Research and application of tristable stochastic resonance based on harmonic and pinning potential model

In view of the unique potential barrier and complex potential function of the pining model, as well as the lack of researches on two-dimensional stochastic resonance, two new potential tristable models are proposed: one-dimensional tristable model and two-dimensional tristable model. The stochastic resonance mechanism and application of two potential systems under Gaussian white noise and weak external driving force are discussed and the differences and advantages of the two systems are analyzed in detail for the first time. First, the potential function and mean first passage time are analyzed. Second, according to the linear response theory, the probability flow method is used to calculate the spectral amplification. The effects of system parameters on spectral amplification of the two models are studied, and the two models are compared. Finally, the two models are applied to the detection of actual bearing fault signals together with the classical tristable system and the performance is compared. Both algorithms can detect fault signals effectively, but the two-dimensional model has better amplitude and difference, and the one-dimensional model has less interference burrs. The theoretical basis and reference value of the system are provided for further application in practical engineering testing.

Dynamics of a hybrid optomechanical system in the framework of the generalized linear response theory

In this article, the linear response of a driven-dissipative hybrid optomechanical system consisting of an interacting one-dimensional Bose–Einstein condensate (BEC) to an external time-dependent perturbation is studied in the framework of the generalized linear response theory (GLRT). It is shown that the Stokes and anti-Stokes amplitudes of the optical and atomic modes of the system can be obtained through the solutions to the equations of motion of the open quantum system Green’s function predicted by the GLRT. In this way, interesting phenomena like anti-resonance and Fano resonance are described and it is shown how the atom-atom interaction affects them. Furthermore, an interpretation of the anti-resonance phenomenon is presented based on the optical spectral function and self-energy.

Linear response theory in stock markets

Linear response theory relates the response of a system to a weak external force with its dynamics in equilibrium, subjected to fluctuations. Here, this framework is applied to financial markets; in particular we study the dynamics of a set of stocks from the NASDAQ during the last 20 years. Because unambiguous identification of external forces is not possible, critical events are identified in the series of stock prices as sudden changes, and the stock dynamics following an event is taken as the response to the external force. Linear response theory is applied with the log-return as the conjugate variable of the force, providing predictions for the average response of the price and return, which agree with observations, but fails to describe the volatility because this is expected to be beyond linear response. The identification of the conjugate variable allows us to define the perturbation energy for a system of stocks, and observe its relaxation after an event.

Comparison of Linear Response Theory, Projected Initial Maximum Overlap Method, and Molecular Dynamics Based Vibronic Spectra: The Case of Methylene Blue

Simulation of optical spectra is essential to molecular characterization and, in many cases, critical for interpreting experimental spectra. The most common method for simulating vibronic absorption spectra relies on the geometry optimization and computation of normal modes for ground and excited states. In this report, we show that utilization of such a procedure within an adiabatic linear response theory framework may lead to state mixings and a breakdown of the Born-Oppenheimer approximation, resulting in a poor description of absorption spectra. In contrast, computing excited states via a self-consistent eld method in conjunction with a maximum overlap model produces states that are not subject to such mixings. We show that this latter method produces vibronic spectra much more aligned with vertical excitation procedures, such as those computed from a vertical gradient or molecular dynamics trajectory-based approach. For the methylene blue chromophore, we compare vibronic absorption spectra computed with: an adiabatic Hessian approach with linear response theory optimized structures and normal modes, a vertical gradient procedure, the Hessian and normal modes of maximum overlap method optimized structures, and excitation energy time correlation functions generated from a molecular dynamics trajectory. Due to mixing between the bright S1 and dark S2 surfaces near the S1 minimum, computing the adiabatic Hessian with linear response theory time-dependent density functional theory with the B3LYP density functional predicts a large vibronic shoulder for the absorption spectrum that is not present for any of the other methods. Spectral densities are analyzed and we compare the behavior of the key normal mode that in linear response theory strongly couples to the optical excitation while showing S1/ S2 state mixings. Overall, our study provides a note of caution in computing vibronic spectra using the excited state adiabatic Hessian of linear response theory optimized structures and also showcases three alternatives that are not as subject to adiabatic state mixing effects.

Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation

Using the second law of local thermodynamics and the first-order Palatini formalism, we formulate relativistic spin hydrodynamics for quantum field theories with Dirac fermions, such as QED and QCD, in a torsionful curved background. We work in a regime where spin density, which is assumed to relax much slower than other non-hydrodynamic modes, is treated as an independent degree of freedom in an extended hydrodynamic description. Spin hydrodynamics in our approach contains only three non-hydrodynamic modes corresponding to a spin vector, whose relaxation time is controlled by a new transport coefficient: the rotational viscosity. We study linear response theory and observe an interesting mode mixing phenomenon between the transverse shear and the spin density modes. We propose several field-theoretical ways to compute the spin relaxation time and the rotational viscosity, via the Green-Kubo formula based on retarded correlation functions.