530 research outputs found
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, , of the shallowest triatomic molecule. For
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 . 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
A complementary metal-oxide-semiconductor compatible monocantilever 12-point probe for conductivity measurements on the nanoscale
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.
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