Related papers: Quantum spectrum as a time series : Fluctuation me…
The power law $1/f^{\alpha}$ in the power spectrum characterizes the fluctuating observables of many complex natural systems. Considering the energy levels of a quantum system as a discrete time series where the energy plays the role of…
We establish the general framework of quantum fluctuation theorems by finding the symmetry between the forward and backward transitions of any given quantum channel. The Petz recovery map is adopted as the reverse quantum channel, and the…
Parametric fluctuations or stochastic signals are introduced into the control pulse sequence to investigate the feasibility of random control over quantum open systems. In a large parameter error region, the out-of-order control pulses work…
Quantum entanglement as the one of the most general quantum resources, can be quantified by von Neumann entropy. However, as we know, the von Neumann entropy is only statistical quantity or operator, it therefore has fluctuation. The…
We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operator on the graph. For the energy-averaged spectral form…
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
We consider the empirical eigenvalue distribution of an $m\times m$ principle submatrix of an $n\times n$ random unitary matrix distributed according to Haar measure. Earlier work of Petz and R\'effy identified the limiting spectral measure…
We study a version of the mathematical Ruijsenaars-Schneider model, and reinterpret it physically in order to describe the spreading with time of quantum wave packets in a system where multifractality can be tuned by varying a parameter. We…
Correlation analysis is convenient and frequently used tool for investigation of time series from complex systems. Recently new methods such as the multifractal detrended fluctuation analysis (MFDFA) and the wavelet transform modulus…
Quantum channels describe the most general dynamics of open quantum systems. A quantum channel, as a linear map on vectorized quantum states, can be represented by a single matrix, whose spectrum is called the channel spectrum. Here we…
Continuously measured quantum systems are characterized by an output current, in the form of a stochastic and correlated time series which conveys crucial information about the underlying quantum system. The many tools used to describe…
A general analytical approach to the statistical description of quantum graph spectra based on the exact periodic orbit expansions of quantum levels is discussed. The exact and approximate expressions obtained in \cite{Anima} for the…
A theoretical model of endogenous fluctuations of the norm of the wave function, consistent with the standard quantum theory, is presented. These fluctuations are a subsystem of endogenous quantum fluctuations and describe one of the…
The Discrete Fourier Transform (DFT) is central to the analysis of uniformly sampled signals, yet many practical applications involve non-uniform sampling, requiring the Non-Uniform Discrete Fourier Transform (NUDFT). While quantum…
We present a full quantum mechanical three dimensional theory describing an electromagnetic field interacting with an ensemble of identical atoms. The theory is constructed such that it describes recent experiments on light-matter quantum…
Quantum reference frames are expected to differ from classical reference frames because they have to implement typical quantum features such as fluctuations and correlations. Here, we show that fluctuations and correlations of reference…
We propose an effective approach to rapid estimation of the energy spectrum of quantum systems with the use of machine learning (ML) algorithm. In the ML approach (back propagation), the wavefunction data known from experiments is…
Quantum Field Theory (QFT) makes predictions by combining two sets of assumptions: (1) quantum dynamics, such as a Schrodinger or Liouville equation; (2) quantum measurement, such as stochastic collapse to an eigenfunction of a measurement…
We study an arbitrary non-equilibrium dynamics of a quantum bipartite system coupled to a reservoir. For its characterization, we present a fluctuation theorem (FT) that explicitly addresses the quantum correlation of subsystems during the…
We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density…