Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSignal to noise ratio in parametrically-driven oscillators
278
0
0.0
(
0
)
Added by
Adriano de Albuquerque Batista
Publication date
2011
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Here we report a theoretical model based on Greens functions and averaging techniques that gives ana- lytical estimates to the signal to noise ratio (SNR) near the first parametric instability zone in parametrically- driven oscillators in the presence of added ac drive and added thermal noise. The signal term is given by the response of the parametrically-driven oscillator to the added ac drive, while the noise term has two dif- ferent measures: one is dc and the other is ac. The dc measure of noise is given by a time-average of the statistically-averaged fluctuations of the position of the parametric oscillator due to thermal noise. The ac measure of noise is given by the amplitude of the statistically-averaged fluctuations at the frequency of the parametric pump. We observe a strong dependence of the SNR on the phase between the external drive and the parametric pump, for some range of the phase there is a high SNR, while for other values of phase the SNR remains flat or decreases with increasing pump amplitude. Very good agreement between analytical estimates and numerical results is achieved.
rate research
Read More
In this paper we report a theoretical model based on Green functions, Floquet theory and averaging techniques up to second order that describes the dynamics of parametrically-driven oscillators with added thermal noise. Quantitative estimates for heating and quadrature thermal noise squeezing near and below the transition line of the first parametric instability zone of the oscillator are given. Furthermore, we give an intuitive explanation as to why heating and thermal squeezing occur. For small amplitudes of the parametric pump the Floquet multipliers are complex conjugate of each other with a constant magnitude. As the pump amplitude is increased past a threshold value in the stable zone near the first parametric instability, the two Floquet multipliers become real and have different magnitudes. This creates two different effective dissipation rates (one smaller and the other larger than the real dissipation rate) along the stable manifolds of the first-return Poincare map. We also show that the statistical average of the input power due to thermal noise is constant and independent of the pump amplitude and frequency. The combination of these effects cause most of heating and thermal squeezing. Very good agreement between analytical and numerical estimates of the thermal fluctuations is achieved.
Exact quantum master equation for a driven Brownian oscillator system is constructed via a Wigner phase-space Gaussian wave packet approach. The interplay between external field and dissipation leads to this system an effective field correction that enhances the polarization. This cooperative property is resulted from an effective bath response to the external field applied on the system. It is important in the low-frequency driving and intermediate bath memory region. We demonstrate this non-Markovian effect on the linear response and nonlinear dynamics and analyze the results together with analytical asymptotic expressions.
We demonstrate that the exact non-equilibrium steady state of the one-dimensional Heisenberg XXZ spin chain driven by boundary Lindblad operators can be constructed explicitly with a matrix product ansatz for the non-equilibrium density matrix where the matrices satisfy a {it quadratic algebra}. This algebra turns out to be related to the quantum algebra $U_q[SU(2)]$. Coherent state techniques are introduced for the exact solution of the isotropic Heisenberg chain with and without quantum boundary fields and Lindblad terms that correspond to two different completely polarized boundary states. We show that this boundary twist leads to non-vanishing stationary currents of all spin components. Our results suggest that the matrix product ansatz can be extended to more general quantum systems kept far from equilibrium by Lindblad boundary terms.
We consider an open isotropic Heisenberg quantum spin chain, coupled at the ends to boundary reservoirs polarized in different directions, which sets up a twisting gradient across the chain. Using a matrix product ansatz, we calculate the exact magnetization profiles and magnetization currents in the nonequilibrium steady steady state of a chain with N sites. The magnetization profiles are harmonic functions with a frequency proportional to the twisting angle {theta}. The currents of the magnetization components lying in the twisting plane and in the orthogonal direction behave qualitatively differently: In-plane steady state currents scale as 1/N^2 for fixed and sufficiently large boundary coupling, and vanish as the coupling increases, while the transversal current increases with the coupling and saturates to 2{theta}/N.
The collective and purely relaxational dynamics of quantum many-body systems after a quench at temperature $T=0$, from a disordered state to various phases is studied through the exact solution of the quantum Langevin equation of the spherical and the $O(n)$-model in the limit $ntoinfty$. The stationary state of the quantum dynamics is shown to be a non-equilibrium state. The quantum spherical and the quantum $O(n)$-model for $ntoinfty$ are in the same dynamical universality class. The long-time behaviour of single-time and two-time correlation and response functions is analysed and the universal exponents which characterise quantum coarsening and quantum ageing are derived. The importance of the non-Markovian long-time memory of the quantum noise is elucidated by comparing it with an effective Markovian noise having the same scaling behaviour and with the case of non-equilibrium classical dynamics.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
