There is an intense debate in the recent literature about correct generalization of Maxwell's velocity distribution special relativity. The most frequently discussed candidate distributions include J\"uttner function as well modifications thereof. Here we report results from fully relativistic one-dimensional molecular dynamics simulations that resolve ambiguity. numerical evidence unequivocally favors distribution. Moreover, our illustrate concept ``thermal equilibrium'' extends naturally...

We study, within the spin-boson dynamics, synchronization of a quantum tunneling system with an external, time-periodic driving signal. As main result, we find that at sufficiently large system-bath coupling strength (i.e., for friction alpha > 1) thermal noise plays constructive role in yielding forced synchronization. This noise-induced can occur when frequency is larger than zero-temperature rate. application evidencing effect, consider charge transfer dynamics molecular complexes.

We study the overdamped motion of a particle in bistable potential subject to action bichromatic force and additive noise, within context vibrational resonance phenomenon. Under appropriate conditions, we obtain analytical expressions for relevant observables which quantifies this The theoretical results are compared with those obtained by numerical solution stochastic differential equation describes dynamics system. limits validity approach also discussed.

An amenable, analytical two-state description of the nonlinear population dynamics a noisy bistable system driven by rectangular subthreshold signal is put forward. Explicit expressions for dynamics, correlation function (its coherent and incoherent parts), signal-to-noise ratio (SNR), stochastic resonance (SR) gain are obtained. Within suitably chosen range parameter values this reduced yields anomalous SR gains exceeding unity and, simultaneously, gives rise to nonmonotonic behavior SNR vs...

We address the phenomenon of stochastic resonance in a noisy bistable system driven by time-dependent periodic force (not necessarily sinusoidal) and its two-state approximation. Even for driving forces with subthreshold amplitudes, behavior response might require nonlinear description. introduce analytical numerical tools to analyze power spectral amplification signal-to-noise ratio regime. Our analysis shows importance effects on fluctuations These can be usefully exploited achieve high...

The effect of a high-frequency signal on the FitzHugh-Nagumo excitable model is analyzed. We show that firing rate diminished as ratio amplitude to its frequency increased. Moreover, it demonstrated character system, and consequently activity, suppressed for ratios above given threshold value. In addition, we vibrational resonance phenomenon turns up sufficiently large noise strength values.

In the context of phenomenon stochastic resonance (SR), we study correlation function, signal-to-noise ratio (SNR), and output over input SNR, i.e., gain, which is associated to nonlinear response a bistable system driven by time-periodic forces white Gaussian noise. These quantifiers for SR are evaluated using techniques linear theory (LRT) beyond usually employed two-mode approximation scheme. We analytically demonstrate within such an extended LRT description that gain can indeed not...

The main objective of this work is to explore aspects stochastic resonance (SR) in noisy bistable, symmetric systems driven by subthreshold periodic rectangular external signals possessing a large duty cycle unity. Using precise numerical solution the Langevin equation, we carry out detailed analysis behavior first two cumulant averages, correlation function, and its coherent incoherent parts. We also depict nonmonotonic versus noise strength several SR quantifiers such as average output...

We investigate the role of noise in phenomenon stochastic synchronization switching events a rocked, overdamped bistable potential driven by white Gaussian noise, archetype description resonance. present an approach to counting process noise-induced events: starting from Markovian dynamics nonstationary, continuous particle dynamics, one finds upon contraction onto two states non-Markovian renewal dynamics. A proper definition output discrete phase is given, and time rate change its average...

Abstract Quantum machine learning (QML) is a discipline that holds the promise of revolutionizing data processing and problem‐solving. However, dissipation noise arising from coupling with environment are commonly perceived as major obstacles to its practical exploitation, they impact coherence performance utilized quantum devices. Significant efforts have been dedicated mitigating controlling their negative effects on these This perspective takes different approach, aiming harness potential...

We analyze the relationship between irrationality and quasiperiodicity in nonlinear driven systems. To that purpose, we consider a system whose steady-state response is very sensitive to periodic or quasiperiodic character of input signal. In infinite time limit, an signal consisting two incommensurate frequencies will be recognized by as quasiperiodic. show this is, general, not true case finite interaction times. An irrational ratio driving sufficient for it quasiperiodic, resulting...

