Dynamical stability of the weakly nonharmonic propeller-shaped planar Brownian rotator
arXiv:1912.09756 · doi:10.1103/PhysRevE.101.012105
Abstract
Dynamical stability is a prerequisite for control and functioning of desired nano-machines. We utilize the Caldeira-Leggett master equation to investigate dynamical stability of molecular cogwheels modeled as a rigid, propeller-shaped planar rotator. In order to match certain expected realistic physical situations, we consider a weakly nonharmonic external potential for the rotator. Two methods for investigating stability are used. First, we employ a quantum-mechanical counterpart of the so-called "First passage time" method. Second, we investigate time dependence of the standard deviation of the rotator for both the angle and angular momentum quantum observables. A perturbation-like procedure is introduced and implemented in order to provide the closed set of differential equations for the moments. Extensive analysis is performed for different combinations of the values of system parameters. The two methods are, in a sense, mutually complementary. Appropriate for the short time behavior, the First passage time exhibits a numerically-relevant dependence only on the damping factor as well as on the rotator size. On the other hand, the standard deviations for both the angle and angular momentum observables exhibit strong dependence on the parameter values for both short and long time intervals. Contrary to our expectations, the time decrease of the standard deviations is found for certain parameter regimes. In addition, for certain parameter regimes nonmonotonic dependence on the rotator size is observed for the standard deviations and for the damping of the oscillation amplitude.
arXiv comment10 figures, no tables, 31 pages, accepted by PRE
References in corpus (22)
- Open Quantum Systems. An Introduction
- The maximum speed of dynamical evolution
- Brownian motion of a self-propelled particle
- Noise Enhanced Stability in Fluctuating Metastable States
- Time-of-arrival in quantum mechanics
- Signatures of Noise Enhanced Stability in Metastable States
- Rotation of quantum impurities in the presence of a many-body environment
- The stabilizing effect of volatility in financial markets
- Stability measures in metastable states with Gaussian colored noise
- Autonomous Rotor Heat Engine
- Rotational friction and diffusion of quantum rotors
- First-passage and risk evaluation under stochastic volatility
- Spatio-Orientational Decoherence of Nanoparticles
- Escape rate of an active Brownian particle over a potential barrier
- Dissipation in the Caldeira-Leggett model
- Quantum Angular Momentum Diffusion of Rigid Bodies
- Brownian motion surviving in the unstable cubic potential and the role of Maxwell's demon
- Generalized open quantum walks on Apollonian networks
- Quantum information processing: The case of vanishing interaction energy
- Application of Lie-group symmetry analysis to an infinite hierarchy of differential equations at the example of first order ODEs
- Dynamical stability of the one-dimensional rigid Brownian rotator: The role of the rotator's spatial size and shape
- Mean first-passage time of quantum transition processes