Random unitary dynamics of quantum networks

We investigate the asymptotic dynamics of quantum networks under repeated applications of random unitary operations. It is shown that in the asymptotic limit of large numbers of iterations this dynamics is generally governed by a typically low dimensional attractor space. This space is determined completely by the unitary operations involved and it is independent of the probabilities with which these unitary operations are applied. Based on this general feature analytical results are presented for the asymptotic dynamics of arbitrarily large cyclic qubit networks whose nodes are coupled by randomly applied controlled-NOT operations.Comment: 4 pages, 2 figure

Calculations of the moon's heat history at different concentrations of radioactive elements taking account of the material differentiation with melting

A mathematical procedure for analyzing the heat conductivity of the lunar surface is discussed. The solution is based on homogeneous and laminated moon models and considers the effects of radioactive elements conveyed to the lunar surface by melting. The various parameters which introduce uncertainties into the numerical analysis are identified. The application of data obtained from radio astronomy and from analyses of lunar samples returned by the Apollo flights is explained. Tables of data are included to show the types and amounts of radioactive materials which have been identified

Calculations of the moon's thermal history at different concentrations of radioactive elements, taking into account differentiation on melting

Calculations of the thermal history of the moon were done by solving the thermal conductivity equation for the case in which the heat sources are the long lived radioactive elements Th, U, and K-40. The concentrations of these elements were adjusted to give 4 variations of heat flow. Calculations indicated that the moon's interior was heated to melting during the first 0.7 to 2.3 x 10 to the 9th power years. The maximum fusion involved practically the entire moon to a distance from 15 to 45 km beneath the surface, and started 3.5 to 4.0 x 10 to the 9th power years ago, or 2.5 x 3.0 x 10 to the 9th power years ago and continued for 1 to 2 x 10 to the 9th power years. The moon today is cooling. The current thickness of the solid crust is from 150 to 200 km and the heat flow exceeds the stationary value 1.5 fold

Completely positive covariant two-qubit quantum processes and optimal quantum NOT operations for entangled qubit pairs

The structure of all completely positive quantum operations is investigated which transform pure two-qubit input states of a given degree of entanglement in a covariant way. Special cases thereof are quantum NOT operations which transform entangled pure two-qubit input states of a given degree of entanglement into orthogonal states in an optimal way. Based on our general analysis all covariant optimal two-qubit quantum NOT operations are determined. In particular, it is demonstrated that only in the case of maximally entangled input states these quantum NOT operations can be performed perfectly.Comment: 14 pages, 2 figure

Complex chaos in conditional qubit dynamics and purification protocols

Selection of an ensemble of equally prepared quantum systems, based on measurements on it, is a basic step in quantum state purification. For an ensemble of single qubits, iterative application of selective dynamics has been shown to lead to complex chaos, which is a novel form of quantum chaos with true sensitivity to the initial conditions. The Julia set of initial valuse with no convergence shows a complicated structre on the complex plane. The shape of the Julia set varies with the parameter of the dynamics. We present here results for the two qubit case demonstrating how a purification process can be destroyed with chaotic oscillations

Complex chaos in the conditional dynamics of qubits

We analyze the consequences of iterative measurement-induced nonlinearity on the dynamical behavior of qubits. We present a one-qubit scheme where the equation governing the time evolution is a complex-valued nonlinear map with one complex parameter. In contrast to the usual notion of quantum chaos, exponential sensitivity to the initial state occurs here. We calculate analytically the Lyapunov exponent based on the overlap of quantum states, and find that it is positive. We present a few illustrative examples of the emerging dynamics.Comment: 4 pages, 3 figure

Antisymmetric multi-partite quantum states and their applications

Entanglement is a powerful resource for processing quantum information. In this context pure, maximally entangled states have received considerable attention. In the case of bipartite qubit-systems the four orthonormal Bell-states are of this type. One of these Bell states, the singlet Bell-state, has the additional property of being antisymmetric with respect to particle exchange. In this contribution we discuss possible generalizations of this antisymmetric Bell-state to cases with more than two particles and with single-particle Hilbert spaces involving more than two dimensions. We review basic properties of these totally antisymmetric states. Among possible applications of this class of states we analyze a new quantum key sharing protocol and methods for comparing quantum states

Quantitative structural mechanobiology of platelet-driven blood clot contraction.

Blood clot contraction plays an important role in prevention of bleeding and in thrombotic disorders. Here, we unveil and quantify the structural mechanisms of clot contraction at the level of single platelets. A key elementary step of contraction is sequential extension-retraction of platelet filopodia attached to fibrin fibers. In contrast to other cell-matrix systems in which cells migrate along fibers, the "hand-over-hand" longitudinal pulling causes shortening and bending of platelet-attached fibers, resulting in formation of fiber kinks. When attached to multiple fibers, platelets densify the fibrin network by pulling on fibers transversely to their longitudinal axes. Single platelets and aggregates use actomyosin contractile machinery and integrin-mediated adhesion to remodel the extracellular matrix, inducing compaction of fibrin into bundled agglomerates tightly associated with activated platelets. The revealed platelet-driven mechanisms of blood clot contraction demonstrate an important new biological application of cell motility principles