Solving the Coulomb scattering problem using the complex scaling method

Based on the work of Nuttall and Cohen [Phys. Rev. {\bf 188} (1969) 1542] and Resigno et al{} [Phys. Rev. A {\bf 55} (1997) 4253] we present a rigorous formalism for solving the scattering problem for long-range interactions without using exact asymptotic boundary conditions. The long-range interaction may contain both Coulomb and short-range potentials. The exterior complex scaling method, applied to a specially constructed inhomogeneous Schr\"odinger equation, transforms the scattering problem into a boundary problem with zero boundary conditions. The local and integral representations for the scattering amplitudes have been derived. The formalism is illustrated with numerical examples.Comment: 3 pages, 3 figure

Silvopastoral Agroforestry in Upland and Lowland UK Grassland: Tree Growth and Animal Performance

Trees, individually protected from herbivore damage using plastic shelters, were planted at two densities (100 and 400 stems/ha) into sheepgrazed pasture in upland and lowland UK grassland sites in 1988. Tree and animal performance were compared with conventional forestry (no sheep) and pasture (no tree) systems. Effects on tree growth and survival are highly species and site dependent although some treatment effects did emerge. Tree shelters encouraged rapid early height growth compared to forestry controls although in some cases tree form was also adversely affected. Generally tree performance within agroforestry treatments was better at the higher planting density. Eight years after planting there has been no reduction in animal production despite interception of up to 10% of total photosynthetically active radiation by the developing tree canopy

Resonances Width in Crossed Electric and Magnetic Fields

We study the spectral properties of a charged particle confined to a two-dimensional plane and submitted to homogeneous magnetic and electric fields and an impurity potential. We use the method of complex translations to prove that the life-times of resonances induced by the presence of electric field are at least Gaussian long as the electric field tends to zero.Comment: 3 figure

Shapes of leading tunnelling trajectories for single-electron molecular ionization

Based on the geometrical approach to tunnelling by P.D. Hislop and I.M. Sigal [Memoir. AMS 78, No. 399 (1989)], we introduce the concept of a leading tunnelling trajectory. It is then proven that leading tunnelling trajectories for single-active-electron models of molecular tunnelling ionization (i.e., theories where a molecular potential is modelled by a single-electron multi-centre potential) are linear in the case of short range interactions and "almost" linear in the case of long range interactions. The results are presented on both the formal and physically intuitive levels. Physical implications of the obtained results are discussed.Comment: 14 pages, 5 figure

Stage-Specific Inhibition of MHC Class I Presentation by the Epstein-Barr Virus BNLF2a Protein during Virus Lytic Cycle

gamma-herpesvirus Epstein-Barr virus (EBV) persists for life in infected individuals despite the presence of a strong immune response. During the lytic cycle of EBV many viral proteins are expressed, potentially allowing virally infected cells to be recognized and eliminated by CD8+ T cells. We have recently identified an immune evasion protein encoded by EBV, BNLF2a, which is expressed in early phase lytic replication and inhibits peptide- and ATP-binding functions of the transporter associated with antigen processing. Ectopic expression of BNLF2a causes decreased surface MHC class I expression and inhibits the presentation of indicator antigens to CD8+ T cells. Here we sought to examine the influence of BNLF2a when expressed naturally during EBV lytic replication. We generated a BNLF2a-deleted recombinant EBV (ΔBNLF2a) and compared the ability of ΔBNLF2a and wild-type EBV-transformed B cell lines to be recognized by CD8+ T cell clones specific for EBV-encoded immediate early, early and late lytic antigens. Epitopes derived from immediate early and early expressed proteins were better recognized when presented by ΔBNLF2a transformed cells compared to wild-type virus transformants. However, recognition of late antigens by CD8+ T cells remained equally poor when presented by both wild-type and ΔBNLF2a cell targets. Analysis of BNLF2a and target protein expression kinetics showed that although BNLF2a is expressed during early phase replication, it is expressed at a time when there is an upregulation of immediate early proteins and initiation of early protein synthesis. Interestingly, BNLF2a protein expression was found to be lost by late lytic cycle yet ΔBNLF2a-transformed cells in late stage replication downregulated surface MHC class I to a similar extent as wild-type EBV-transformed cells. These data show that BNLF2a-mediated expression is stage-specific, affecting presentation of immediate early and early proteins, and that other evasion mechanisms operate later in the lytic cycle

Spectral Analysis for Matrix Hamiltonian Operators

In this work, we study the spectral properties of matrix Hamiltonians generated by linearizing the nonlinear Schr\"odinger equation about soliton solutions. By a numerically assisted proof, we show that there are no embedded eigenvalues for the three dimensional cubic equation. Though we focus on a proof of the 3d cubic problem, this work presents a new algorithm for verifying certain spectral properties needed to study soliton stability. Source code for verification of our comptuations, and for further experimentation, are available at http://www.math.toronto.edu/simpson/files/spec_prop_code.tgz.Comment: 57 pages, 22 figures, typos fixe

Generating GHZ state in 2m-qubit spin network

We consider a pure 2m-qubit initial state to evolve under a particular quantum me- chanical spin Hamiltonian, which can be written in terms of the adjacency matrix of the Johnson network J(2m;m). Then, by using some techniques such as spectral dis- tribution and stratification associated with the graphs, employed in [1, 2], a maximally entangled GHZ state is generated between the antipodes of the network. In fact, an explicit formula is given for the suitable coupling strengths of the hamiltonian, so that a maximally entangled state can be generated between antipodes of the network. By using some known multipartite entanglement measures, the amount of the entanglement of the final evolved state is calculated, and finally two examples of four qubit and six qubit states are considered in details.Comment: 22 page

Norm estimates of complex symmetric operators applied to quantum systems

This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, we propose a formula for computing the norm of a compact complex symmetric operator. This observation is applied to two concrete problems related to quantum mechanical systems. First, we give sharp estimates on the exponential decay of the resolvent and the single-particle density matrix for Schr\"odinger operators with spectral gaps. Second, we provide new ways of evaluating the resolvent norm for Schr\"odinger operators appearing in the complex scaling theory of resonances

Diamonds's Temperature: Unruh effect for bounded trajectories and thermal time hypothesis

We study the Unruh effect for an observer with a finite lifetime, using the thermal time hypothesis. The thermal time hypothesis maintains that: (i) time is the physical quantity determined by the flow defined by a state over an observable algebra, and (ii) when this flow is proportional to a geometric flow in spacetime, temperature is the ratio between flow parameter and proper time. An eternal accelerated Unruh observer has access to the local algebra associated to a Rindler wedge. The flow defined by the Minkowski vacuum of a field theory over this algebra is proportional to a flow in spacetime and the associated temperature is the Unruh temperature. An observer with a finite lifetime has access to the local observable algebra associated to a finite spacetime region called a "diamond". The flow defined by the Minkowski vacuum of a (four dimensional, conformally invariant) quantum field theory over this algebra is also proportional to a flow in spacetime. The associated temperature generalizes the Unruh temperature to finite lifetime observers. Furthermore, this temperature does not vanish even in the limit in which the acceleration is zero. The temperature associated to an inertial observer with lifetime T, which we denote as "diamond's temperature", is 2hbar/(pi k_b T).This temperature is related to the fact that a finite lifetime observer does not have access to all the degrees of freedom of the quantum field theory.Comment: One reference correcte