We consider the kinetics of electron transfer reactions in condensed media with different reorganization energies for forward and backward processes. The starting point our analysis is an extension well-known Zusman equations to case parabolic diabatic curves curvatures. A generalized master equation populations as well formal expressions their long-time limit derived. discuss conditions under which time evolution reactants products can be described at all times by a single exponential law....

Quantum phase transitions encompass a variety of phenomena that occur in quantum systems exhibiting several possible symmetries. Traditionally, these are explored by continuously varying control parameter connects two different symmetry configurations. Here we propose an alternative approach where the undergoes abrupt and time-periodic jumps between only values. This yields results surprisingly similar to those obtained traditional one may prove experimentally useful situations accessing is...

We present a very simple Markovian kinetic model displaying stochastic resonant behavior which is similar to the one found in escape of particle over fluctuating potential barrier. The basic mechanism that responsible for existence resonance identified. This allows generalization different ways, leading variety models where phenomenon be expected. It also shown initial conditions play an important role determining whether activation actually shows up.

The response of a nonlinear stochastic system driven by an external sinusoidal time-dependent force is studied variety numerical and analytical approximations. validity linear theory put to critical test comparing its predictions with solutions over extended parameter regime driving amplitudes frequencies. relevance the frequency for applicability explored.

We study the effects of a high-frequency (HF) signal on response noisy bistable system to low-frequency subthreshold sinusoidal signal. show that, by conveniently choosing ratio amplitude HF its frequency, stochastic resonance gains greater than unity can be measured at value. Thus, addition entail an improvement in detection weak monochromatic signals. The results are explained terms effective model and illustrated means numerical simulations.

Dynamical systems often contain oscillatory forces or depend on periodic potentials. Time space periodicity is reflected in the properties of these through a dependence parameters their terms. In this paper we provide general theoretical framework for dealing with kinds systems, regardless whether they are classical quantum, stochastic deterministic, dissipative nondissipative, linear nonlinear, etc. particular, able to show that simple symmetry considerations determine, large extent, how...

A study of the effect thermal dissipation on quantum reinforcement learning is performed. For this purpose, a nondissipative protocol adapted to presence dissipation. Analytical calculations as well numerical simulations are carried out, obtaining evidence that does not significantly degrade performance for sufficiently low temperatures, in some cases even being beneficial. Quantum under realistic experimental conditions opens an avenue realization agents be able interact with changing...

We study the phenomenon of nonlinear stochastic resonance (SR) in a complex noisy system formed by finite number interacting subunits driven rectangular pulsed time periodic forces. find that very large SR gains are obtained for subthreshold driving forces with frequencies much larger than values observed simpler one-dimensional systems. These effects explained using simple considerations.

We examine the time-dependent behavior of a nonlinear system driven by two-frequency forcing. By using nonperturbative approach, we are able to derive an asymptotic expression, valid in long-time limit, for time average output variable which describes response system. identify several universal features system, independent details model. In particular, determine expression width resonance observed keeping one frequency fixed and varying other one. show that this is smaller than usually...

The emergence of directed motion is investigated in a system consisting sphere immersed viscous fluid and subjected to time-periodic forces zero average. arises from the combined action nonlinear drag force applied driving forces, absence any periodic substrate potential. Necessary conditions for existence such are obtained an analytical expression average terminal velocity derived within adiabatic approximation. Special attention paid case two mutually perpendicular with sinusoidal time...

We analyze the phenomenon of nonlinear stochastic resonance (SR) in noisy bistable systems driven by pulsed time periodic forces. The driving force contains, within each period, two pulses equal constant amplitude and duration but opposite signs. Each pulse starts every half-period its is varied. For subthreshold amplitudes, we study dependence output signal-to-noise ratio (SNR) SR gain on noise strength relative pulses. find that gains can reach values larger than unity, with maximum...

The validity of linear response theory to describe the a nonlinear stochastic system driven by an external periodical time dependent force is put critical test. A variety numerical and analytical approximations used compare its predictions with solutions over extended parameter regime driving amplitudes frequencies noise strengths. relevance frequency value for applicability explored single multi-frequency input signals.

Very recently Willis et al. [Phys. Rev. E 69, 056612 (2004)] have used a collective variable theory to explain the appearance of nonzero energy current in an ac-driven, damped sine-Gordon equation. In this Comment, we prove rigorously that time-averaged ac-driven nonlinear Klein-Gordon system is strictly zero.