The most general admissible boundary conditions are derived for an idealized AharonovBohm flux intersecting the plane at the origin on the background of a homogeneous magnetic field. A standard technique based on self-adjoint extensions yields a four-parameter family of boundary conditions; the other two parameters of the model are the AharonovBohm flux and the homogeneous magnetic field. The generalized boundary conditions may be regarded as a combination of the AharonovBohm effect with a point interaction. Spectral properties of the derived Hamtonians are studied in detail.

This paper proposes a two-level continuum transportation system approach to modeling a dynamic taxi traffic assignment (DTTA) problem in a dense network with real-time traffic information provision and three types of vehicles, including private cars, occupied taxis, and vacant taxis. The proposed approach treats the dense network as a continuum in the first level, in which private car and occupied taxi drivers are free to choose their paths in a two-dimensional continuous space. The proposed approach also divides the modeling region into many identical squares to form a cell-based network in the second level, in which the cells are classified into two categories: target cell with an acceptable expected rate of return (EROR) to vacant taxi drivers and non-target cell with an unacceptable EROR. The EROR associated with a cell is the ratio of the cumulative expected profit of a taxi driver who successfully picks up a customer during the customer search that starts from that cell to the sum of expected search time for this customer and expected occupied travel time to serve this customer. Based on the cell-based network, we develop a cell-based intervening opportunity model to capture the fact that vacant taxi drivers can meet a customer on the way to their destination zones and estimate the EROR. Each vacant taxi driver has a mixed strategy to determine his/her customer-search direction according to the EROR: Each vacant taxi driver in a target cell selects its neighbor cells with maximum EROR, and each vacant taxi driver in a non-target cell selects the travel time-based shortest path to his/her target cell. Meanwhile, each private car driver chooses the path that minimizes his/her own generalized travel cost, and each occupied taxi driver chooses the path that minimizes his/her customer's generalized in-vehicle travel cost. In our model, traffic density in the system is governed by the conservation law (CL), and the flow directions of different vehicles are determined by the path-choice strategies of their drivers, which are captured by Hamilton–Jacobi (HJ) equations. Both the proposed CL and HJ equations can be solved by the Lax–Friedrichs scheme, which forms the backbone of the developed solution algorithm. Finally, numerical examples and a case study are used to demonstrate the properties of the model, the performance of the solution algorithm, and the value of using our methodology for estimating network performance.

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The subject of the paper is Schrdinger operators on tree graphs which are radial, having the branching number bn at all the vertices at the distance tn from the root. We consider a family of coupling conditions at the vertices characterized by (bn1)2+4 real parameters. We prove that if the graph is sparse so that there is a subsequence of {tn+1tn} growing to infinity, in the absence of the potential the absolutely continuous spectrum is empty for a large subset of these vertex couplings, but on the the other hand, there are cases when the spectrum of such a Schrdinger operator can be purely absolutely continuous.

The initial decay rate of a mixed state is discussed; is shown to be zero for finite energy states. In the previous paper [1] we investigated a general scheme for description of unstable systems. One of our results concerned the initial decay rate. Generalizing the earlier results of Horwitz and Marchand (see [2] and other references contained in [1]) we proved there, that the initial decay rate of any pure state of the unstable system equals to zero, if this state is so called finite energy state. Here we shall be interested in the same problem, assuming now the state of the decaying system to be in general mixed. Such assumption seems to be reasonable: firstly, from the point of view of an experiment it is too restrictive to treat only pure states of unstable systems. In particular, mixed states are generally considered in the recent studies about the influence of measuring devices on the time evolution of the unstable system [3

We consider a Schrdinger particle on a graph consisting of <i>N</i> links joined at a single point. Each link supports a real locally integrable potential <i>V</i> _<i>j</i>; the self-adjointness is ensured by the type boundary condition at the vertex. If all the links are semi-infinite and ideally coupled, the potential decays as <i>x</i> ¹ along each of them, is nonrepulsive in the mean and weak enough, the corresponding Schrdinger operator has a single negative eigenvalue; we find its asymptotic behavior. We also derive a bound on the number of bound states and explain how the coupling constant may be interpreted in terms of a family of squeezed potentials.

We study the behavior of a quantum particle confined to a hard-wall strip of a constant width in which there is a finite number<i>N</i>of point perturbations. Constructing the resolvent of the corresponding Hamiltonian by means of Krein's formula, we analyze its spectral and scattering properties. The bound state problem is analogous to that of point interactions in the plane: since a two-dimensional point interaction is never repulsive, there are<i>m</i>discrete eigenvalues, 1<i>m</i><i>N</i>, the lowest of which is nondegenerate. On the other hand, due to the presence of the boundary the point interactions give rise to infinite series of resonances; if the coupling is weak they approach the thresholds of higher transverse modes. We derive also spectral and scattering properties for point perturbations in several related models: a cylindrical surface, both of a finite and of an infinite height, threaded by a magnetic flux, and a straight strip which

In this paper, we attempt to reconstruct one of the last and incomplete projects of Volodya Geyler. We study the motion of a quantum particle in the plane to which a halfline lead is attached, assuming that the particle has spin and the plane component of the Hamiltonian contains a spin-orbit interaction, of Rashba or Dresselhaus type. We construct a class of admissible Hamiltonians and derive an explicit expression for the Green function, which is applied to scattering in a system of this kind.

We consider scattering of a three-dimensional particle on a finite family of potentials. For some parameter values the scattering wavefunctions exhibit nodal lines in the form of closed loops, which may touch but do not entangle. The corresponding probability current forms vortical singularities around these lines; if the scattered particle is charged, this gives rise to magnetic flux loops in the vicinity of the nodal lines. The conclusions extend to scattering on hard obstacles or smooth potentials.

Convergence theories and a deluxe dual and primal finite element tearing and interconnecting algorithm are developed for a hybrid staggered DG finite element approximation of H(curl) elliptic problems in two dimensions. In addition to the advantages of staggered DG methods, the basis functions of the new hybrid staggered DG method are all locally supported in the triangular elements, and a Lagrange multiplier approach is applied to enforce the global connections of these basis functions. The interface problem on the Lagrange multipliers is further reduced to the resulting problem on the subdomain interfaces, and a dual and primal finite element tearing and interconnecting algorithm with an enriched weight factor is then applied to the resulting problem. Our algorithm is shown to give a condition number bound of <i>C</i>(1+log(<i>H</i><i>h</i>))², independent of the two parameters, where <i>H</i><i>h</i> is the number of