525 research outputs found
Comment on "Influence of Noise on Force Measurements"
In a recent Letter [arXiv:1004.0874], Volpe et al. describe experiments on a
colloidal particle near a wall in the presence of a gravitational field for
which they study the influence of noise on the measurement of force. Their
central result is a striking discrepancy between the forces derived from
experimental drift measurements via their Eq. (1), and from the equilibrium
distribution. From this discrepancy they infer the stochastic calculus realised
in the system.
We comment, however: (a) that Eq. (1) does not hold for space-dependent
diffusion, and corrections should be introduced; and (b) that the "force"
derived from the drift need not coincide with the "force" obtained from the
equilibrium distribution.Comment: Comment submitted to a PRL letter; 1 page, 1 figur
Fast Monte Carlo simulations and singularities in the probability distributions of non-equilibrium systems
A numerical technique is introduced that reduces exponentially the time
required for Monte Carlo simulations of non-equilibrium systems. Results for
the quasi-stationary probability distribution in two model systems are compared
with the asymptotically exact theory in the limit of extremely small noise
intensity. Singularities of the non-equilibrium distributions are revealed by
the simulations.Comment: 4 pages, 4 figure
Stochastic resonance in electrical circuits—II: Nonconventional stochastic resonance.
Stochastic resonance (SR), in which a periodic signal in a nonlinear system can be amplified by added noise, is discussed. The application of circuit modeling techniques to the conventional form of SR, which occurs in static bistable potentials, was considered in a companion paper. Here, the investigation of nonconventional forms of SR in part using similar electronic techniques is described. In the small-signal limit, the results are well described in terms of linear response theory. Some other phenomena of topical interest, closely related to SR, are also treate
Enlargement of a low-dimensional stochastic web
We consider an archetypal example of a low-dimensional stochastic web, arising in a 1D oscillator driven by a plane wave of a frequency equal or close to a multiple of the oscillator’s natural frequency. We show that the web can be greatly enlarged by the introduction of a slow, very weak, modulation of the wave angle. Generalizations are discussed. An application to electron transport in a nanometre-scale semiconductor superlattice in electric and magnetic fields is suggested
Stochastic resonance in electrical circuits—I: Conventional stochastic resonance.
Stochastic resonance (SR), a phenomenon in which a periodic signal in a nonlinear system can be amplified by added noise, is introduced and discussed. Techniques for investigating SR using electronic circuits are described in practical terms. The physical nature of SR, and the explanation of weak-noise SR as a linear response phenomenon, are considered. Conventional SR, for systems characterized by static bistable potentials, is described together with examples of the data obtainable from the circuit models used to test the theory
A phase transition in a system driven by coloured noise
For a system driven by coloured noise, we investigate the activation energy of escape, and the dynamics during the escape. We have performed analogue experiments to measure the change in activation energy as the power spectrum of the noise varies. An adiabatic approach based on path integral theory allows us to calculate analytically the critical value at which a phase transition in the activation energy occurs
A new approach to the treatment of Separatrix Chaos and its applications
We consider time-periodically perturbed 1D Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small or moderate ranges: this corresponds to the involvement of resonance dynamics into the separatrix chaos. We develop a method matching the discrete chaotic dynamics of the separatrix map and the continuous regular dynamics of the resonance Hamiltonian. The method has allowed us to solve the long-standing problem of an accurate description of the maximum of the separatrix chaotic layer width as a function of the perturbation frequency. It has also allowed us to predict and describe
new phenomena including, in particular: (i) a drastic facilitation of the onset of global chaos between neighbouring separatrices, and (ii) a huge increase in the
size of the low-dimensional stochastic web
Large fluctuations and irreversibility in nonequilibrium systems.
Large rare fluctuations in a nonequilibrium system are investigated theoretically and by analogue electronic experiment. It is emphasized that the optimal paths calculated via the eikonal approximation of the Fokker-Planck equation can be identified with the locus of the ridges of the prehistory probability distributions which can be calculated and measured experimentally for paths terminating at a given final point in configuration sspace. The pattern of optimal paths and its singularities, such as caustics, cusps and switching lines has been calculated and measured experimentally for a periodically driven overdamped oscillator, yielding results that are shown to be in good agreement with each other
Time-resolved measurement of Landau--Zener tunneling in different bases
A comprehensive study of the tunneling dynamics of a Bose--Einstein
condensate in a tilted periodic potential is presented. We report numerical and
experimental results on time-resolved measurements of the Landau--Zener
tunneling of ultracold atoms introduced by the tilt, which experimentally is
realized by accelerating the lattice. The use of different protocols enables us
to access the tunneling probability, numerically as well as experimentally, in
two different bases, namely, the adiabatic basis and the diabatic basis. The
adiabatic basis corresponds to the eigenstates of the lattice, and the diabatic
one to the free-particle momentum eigenstates. Our numerical and experimental
results are compared with existing two-state Landau--Zener models
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