Local distortion techniques and unitarity of the S-matrix for the 2-body problem

AbstractThe two-body S-matrix for an interaction with exponential decay at infinity is defined in a time-independent way and its unitarity is proved directly by local distortion techniques. Complete sets of incoming and outgoing states, or delicate resolvent estimates are not needed for the proof

Triatomic continuum resonances for large negative scattering lengths

We study triatomic systems in the regime of large negative scattering lengths which may be more favorable for the formation of condensed trimers in trapped ultracold monoatomic gases as the competition with the weakly bound dimers is absent. The manipulation of the scattering length can turn an excited weakly bound Efimov trimer into a continuum resonance. Its energy and width are described by universal scaling functions written in terms of the scattering length and the binding energy, $B_3$, of the shallowest triatomic molecule. For $a^{-1}<-0.0297 \sqrt{m B_3/\hbar^2}$ the excited Efimov state turns into a continuum resonance.Comment: 4 pages, 4 figure

Fermion mixing in quasi-free states

Quantum field theoretic treatments of fermion oscillations are typically restricted to calculations in Fock space. In this letter we extend the oscillation formulae to include more general quasi-free states, and also consider the case when the mixing is not unitary.Comment: 10 pages, Plain Te

Quantizing the damped harmonic oscillator

We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that unitary dilation of the contraction semigroup governing the dynamics of the system is a logical extension of the doubling procedure, and it allows one to avoid the mathematical difficulties encountered with the previous method.Comment: 4 pages, no figure

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

Calculation of the Density of States Using Discrete Variable Representation and Toeplitz Matrices

A direct and exact method for calculating the density of states for systems with localized potentials is presented. The method is based on explicit inversion of the operator $E-H$. The operator is written in the discrete variable representation of the Hamiltonian, and the Toeplitz property of the asymptotic part of the obtained {\it infinite} matrix is used. Thus, the problem is reduced to the inversion of a {\it finite} matrix

Second order perturbation theory for embedded eigenvalues

We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate operator, we prove upper semicontinuity of the point spectrum and establish the Fermi Golden Rule criterion. Our results apply to massless Pauli-Fierz Hamiltonians for arbitrary coupling.Comment: 30 pages, 2 figure

Searching for three-nucleon resonances

We search for three-neutron resonances which were predicted from pion double charge exchange experiments on He-3. All partial waves up to J=5/2 are nonresonant except the J=3/2^+ one, where we find a state at E=14 MeV energy with 13 MeV width. The parameters of the mirror state in the three-proton system are E=15 MeV and Gamma=14 MeV. The possible existence of an excited state in the triton, which was predicted from a H(He-6,alpha) experiment, is also discussed.Comment: LaTex with RevTe

Algebraic Model for scattering of three-s-cluster systems. II. Resonances in the three-cluster continuum of 6He and 6Be

The resonance states embedded in the three-cluster continuum of 6He and 6Be are obtained in the Algebraic Version of the Resonating Group Method. The model accounts for a correct treatment of the Pauli principle. It also provides the correct three-cluster continuum boundary conditions by using a Hyperspherical Harmonics basis. The model reproduces the observed resonances well and achieves good agreement with other models. A better understanding for the process of formation and decay of the resonance states in six-nucleon systems is obtained.Comment: 8 pages, 10 postscript figures, submitted to Phys. Rev.