Diffusion in a bistable potential. General inverse friction expansion

1986 ◽  
Vol 45 (1-2) ◽  
pp. 267-293 ◽  
Author(s):  
J. -F. Gouyet
Keyword(s):  
Bistable Potential ◽  
Inverse Friction Expansion

scholarly journals Escape dynamics of active particles in multistable potentials

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
A. Militaru ◽  
M. Innerbichler ◽  
M. Frimmer ◽  
F. Tebbenjohanns ◽  
L. Novotny ◽  
...  
Keyword(s):  
Transition State Theory ◽  
Silica Nanoparticle ◽  
State Theory ◽  
Biological Processes ◽  
Correlated Noise ◽  
Stochastic Force ◽  
Escape Dynamics ◽  
Active Particles ◽  
Bistable Potential ◽  
Quantitative Understanding

AbstractRare transitions between long-lived metastable states underlie a great variety of physical, chemical and biological processes. Our quantitative understanding of reactive mechanisms has been driven forward by the insights of transition state theory and in particular by Kramers’ dynamical framework. Its predictions, however, do not apply to systems that feature non-conservative forces or correlated noise histories. An important class of such systems are active particles, prominent in both biology and nanotechnology. Here, we study the active escape dynamics of a silica nanoparticle trapped in a bistable potential. We introduce activity by applying an engineered stochastic force that emulates self-propulsion. Our experiments, supported by a theoretical analysis, reveal the existence of an optimal correlation time that maximises the transition rate. We discuss the origins of this active turnover, reminiscent of the much celebrated Kramers turnover. Our work establishes a versatile experimental platform to study single particle dynamics in non-equilibrium settings.

scholarly journals The Fokker–Planck equation for a bistable potential

2014 ◽  
Vol 412 ◽  
pp. 92-100 ◽  
Author(s):  
Denise Caldas ◽  
Jorge Chahine ◽  
Elso Drigo Filho
Keyword(s):  
Planck Equation ◽  
Fokker Planck Equation ◽  
Bistable Potential ◽  
Fokker Planck

scholarly journals Direct Optimal Control Approach to Laser-Driven Quantum Particle Dynamics

2021 ◽  
Vol 9 ◽  
Author(s):  
A. R. Ramos Ramos ◽  
O. Kühn
Keyword(s):  
Optimal Control ◽  
Gaussian Approximation ◽  
Gaussian Function ◽  
Dynamical Equations ◽  
Control Approach ◽  
Wide Range ◽  
Bistable Potential ◽  
Wavepacket Dynamics ◽  
Direct Optimal Control ◽  
Backward Propagation

Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets. Here, we propose direct optimal control as a robust and flexible alternative. It is based on a discretization of the dynamical equations resulting in a nonlinear optimization problem. The method is illustrated for the case of laser-driven wavepacket dynamics in a bistable potential. The wavepacket is parameterized in terms of a single Gaussian function and field optimization is performed for a wide range of particle masses and lengths of the control interval. Using the optimized field in a full quantum propagation still yields reasonable control yields for most of the considered cases. Analysis of the deviations leads to conditions which have to be fulfilled to make the semiclassical single Gaussian approximation meaningful for field optimization.

Modifying the onset of homoclinic chaos: Application to a bistable potential

1993 ◽  
Vol 47 (6) ◽  
pp. 4585-4588 ◽  
Author(s):  
G. Cicogna ◽  
L. Fronzoni
Keyword(s):  
Homoclinic Chaos ◽  
Bistable Potential
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