相关论文: Stochastic Quantisation and Non-Equilibrium Statis…

Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…

A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over…

We introduce a software generator for a class of colored (self-correlated) and non-Gaussian noise, whose statistics and spectrum depend on two parameters, $q$ and $\tau$. Inspired by Tsallis' nonextensive formulation of statistical physics,…

We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the…

We derive a set of spectral statistics whose power spectrum is characterized, in the case of chaotic quantum systems, by colored noise $1/f^{\gamma}$, where the integer parameter $\gamma$ critically depends on the specific energy-level…

We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic processes with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary…

We develop a new method for stochastic optimization using the Bayesian statistics approach. More precisely, we optimize parameters of chess engines as those data are available to us, but the method should apply to all situations where we…

We consider a statistical model of a n-mode quantum Gaussian state which is shift invariant and also gauge invariant. Such models can be considered analogs of classical Gaussian stationary time series, parametrized by their spectral…

The Ito and Stratonovich approaches are carried over to quantum stochastic systems. Here the white noise representation is shown to be the most appropriate as here the two approaches appear as Wick and Weyl orderings, respectively. This…

A stochastic averaging technique based on energy-dependent frequency is extended to dynamical systems with triple-well potential driven by colored noise. The key procedure is the derivation of energy-dependent frequency according to the…

Squeezed states of the harmonic oscillator are a common resource in applications of quantum technology. If the noise is suppressed in a nonlinear combination of quadrature operators below threshold for all possible up-to-quadratic…

We consider the effect of multiple stochastic parameters on the time-average quantities of chaotic systems. We employ the recently proposed \cite{Kantarakias_Papadakis_2023} sensitivity-enhanced generalized polynomial chaos expansion,…

It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it…

In this thesis, I present several results on quantum statistical inference in the following two directions. Firstly, I demonstrate that quantum algorithms can be applied to enhance the computing and training of Gaussian processes (GPs), a…

Thanks to the nonstandard formalization of fast oscillating functions, due to P. Cartier and Y. Perrin, an appropriate mathematical framework is derived for new non-asymptotic estimation techniques, which do not necessitate any statistical…

In this paper we study a large class of nonlinear stochastic wave equations that arise in laser generation models and models for propagation in random media in a unified mathematical framework. Continuous and pulse-wave propagation models,…

We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…

Classical, self-consistent theory of statistical mechanics was developed for the thermodynamic and conservative Hamiltonian systems. Later there were many attempts (Sinai-Bowen-Ruelle's temperature, Tsallis' non-extensive theory) to apply…

Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a…

We describe a slightly sub-exponential time algorithm for learning parity functions in the presence of random classification noise. This results in a polynomial-time algorithm for the case of parity functions that depend on only the first…