Open quantum random walks, quantum Markov chains and recurrence

In the present paper, we construct QMCs (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC to the commutative subalgebra coincides with the distribution [Formula: see text] of OQRW. This sheds new light on some properties of the measure [Formula: see text]. As an example, we simply mention that the measure can be considered as a distribution of some functions of certain Markov processes. Furthermore, we study several properties of QMC and associated measures. A new notion of [Formula: see text]-recurrence of QMC is studied, and the relations between the concepts of recurrence introduced in this paper and the existing ones are established.

Eigenvalues, absolute continuity and localizations for periodic unitary transition operators

The localization phenomenon for periodic unitary transition operators on a Hilbert space consisting of square summable functions on an integer lattice with values in a finite-dimensional Hilbert space, which is a generalization of the discrete-time quantum walks with constant coin matrices, is discussed. It is proved that a periodic unitary transition operator has an eigenvalue if and only if the corresponding unitary matrix-valued function on a torus has an eigenvalue which does not depend on the points on the torus. It is also proved that the continuous spectrum of a periodic unitary transition operator is absolutely continuous. As a result, it is shown that the localization happens if and only if there exists an eigenvalue, and when there exists only one eigenvalue, the long-time limit of transition probabilities coincides with the point-wise norm of the projection of the initial state to the eigenspace. The results can be applied to certain unitary operators on a Hilbert space on a covering graph, called a topological crystal, over a finite graph. An analytic perturbation theory for matrices in several complex variables is employed to show the result about absolute continuity for periodic unitary transition operators.

Radiative pion capture in 2H, 3He and 3H

We investigate the π– + 2H → γ + n + n, π– + 3He → γ + 3H, π– + 3He → γ + n + d, π– + 3He → γ + n + n + p and π– + 3H → γ + n + n + n capture reactions using realistic two-nucleon and three-nucleon potentials and the single nucleon Kroll-Ruderman-type transition operator. We obtain predictions for the total capture rates for all these processes, calculating rigorously the initial and final nuclear states.

Matrix model of strength distribution: Extension and phase transition

In this work, we extend a previous study of matrix models of strength distributions. We still retain the nearest neighbor coupling mode but we extend the values of the coupling parameter [Formula: see text]. We consider extremes, from very small [Formula: see text] to very large [Formula: see text]. We first use the same transition operator as before [Formula: see text]. For this case, we get an exponential decrease for small [Formula: see text], as expected, but we get a phase transition beyond [Formula: see text]=10, where we get separate exponentials for even [Formula: see text] and for odd [Formula: see text]. We now also consider the dipole choice where [Formula: see text].

Spectator isobar production in the A(γ,πNN)B reaction

We present an analysis of the spectator mechanism of [Formula: see text]-isobar production in the pion photoproduction on nuclei with the emission of two nucleons. The reaction mechanism is studied within the framework of the [Formula: see text]-correlation model, which considers the isobar and nucleon of the [Formula: see text]-system produced in the nucleus at the virtual [Formula: see text] transition to be in a dynamic relationship. The two-particle transition operator for nuclei is obtained by the S-matrix approach. We consider the properties of the spectator mechanism of isobar production using the example of the reaction [Formula: see text]O[Formula: see text]O. Numerical estimates of the cross-section are obtained in the kinematic region, where it is possible to expect the manifestation of bound isobar-nuclear states.

Design of Optimal Fractional Luenberger Observers for Linear Fractional-Order Systems

Optimal fractional Luenberger observers for linear fractional-order systems are developed using the fractional Chebyshev collocation (FCC) method. It is shown that the design method has advantages over existing Luenberger design methods for fractional order systems. To accomplish this, the state transition operator for the solution of linear fractional-order systems is defined in a Banach space and discretized using the FCC method. In addition, the discretized state transition operator is obtained by using the FCC method. Next, the optimal observer gains are obtained by minimizing the spectral radius of the state transition operator for the observer,while ensuring that the observer responds faster than the controller. Finally, a numerical example is provided to demonstrate the validity and the efficiency of the proposed method.