Abstract:
A dynamical theory which incorporates the electron-electron correlations and the effects of external magnetic fields for an electron escaping from a helium surface is presented. The degrees of freedom in the calculation of the escape rate is reduced from $3N$ to 3 as compared with other approach. Explicit expressions for the escape rate in various situations are obtained. In particular, in the weak parallel magnetic field limit the tunneling rate has an exponential dependence quadratic with magnetic field strength and an unusual exponential increase linear with temperature.

Abstract:
We present a semiclassical study of a transport process, the tunneling, in the presence of a magnetic field and a dissipative environment. We have found that the problem can be mapped onto an effective one-dimensional one, and the tunneling rate is strongly affected by the magnetic field, such as a complete suppression by a large parallel magnetic field, an example of the dynamical localization. In such case a small perpendicular component of the field, or the dissipation, can enhance the tunneling rate. In the small parallel field and finite temperatures the tunneling rate is finite. Explicit expressions will be presented in those cases. If viewing the tunneling in the presence of a magnetic field as a dissipative tunneling process, by varying the magnetic field and the potential one can obtain the dissipative spectral function between the subohmic $s =0$ and the superohmic $s = \infty$. In combination with a real dissipative spectral function, the effect of the magnetic field can map the spectral function from $s $ to $2-s$, with $s>2$ mapping to $ s = 0$, revealing a dual symmetry between the friction and the Lorentz force. Two cases relevant to experiments, the edge state tunneling in a Hall bar and the tunneling near the dynamical localization will be discussed in detail.

Abstract:
We present a dynamical theory which incorporates the electron-electron correlations and the effects of external magnetic fields for an electron escaping from a helium surface. Analytical expressions for the escape rate can be obtained in various limits. In particular, the tunneling rate with a parallel magnetic field is presented explicitly.

Abstract:
We argue that the motion of vacancies in a pinned vortex lattice may dominate the contribution to the Hall effect in an appropriate parameter regime for a superconductor. Based on this consideration a model is constructed to explain the anomalous Hall effect without any modification of the basic vortex dynamic equation. Quantitative predictions are obtained. Present model can be directly tested by an observation of the vacancy motion.

Abstract:
The influence of a magnetic field on the tunneling of an electron out of a confining plane is studied by a path integral method. We map this 3-d problem on to a 1-d one, and find that the tunneling is strongly affected by the field. Without a perpendicular field the tunneling at zero temperature can be completely suppressed by a large parallel field, but in the small parallel field and low temperature limit the tunneling rate is finite. An explicit formula is obtained in this case. A quantitative explanation without fitting parameter to a recent experiment is provided.

Abstract:
It has been suggested recently that action and perception can be understood as minimising the free energy of sensory samples. This ensures that agents sample the environment to maximise the evidence for their model of the world, such that exchanges with the environment are predictable and adaptive. However, the free energy account does not invoke reward or cost-functions from reinforcement-learning and optimal control theory. We therefore ask whether reward is necessary to explain adaptive behaviour. The free energy formulation uses ideas from statistical physics to explain action in terms of minimising sensory surprise. Conversely, reinforcement-learning has its roots in behaviourism and engineering and assumes that agents optimise a policy to maximise future reward. This paper tries to connect the two formulations and concludes that optimal policies correspond to empirical priors on the trajectories of hidden environmental states, which compel agents to seek out the (valuable) states they expect to encounter.

Abstract:
We investigate the properties of the nonequilibrium steady state for the stochastic system driven by a nonlinear drift force and influenced by noises which are not identically and independently distributed. The nonequilibrium steady state (NESS) current results from a residual part of the drift force which is not cancelled by the diffusive action of noises. From our previous study for the linear drift force the NESS current was found to circulate on the equiprobability surface with the maximum at a stable fixed point of the drift force. For the nonlinear drift force, we use the perturbation theory with respect to the cubic and quartic coefficients of the drift force. We find an interesting potential landscape picture where the probability maximum shifts from the fixed point of the drift force and, furthermore, the NESS current has a nontrivial circulation which flows off the equiprobability surface and has various centers not located at the probability maximum. The theoretical result is well confirmed by the computer simulation.

Abstract:
In this paper, we study the properties of a phase slip in a superfluid Fermi gas near a Feshbach resonance. The phase slip can be generated by the phase imprinting method. Below the superfluid transition temperature, it appears as a dip in the density profile, and becomes more pronounced when the temperature is lowered. Therefore the phase slip can provide a direct evidence of the superfluid state. The condensation energy of the superfluid state can be extracted from the density profile of the phase slip, due to the unitary properties of the Fermi gas near the resonance. The width of the phase slip is proportional to the square root of the difference between the transition temperature and the temperature. The signature of the phase slip in the density profile becomes more robust across the BCS-BEC crossover.

Abstract:
J. M. Sancho [Phys. Rev. E 84, 062102 (2011)] analyzed two stochastic interpretations on a recent experiment [Phys. Rev. Lett. 104, 170602 (2010)] of Brownian colloidal particles. The author asserted that the stochastic interpretation "obtained by simply setting the acceleration equal to zero" should not be taken and that the zero-mass limit interpretation of the experimental data would not be physically correct. In this Comment we show that Sancho's analysis is incomplete in that it pre-excludes zero mass limit and hence his assertions are incorrect. Our reasoning will be both mathematical and physical.