486 research outputs found
Smoothness of Correlations in the Anderson Model at Strong Disorder
We study the higher-order correlation functions of covariant families of
observables associated with random Schr\"odinger operators on the lattice in
the strong disorder regime. We prove that if the distribution of the random
variables has a density analytic in a strip about the real axis, then these
correlation functions are analytic functions of the energy outside of the
planes corresponding to coincident energies. In particular, this implies the
analyticity of the density of states, and of the current-current correlation
function outside of the diagonal. Consequently, this proves that the
current-current correlation function has an analytic density outside of the
diagonal at strong disorder
Correlations Estimates in the Lattice Anderson Model
We give a new proof of correlation estimates for arbitrary moments of the
resolvent of random Schr\"odinger operators on the lattice that generalizes and
extends the correlation estimate of Minami for the second moment. We apply this
moment bound to obtain a new -level Wegner-type estimate that measures
eigenvalue correlations through an upper bound on the probability that a local
Hamiltonian has at least eigenvalues in a given energy interval. Another
consequence of the correlation estimates is that the results on the Poisson
statistics of energy level spacing and the simplicity of the eigenvalues in the
strong localization regime hold for a wide class of translation-invariant,
selfadjoint, lattice operators with decaying off-diagonal terms and random
potentials.Comment: 16 page
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
Spectral Asymptotics of the Dirichlet-To-Neumann Map on Multiply Connected Domains in R^d
We study the spectral asymptotics of the Dirichlet-to-Neumann operator Λγ on a multiply-connected, bounded, domain in R^d, d≥3, associated with the uniformly elliptic operator Lγ = − ∑di,j=1 ∂i γij∂j, where γ is a smooth, positive-definite, symmetric matrix-valued function on Ω. We prove that the operator is approximately diagonal in the sense that Λγ = Dγ + Rγ, where Dγ is a direct sum of operators, each of which acts on one boundary component only, and Rγ is a smoothing operator. This representation follows from the fact that the γ-harmonic extensions of eigenfunctions of Λγ vanish rapidly away from the boundary. Using this representation, we study the inverse problem of determining the number of holes in the body, that is, the number of the connected components of the boundary, by using the high-energy spectral asymptotics of Λγ (Refer to PDF file for exact formulas)
Singular Modes of the Electromagnetic Field
We show that the mode corresponding to the point of essential spectrum of the
electromagnetic scattering operator is a vector-valued distribution
representing the square root of the three-dimensional Dirac's delta function.
An explicit expression for this singular mode in terms of the Weyl sequence is
provided and analyzed. An essential resonance thus leads to a perfect
localization (confinement) of the electromagnetic field, which in practice,
however, may result in complete absorption.Comment: 14 pages, no 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
Ground State and Resonances in the Standard Model of Non-relativistic QED
We prove existence of a ground state and resonances in the standard model of
the non-relativistic quantum electro-dynamics (QED). To this end we introduce a
new canonical transformation of QED Hamiltonians and use the spectral
renormalization group technique with a new choice of Banach spaces.Comment: 50 pages change
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
Anomalous Scale Dimensions from Timelike Braiding
Using the previously gained insight about the particle/field relation in
conformal quantum field theories which required interactions to be related to
the existence of particle-like states associated with fields of anomalous
scaling dimensions, we set out to construct a classification theory for the
spectra of anomalous dimensions. Starting from the old observations on
conformal superselection sectors related to the anomalous dimensions via the
phases which appear in the spectral decomposition of the center of the
conformal covering group we explore the possibility
of a timelike braiding structure consistent with the timelike ordering which
refines and explains the central decomposition. We regard this as a preparatory
step in a new construction attempt of interacting conformal quantum field
theories in D=4 spacetime dimensions. Other ideas of constructions based on the
- or the perturbative SYM approach in their relation to the
present idea are briefly mentioned.Comment: completely revised, updated and shortened replacement, 24 pages
tcilatex, 3 latexcad figure
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