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The discovery of superconductivity in the quantum critical Kondo-lattice system YbRh _2 Si _2 at an extremely low temperature of 2 mK has inspired efforts to perform high-resolution electrical resistivity measurements down to this temperature range in highly conductive materials. Here we show that control over the sample geometry by microstructuring using focused-ion-beam techniques allows to reach ultra-low temperatures and increase signal-to-noise ratios (SNRs) tenfold, without adverse effects to sample quality. In five experiments we show four-terminal sensing resistance and magnetoresistance measurements which exhibit sharp phase transitions at the Néel temperature, and Shubnikov–de-Haas (SdH) oscillations between 13 T and 18 T where we identified a new SdH frequency of 0.39 kT. The increased SNR allowed resistance fluctuation (noise) spectroscopy that would not be possible for bulk crystals, and confirmed intrinsic $1/f$ -type fluctuations. Under controlled strain, two thin microstructured samples exhibited a large increase of $T_\mathrm{N}$ from 67 mK up to 188 mK while still showing clear signatures of the phase transition and SdH oscillations. Superconducting quantum interference device-based thermal noise spectroscopy measurements in a nuclear demagnetization refrigerator down to 0.95 mK, show a sharp superconducting transition at $T_\mathrm{c} = 1.2$ mK. These experiments demonstrate microstructuring as a powerful tool to investigate the resistance and the noise spectrum of highly conductive correlated metals over wide temperature ranges.

We design new navigation strategies for travel time optimization of microscopic self-propelled particles in complex and noisy environments. In contrast to strategies relying on the results of optimal control theory or machine learning approaches, implementation of these protocols can be done in a semi-autonomous fashion, as it does not require control over the microswimmer motion via external feedback loops. Although the strategies we propose rely on simple principles, they show arrival time statistics strikingly close to optimality, as well as performances that are robust to environmental changes and strong fluctuations. These features, as well as their applicability to more general optimization problems, make these strategies promising candidates for the realization of optimized semi-autonomous navigation.

Fluctuation characteristics of plasma jet flow in an innovative long DC arc system with ring-shaped anode were successfully clarified on the basis of the high-speed camera visualization. The long DC arc with long electrode gap distance more than 350 mm has been applied to gas decomposition due to its advantages such as large plasma volume and long residence time of treated gas. However, large heat loss at a conventional hemispherical-shaped anode was critical issue in the long DC arc system. Therefore, a ring-shaped anode was utilized to convert large energy loss at the anode into the plasma jet flow. Two kinds of the experiments were conducted. One was the estimation of energy balance in the long DC arc system. Calorimetric measurements were carried out. Another was the high-speed camera observation of the arc fluctuation and the plasma jet fluctuation. Results indicated that the 60% of heat loss at the conventional hemispherical-shaped anode was converted into the plasma jet flow when the ring-shaped anode was utilized. High-speed camera observation revealed that the plasma jet fluctuation with sharp FFT peak in the range of 25-500Hz was attributed to the arc fluctuation, which originated from the restrike phenomena of the anode spot. In contrast, results also suggested that the plasma jet fluctuation with broad FFT peaks in the range of 100-300Hz was attributed to the eddy formation due to the entrainment of ambient cold gas. To understand and control the fluctuation phenomena in the plasma jet enables to establish the innovative waste treatment by thermal plasmas.

Scale free Lévy motion is a generalized analogue of the Wiener process. Its time derivative extends the notion of “white noise” to non-Gaussian noise sources, and as such, it has been widely used to model natural signal variations described by an overdamped Langevin stochastic differential equation. Here, we consider the dynamics of an archetypal model: a Brownian-like particle is driven by external forces, and noise is represented by uncorrelated Lévy fluctuations. An unperturbed system of that form eventually attains a steady state which is uniquely determined by the set of parameter values. We show that the analyzed Markov process with the stability index α < 2 violates the detailed balance, i.e., its stationary state is quantified by a stationary probability density and nonvanishing current. We discuss consequences of the non-Gibbsian character of the stationary state of the system and its impact on the general form of the fluctuation–dissipation theorem derived for weak external forcing.

