Related papers: Gaussian theory for estimating fluctuating perturb…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
We present a novel and flexible data-driven framework for estimating the response of higher-order moments of nonlinear stochastic systems to small external perturbations. The classical Generalized Fluctuation--Dissipation Theorem (GFDT)…
Using the post-Gaussian trial functions, we calculate the variational solutions to the quantum-mechanical anharmonic oscillator. We evaluate not only the ground state but also some excited energies, and compare them with numerical results.
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
We explore analytically the quantum dynamics of a point mass pendulum using the Heisenberg equation of motion. Choosing as variables the mean position of the pendulum, a suitably defined generalised variance and a generalised skewness, we…
For the paradigmatic case of the damped quantum harmonic oscillator we present two measurement-based feedback schemes to control the stability of its fixed point. The first scheme feeds back a Pyragas-like time-delayed reference signal and…
Common ground to recent studies exploiting relations between dynamical systems and non-equilibrium statistical mechanics is, so we argue, the standard Gibbs formalism applied on the level of space-time histories. The assumptions (chaoticity…
The celebrated Evans-Searles, respectively Gallavotti-Cohen, fluctuation theorem concerns certain universal statistical features of the entropy production rate of a classical system in a transient, respectively steady, state. In this paper,…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
Dynamical phase transitions are nonequilibrium counterparts of thermodynamic phase transitions and share many similarities with their equilibrium analogs. In continuous phase transitions, critical exponents play a key role in characterizing…
For systems in nonequilibrium steady states, a novel modulated Gaussian probability distribution is derived to incorporate a new phenomenon of biased current fluctuations, discovered by recent laboratory experiments and confirmed by…
We introduce an approximation scheme to perform an analytic study of the oscillation phenomena in a pedagogical and comprehensive way. By using Gaussian wave packets, we show that the oscillation is bounded by a time-dependent vanishing…
We carry out a theoretical investigation on the collective dynamics of an ensemble of correlated atoms, subject to both vacuum fluctuations of spacetime and stochastic gravitational waves. A general approach is taken with the derivation of…
We point out that the Gaussian wave-packet formalism can serve as a concrete realization of the joint measurement of position and momentum, which is an essential element in understanding Heisenberg's original philosophy of the uncertainty…
We study classical and quantum caustics for system with quadratic Lagrangian. Gaussian slit experiment is examined and it is pointed out that the focusing around caustics is stabilized against initial momentum fluctuations by quantum…
We introduce a response theory for open quantum systems within nonequilibrium steady-states subject to a Hamiltonian perturbation. Working in the weak system-bath coupling regime, our results are derived within the…
We develop a consistent perturbation theory in quantum fluctuations around the classical evolution of a system of interacting bosons. The zero order approximation gives the classical Gross-Pitaevskii equations. In the next order we recover…
We consider high order current cumulants in disordered systems out of equilibrium. They are interesting and reveal information which is not easily exposed by the traditional shot noise. Despite the fact that the dynamics of the electrons is…
Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the…