Observable and hidden singular features of large fluctuations in nonequilibrium systems

We study local features, and provide a topological insight into the global structure of the probability density distribution and of the pattern of the optimal paths for large rare fluctuations away from a stable state. In contrast to extremal paths in quantum mechanics, the optimal paths do {\it not} encounter caustics. We show how this occurs, and what, instead of caustics, are the experimentally observable singularities of the pattern. We reveal the possibility for a caustic and a switching line to start at a saddle point, and discuss the consequences.Comment: 10 pages, 3 ps figures by request, LaTeX Article Format (In press, Phys. Lett. A

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

Design and analysis issues of integrated control systems for high-speed civil transports

A study was conducted to identify, rank, and define development plans for the critical guidance and control design and analysis issues as related to economically viable and environmentally acceptable high-speed civil transport. The issues were identified in a multistep process. First, pertinent literature on supersonic cruise aircraft was reviewed, and experts were consulted to establish the fundamental characteristics and problems inherent to supersonic cruise aircraft. Next, the advanced technologies and strategies being pursued for the high-speed civil transport were considered to determine any additional unique control problems the transport may have. Finally, existing technologies and methods were examined to determine their capabilities for the design and analysis of high-speed civil transport control systems and to identify the shortcomings and issues. Three priority levels - mandatory, highly beneficial, and desirable - were established. Within each of these levels, the issues were further ranked. Technology development plans for each issue were defined. Each plan contains a task breakdown and schedule

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

Foundations for Cooperating with Control Noise in the Manipulation of Quantum Dynamics

This paper develops the theoretical foundations for the ability of a control field to cooperate with noise in the manipulation of quantum dynamics. The noise enters as run-to-run variations in the control amplitudes, phases and frequencies with the observation being an ensemble average over many runs as is commonly done in the laboratory. Weak field perturbation theory is developed to show that noise in the amplitude and frequency components of the control field can enhance the process of population transfer in a multilevel ladder system. The analytical results in this paper support the point that under suitable conditions an optimal field can cooperate with noise to improve the control outcome.Comment: submitted to Phys. Rev.

Symmetry breaking of fluctuation dynamics by noise color.

Activated escape is investigated for systems that are driven by noise whose power spectrum peaks at a finite frequency. Analytic theory and analog and digital experiments show that the system dynamics during escape exhibit a symmetry-breaking transition as the width of the fluctuational spectral peak is varied. For double-well potentials, even a small asymmetry may result in a parametrically large difference of the activation energies for escape from different wells

Quantum dynamics of a domain wall in the presence of dephasing

We compare quantum dynamics in the presence of Markovian dephasing for a particle hopping on a chain and for an Ising domain wall whose motion leaves behind a string of flipped spins. Exact solutions show that on an infinite chain, the transport responses of the models are nearly identical. However, on finite-length chains, the broadening of discrete spectral lines is much more noticeable in the case of a domain wall.This work was supported in part by the ARO grant W911NF-14-1-0272, the NSF grant PHY-1416578, and EPSRC grants EP/K028960/1 and EP/M007065/1