Improving the steady-state coherence and entanglement of two coupled qubits via composite system-reservoir interactions

In this work, we study the improvement of steady-state coherence (SSC) and steady-state entanglement (SSE) of two coupled qubits by means of composite system-reservoir interaction constructed by a linear combination of orthogonal and parallel ones. We show that in the non-equilibrium case, the SSC and SSE can be significantly enhanced by increasing the parallel components of the interaction Hamiltonian between the system of interest and the heat reservoirs. In addition, we find that in the non-equilibrium case, increasing the parallel components can enlarge the temperature (temperature difference) region where the SSC can maintain nonzero values. In the equilibrium situation, however, the SSC and SSE are not affected by the parallel components of the composite system-reservoir interactions.

A differential game of N persons in which there is Pareto equilibrium of objections and counterobjections and no Nash equilibrium

A linear-quadratic positional differential game of N persons is considered. The solution of a game in the form of Nash equilibrium has become widespread in the theory of noncooperative differential games. However, Nash equilibrium can be internally and externally unstable, which is a negative in its practical use. The consequences of such instability could be avoided by using Pareto maximality in a Nash equilibrium situation. But such a coincidence is rather an exotic phenomenon (at least we are aware of only three cases of such coincidence). For this reason, it is proposed to consider the equilibrium of objections and counterobjections. This article establishes the coefficient criteria under which in a differential positional linear-quadratic game of N persons there is Pareto equilibrium of objections and counterobjections and at the same time no Nash equilibrium situation; an explicit form of the solution of the game is obtained.

The Sparta Game

In this chapter, Ober and Weingast find the roots of some of the most unusual features of Archaic/Classical-era Sparta in the “proportionality principle.” That principle holds that the stability of a regime in which ruling elites extract revenues from nonelites through violence (or its threat) requires that each elite receive a share of rents proportionate to his potential to employ disruptive violence. When proportionality is respected, no one with the power to disrupt society has an incentive to do so. This equilibrium situation helps explain the high degree of stability in Sparta’s sociopolitical system, but it also held the seeds of Sparta’s demise. Proportionality meant that rents could not be redistributed in ways that would have been more economically productive, and the Spartans’ failure to redistribute rents led to the regular demotion of the least successful Spartiates from the ruling class and hence to demographic and military collapse.

Control parameters for electrochemically relevant materials: the significance of size and complexity

This contribution is concerned with the control parameters for arriving at defined, electrochemically relevant materials. The treatment is precise as far as the equilibrium situation of simple crystals is concerned, but becomes more and more qualitative if the distance from equilibrium or the (structural or compositional) complexity increases. It proves useful to distinguish between in situ parameters and ex situ parameters, the number ratio of which decreases with increasing distance from equilibrium. A particularly complex situation is met if not only size, shape and phase distribution are important, but even morphological details are of relevance, as it is the case for modern battery electrodes (“electrochemical integrated circuits”). For such cases archetypical examples along with their advantages or disadvantages for electrochemical storage properties are discussed. In this context, special emphasis is placed upon the dimensionality and distribution topology of building elements.

Transient fields produced by a cylindrical electron beam flowing through a plasma

The out-of-equilibrium situation in which an initially sharp-edged cylindrical electron beam, that could, e.g., model electrons flowing within a wire, is injected into a plasma is considered. A detailed computation of the subsequently produced magnetic field is presented. The control parameter of the problem is shown to be the ratio of the beam radius to the electron skin depth. Two alternative ways to address analytically the problem are considered: one uses the usual Laplace transform approach, the other one involves Riemann's method in which causality conditions manifest through some integrals of triple products of Bessel functions.