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Properties of non-hermitian quantum field theories

Carl M. Bender (2003)

Annales de l’institut Fourier

In this paper I discuss quantum systems whose Hamiltonians are non-Hermitian but whose energy levels are all real and positive. Such theories are required to be symmetric under 𝒞 𝒫 𝒯 , but not symmetric under 𝒫 and 𝒯 separately. Recently, quantum mechanical systems having such properties have been investigated in detail. In this paper I extend the results to quantum field theories. Among the systems that I discuss are - φ 4 and i φ 3 theories. These theories all have unexpected and remarkable properties. I discuss...

Quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field

Michael Melgaard (2003)

Open Mathematics

For fixed magnetic quantum number m results on spectral properties and scattering theory are given for the three-dimensional Schrödinger operator with a constant magnetic field and an axisymmetrical electric potential V. In various, mostly singular settings, asymptotic expansions for the resolvent of the Hamiltonian H m+Hom+V are deduced as the spectral parameter tends to the lowest Landau threshold. Furthermore, scattering theory for the pair (H m, H om) is established and asymptotic expansions...

Recovering the total singularity of a conormal potential from backscattering data

Mark S. Joshi (1998)

Annales de l'institut Fourier

The problem of recovering the singularities of a potential from backscattering data is studied. Let Ω be a smooth precompact domain in ℝ n which is convex (or normally accessible). Suppose V i = v + w i with v ∈ C c ∞ ( ℝ n ) and w i conormal to the boundary of Ω and supported inside Ω ‾ then if the backscattering data of V 1 and V 2 are equal up to smoothing, we show that w 1 - w 2 is smooth.

Resolvent and Scattering Matrix at the Maximum of the Potential

Alexandrova, Ivana, Bony, Jean-François, Ramond, Thierry (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.We study the microlocal structure of the resolvent of the semiclassical Schrödinger operator with short range potential at an energy which is a unique non-degenerate global maximum of the potential. We prove that it is a semiclassical Fourier integral operator quantizing the incoming and outgoing Lagrangian submanifolds associated to the fixed hyperbolic point. We then discuss two applications of this result to describing...

Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations

Tanya Christiansen, M. S. Joshi (2003)

Annales de l’institut Fourier

The scattering matrix is defined on a perturbed stratified medium. For a class of perturbations, its main part at fixed energy is a Fourier integral operator on the sphere at infinity. Proving this is facilitated by developing a refined limiting absorption principle. The symbol of the scattering matrix determines the asymptotics of a large class of perturbations.

Scattering theory for 3-particle systems in constant magnetic fields : dispersive case

Christian Gérard, Izabella Łaba (1996)

Annales de l'institut Fourier

We develop a scattering theory for quantum systems of three charged particles in a constant magnetic field. For such systems, we generalize our earlier results in that we make no additional assumptions on the electric charges of subsystems. The main difficulty is the analysis of the scattering channels corresponding to the motion of the bound states of the neutral subsystems in the directions transversal to the field. The effective kinetic energy of this motion is given by certain dispersive Hamiltonians;...

Currently displaying 101 – 120 of 191