Quantum non-locality co-exists with locality

Quantum non-locality is normally defined via violations of Bell's inequalities that exclude certain classical hidden variable theories from explaining quantum correlations. Another definition of non-locality refers to the wave-function collapse thereby one can prepare a quantum state from arbitrary far away. In both cases one can debate on whether non-locality is a real physical phenomenon, e.g. one can employ formulations of quantum mechanics that does not use collapse, or one can simply refrain from explaining quantum correlations via classical hidden variables. Here we point out that there is a non-local effect within quantum mechanics, i.e. without involving hidden variables or collapse. This effect is seen via imprecise (i.e. interval-valued) joint probability of two observables, which replaces the ill-defined notion of the precise joint probability for non-commuting observables. It is consistent with all requirements for the joint probability, e.g. those for commuting observales. The non-locality amounts to a fact that (in a two-particle system) the joint imprecise probability of non-commuting two-particle observables (i.e. tensor product of single-particle observables) does not factorize into single-particle contributions, even for uncorrelated states of the two-particle system. The factorization is recovered for a less precise (i.e. the one involving a wider interval) joint probability. This approach to non-locality reconciles it with locality, since the latter emerges as a less precise description.Comment: 6 pages, no figure

Emergence of Leadership in Communication

We study a neuro-inspired model that mimics a discussion (or information dissemination) process in a network of agents. During their interaction, agents redistribute activity and network weights, resulting in emergence of leader(s). The model is able to reproduce the basic scenarios of leadership known in nature and society: laissez-faire (irregular activity, weak leadership, sizable inter-follower interaction, autonomous sub-leaders); participative or democratic (strong leadership, but with feedback from followers); and autocratic (no feedback, one-way influence). Several pertinent aspects of these scenarios are found as well---e.g., hidden leadership (a hidden clique of agents driving the official autocratic leader), and successive leadership (two leaders influence followers by turns). We study how these scenarios emerge from inter-agent dynamics and how they depend on behavior rules of agents---in particular, on their inertia against state changes.Comment: 17 pages, 11 figure

Quantum Brownian motion and its conflict with the second law

The Brownian motion of a harmonically bound quantum particle and coupled to a harmonic quantum bath is exactly solvable. At low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. This happens when a cloud of bath modes around the particle is formed. Equilibrium thermodynamics for particle plus bath together, does not imply standard thermodynamics for the particle itself at low T. Various formulations of the second law are then invalid. First, the Clausius inequality can be violated. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the rate of entropy production is partly negative. Third, for non-adiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobile of the second kind, having several work extraction cycles, enter the realm of condensed matter physics.Comment: 6 pages Latex, uses aip-proceedings style files. Proceedings `Quantum Limits to the Second Law', San Diego, July 200

Phase transitions and quantum measurements

In a quantum measurement, a coupling $g$ between the system S and the apparatus A triggers the establishment of correlations, which provide statistical information about S. Robust registration requires A to be macroscopic, and a dynamical symmetry breaking of A governed by S allows the absence of any bias. Phase transitions are thus a paradigm for quantum measurement apparatuses, with the order parameter as pointer variable. The coupling $g$ behaves as the source of symmetry breaking. The exact solution of a model where S is a single spin and A a magnetic dot (consisting of $N$ interacting spins and a phonon thermal bath) exhibits the reduction of the state as a relaxation process of the off-diagonal elements of S+A, rapid due to the large size of $N$. The registration of the diagonal elements involves a slower relaxation from the initial paramagnetic state of A to either one of its ferromagnetic states. If $g$ is too weak, the measurement fails due to a ``Buridan's ass'' effect. The probability distribution for the magnetization then develops not one but two narrow peaks at the ferromagnetic values. During its evolution it goes through wide shapes extending between these values.Comment: 12 pages, 2 figure

The Quantum Measurement Process: Lessons from an Exactly Solvable Model

The measurement of a spin-\half is modeled by coupling it to an apparatus, that consists of an Ising magnetic dot coupled to a phonon bath. Features of quantum measurements are derived from the dynamical solution of the measurement, regarded as a process of quantum statistical mechanics. Schr\"odinger cat terms involving both the system and the apparatus, die out very quickly, while the registration is a process taking the apparatus from its initially metastable state to one of its stable final states. The occurrence of Born probabilities can be inferred at the macroscopic level, by looking at the pointer alone. Apparent non-unitary behavior of the measurement process is explained by the arisal of small many particle correlations, that characterize relaxation.Comment: 13 pages, discussion of pre-measurement added. World Scientific style. To appear in proceedings "Beyond The Quantum", Th.M. Nieuwenhuizen et al, eds, (World Scientific, 2007