Highlights of 2012

We show that the description of the quantum phase transition in terms of the entropic uncertainty relation turns out to be more suitable than in terms of the standard variance-based uncertainty relation. The entropic uncertainty relation detects the quantum phase transition in the Dicke model and it provides a correct description of the quantum fluctuations or quantum uncertainty of the system.

We consider a molecular machine described as a Brownian particle diffusing in a tilted periodic potential. We evaluate the absorbed and released power of the machine as a function of the applied molecular and chemical forces, by using the fact that the times for completing a cycle in the forward and the backward direction have the same distribution, and that the ratio of the corresponding splitting probabilities can be simply expressed as a function of the applied force. We explicitly evaluate the efficiency at maximum power for a simple sawtooth potential. We also obtain the efficiency at maximum power for a broad class of 2-D models of a Brownian machine and find that loosely coupled machines operate with a smaller efficiency at maximum power than their strongly coupled counterparts.

Non-Markovian processes have recently become a central topic in the study of open quantum systems. We realize experimentally non-Markovian decoherence processes of single photons by combining time delay and evolution in a polarization-maintaining optical fiber. The experiment allows the identification of the process with strongest memory effects as well as the determination of a recently proposed measure for the degree of quantum non-Markovianity based on the exchange of information between the open system and its environment. Our results show that an experimental quantification of memory in quantum processes is indeed feasible which could be useful in the development of quantum memory and communication devices.

We propose the minimally nonlinear irreversible heat engine as a new general theoretical model to study the efficiency at the maximum power η^* of heat engines operating between the hot heat reservoir at the temperature T_h and the cold one at T_c (T_c⩽T_h). Our model is based on the extended Onsager relations with a new nonlinear term meaning the power dissipation. In this model, we show that η^* is bounded from the upper side by a function of the Carnot efficiency η_C≡1−T_c/T_h as η^*⩽η_C/(2−η_C). We demonstrate the validity of our theory by showing that the low-dissipation Carnot engine can easily be described by our theory.

The proximity force approximation (PFA) relates the interaction between closely spaced, smoothly curved objects to the force between parallel plates. Precision experiments on Casimir forces necessitate, and spur research on, corrections to the PFA. We use a derivative expansion for gently curved surfaces to derive the leading curvature modifications to the PFA. Our methods apply to any homogeneous and isotropic materials; here we present results for Dirichlet and Neumann boundary conditions and for perfect conductors. A Padé extrapolation constrained by a multipole expansion at large distance and our improved expansion at short distances, provides an accurate expression for the sphere/plate Casimir force at all separations.

We study the entanglement entropy of connected bipartitions in free-fermion gases of N particles in arbitrary dimension d. We show that the von Neumann and Rényi entanglement entropies grow asymptotically as N^(d−1)/d ln N, with a prefactor that is analytically computed using the Widom conjecture both for periodic and open boundary conditions. The logarithmic correction to the power-law behavior is related to the area-law violation in lattice free fermions. These asymptotic large-N behaviors are checked against exact numerical calculations for N-particle systems.