilometers - years) to turbulence (millimeters - seconds) exhibit the universal symmetry of self-similarity.…

A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…

Using Gutzwiller's semiclassical periodic-orbit theory we demonstrate universal behaviour of the two-point correlator of the density of levels for quantum systems whose classical limit is fully chaotic. We go beyond previous work in…

The free metaplectic transformation (FMT) has gained much popularity in recent times because of its various application in signal processing, paraxial optical systems, digital algorithms, optical encryption and so on. However, the FMT is…

The inherent non-linearity of intensity correlation functions can be used to spatially distinguish identical emitters beyond the diffraction limit, as achieved, for example, in Super-Resolution Optical Fluctuation Imaging (SOFI). Here, we…

We investigate how the dynamical fluctuations of many-body quantum systems out of equilibrium can be mitigated when they are opened to a dephasing environment. We consider the survival probability (spectral form factor with a filter)…

Multicomponent-multiband fluxes of spim-charge carriers, whose components propagate mixed and synchronously, with \emph{a priori} nonzero incoming amplitudes, do not obey the standard unitarity condition on the scattering matrix for an…

Coherent time is a characteristic time in the extreme nonlinear optics regime and thus generally introduced as the dephasing time in the simulations of the solid-state high-harmonic generation. This characteristic time linked with the…

Unitarity is a cornerstone of quantum theory, ensuring the conservation of probability and information. Although non-Hermitian Hamiltonians are typically associated with open or dissipative systems, pseudo-Hermitian quantum mechanics shows…

Spectral characterization of noise environments that lead to the decoherence of qubits is critical to developing robust quantum technologies. While dynamical decoupling offers one of the most successful approaches to characterize noise…

The Fractional Fourier Transform (FRT) corresponds to an arbitrary-angle rotation in the phase space, e.g. the time-frequency (TF) space, and generalizes the fundamentally important Fourier Transform. FRT applications range from classical…