The time-delayed feedback control mechanisms of the nervous system are continuously subjected to the effects of uncontrolled random perturbations (herein referred to as noise). In this setting the statistical properties of the fluctuations in the controlled variable(s) can provide non-invasive insights into the nature of the underlying control mechanisms. We illustrate this concept through a study of stick balancing at the fingertip using high speed motion capture techniques. Experimental observations together with numerical studies of a stochastic delay differential equation demonstrate that on time scales short compared to the neural time delay ("fast control"), parametric noise provides a non-predictive mechanism that transiently stabilizes the upright position of the balanced stick. Moreover, numerical simulations of a delayed random walker with a repulsive origin indicate that even an unstable fixed point can be transiently stabilized by the interplay between noise and time delay. In contrast, on time scales comparable to the neural time delay ("slow control"), feedback and feedforward control mechanisms become more important. The relative contribution of the fast and slow control mechanisms to stick balancing is dynamic and, for example, depends on the context in which stick balancing is performed and the expertise of the balancer.

We present a stylized model of controlled equilibration of a small system in a fluctuating environment. We derive the optimal control equations steering in finite-time the system between two equilibrium states. The corresponding thermodynamic transition is optimal in the sense that it occurs at minimum entropy if the set of admissible controls is restricted by certain bounds on the time derivatives of the protocols. We apply our equations to the engineered equilibration of an optical trap considered in a recent proof of principle experiment. We also analyze an elementary model of nucleation previously considered by Landauer to discuss the thermodynamic cost of one bit of information erasure. We expect our model to be a useful benchmark for experiment design as it exhibits the same integrability properties of well-known models of optimal mass transport by a compressible velocity field.

The thermodynamic entropy production for the scattering processes of noninteracting bosons and fermions in mesoscopic systems is shown to be related to the difference between the Connes–Narnhofer–Thirring entropy per unit time, characterizing temporal disorder in the motion of quantum particles, and the associated time-reversed coentropy per unit time. Under nonequilibrium conditions, the positivity of thermodynamic entropy production can thus be interpreted as a time-reversal symmetry breaking in the temporal disorder of the quantum transport process. Moreover, the full counting statistics of both fermionic and bosonic quantum transport is formulated in relation with the energy and particle currents producing thermodynamic entropy in nonequilibrium steady states.

We introduce a model described in terms of a scalar velocity field on a 1D lattice, evolving through collisions that conserve momentum but do not conserve energy. Such a system possesses some of the main ingredients of fluidized granular media and naturally models them. We deduce non-linear fluctuating hydrodynamics equations for the macroscopic velocity and temperature fields, which replicate the hydrodynamics of shear modes in a granular fluid. Moreover, this Landau-like fluctuating hydrodynamics predicts an essential part of the peculiar behaviour of granular fluids, like the instability of homogeneous cooling state at large size or inelasticity. We also compute the exact shape of long range spatial correlations which, even far from the instability, have the physical consequence of noticeably modifying the cooling rate. This effect, which stems from momentum conservation, has not been previously reported in the realm of granular fluids.

We argue that the theories of Volokitin and Persson (2014 New J. Phys. http://dx.doi.org/10.1088/1367-2630/16/11/118001 16 http://dx.doi.org/10.1088/1367-2630/16/11/118001 ), Dedkov and Kyasov (2008 J. Phys.: Condens. Matter http://dx.doi.org/10.1088/0953-8984/20/35/354006 20 http://dx.doi.org/10.1088/0953-8984/20/35/354006 ), and Pieplow and Henkel (2013 New J. Phys. http://dx.doi.org/10.1088/1367-2630/15/2/023027 15 http://dx.doi.org/10.1088/1367-2630/15/2/023027 ) agree on the electromagnetic force on a small, polarizable particle that is moving parallel to a planar, macroscopic body, as far as the contribution of evanescent waves is concerned. The apparent differences are discussed in detail and explained by choices of units and integral transformations. We point out in particular the role of the Lorentz contraction in the procedure used by Volokitin and Persson, where a macroscopic body is ‘diluted’ to obtain the force on a small particle. Differences that appear in the contribution of propagating photons are briefly mentioned.