Related papers: Random Quadratic Form on a Sphere: Synchronization…
Model-based controllers learned from data have the biases and noise of their training trajectories, making it important to know which trajectories help or hurt closed-loop performance. Influence functions, widely used in machine learning…
We investigate synchronization caused by long-range hydrodynamic interaction in a two-dimensional, substrated array of rotors with random intrinsic frequencies. The rotor mimics a flagellated bacterium that is attached to the substrate…
We unify Brownian motion and quantum mechanics in a single mathematical framework. In particular, we show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a Wiener process that is…
We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model…
This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential…
We undertake a detailed numerical study of the twin phenomena of stochastic and vibrational resonance in a discrete model system in the presence of bichromatic input signal. A two parameter cubic map is used as the model that combines the…
In this paper, we attempt to shed light on a new class of nonstationary random fields which exhibit, what we call, local invariant nonstationarity. We argue that the local invariant property has a special interaction with a new generalized…
It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the behavior of the power spectrum of the excitation energy fluctuations, which is…
We investigate theoretically and experimentally stochastic resonance in a quantum dot coupled to electron source and drain via time-dependent tunnel barriers. A central finding is a transition visible in the current noise spectrum as a…
Coherence resonance (CR) characterizes noise-induced regularity in excitable systems, yet its evaluation in quiescent biological media is often obscured by flattened energy landscapes and complex nonlinear dynamics. In this study, we…
As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how…
We study the stochastic dynamics of a two-level quantum system interacting with a stochastic magnetic field, and a single frequency electromagnetic field, with and without making the rotating wave approximation (RWA). The transformation to…
Identifying an appropriate covariance function is one of the primary interests in spatial and spatio-temporal statistics because it allows researchers to analyze the dependence structure of the random process. For this purpose, spatial…
Quantum noise in a model of singly resonant frequency doubling including phase mismatch and driving in the harmonic mode is analyzed. The general formulae about the fixed points and their stability as well as the squeezing spectra…
Stochastic resonance is a general phenomenon usually observed in one-dimensional, amplitude modulated, bistable systems.We show experimentally the emergence of phase stochastic resonance in the bidimensional response of a forced…
We demonstrate the existence of stochastic resonance (SR) in confined systems arising from entropy variations associated to the presence of irregular boundaries. When the motion of a Brownian particle is constrained to a region with uneven…
Variational quantum algorithms have received substantial theoretical and empirical attention. As the underlying variational quantum circuit (VQC) can be represented by Fourier series that contain an exponentially large spectrum in the…
We show that the core components of the Transformer block -- attention, residual connections, and normalization -- arise naturally from a single geometric estimation problem. Modeling the latent state as a direction on the hypersphere, with…
Synchronization is a universal phenomenon that is important both in fundamental studies and in technical applications. Here we investigate synchronization in the simplest quantum-mechanical scenario possible, i.e., a quantum-mechanical…
We propose a general framework for computing Retarded Green's Functions (RGFs) on quantum computers by recasting their evaluation as a problem of circuit differentiation. Our proposal is based on real-time evolution and specifically…