18 research outputs found
THE PACKING SIMULATION MODEL
The Packing Simulation Model is a microcomputer application program designed for researchers, extension personnel, bankers, packing managers, or other specialists who plan the operations of a packing facility or simulate its financial performance. PACKSIM produces pro forma financial statements for packing facilities based on flexible crop mixes and packing assumptions. Variations can be made in the product harvest schedule, price, quality, quantity, input costs and requirements, packing efficiency, overhead, and loan terms.Research and Development/Tech Change/Emerging Technologies,
How to Test for Diagonalizability: The Discretized PT-Invariant Square-Well Potential
Given a non-hermitean matrix M, the structure of its minimal polynomial
encodes whether M is diagonalizable or not. This note will explain how to
determine the minimal polynomial of a matrix without going through its
characteristic polynomial. The approach is applied to a quantum mechanical
particle moving in a square well under the influence of a piece-wise constant
PT-symmetric potential. Upon discretizing the configuration space, the system
is decribed by a matrix of dimension three. It turns out not to be
diagonalizable for a critical strength of the interaction, also indicated by
the transition of two real into a pair of complex energy eigenvalues. The
systems develops a three-fold degenerate eigenvalue, and two of the three
eigenfunctions disappear at this exceptional point, giving a difference between
the algebraic and geometric multiplicity of the eigenvalue equal to two.Comment: 5 page
Level splittings in exchange-biased spin tunneling
The level splittings in a dimer with the antiferromagnetic coupling between
two single-molecule magnets are calculated perturbatively for arbitrary spin.
It is found that the exchange interaction between two single-molecule magnets
plays an important role in the level splitting. The results are discussed in
comparison with the recent experiment.Comment: 12 pages, to be published in Phys. Rev.
Solvable three-state model of a driven double-well potential and coherent destruction of tunneling
A simple model for a particle in a double well is derived from discretizing its configuration space. The model contains as many free parameters as the original system and it respects all the existing symmetries. In the presence of an external periodic force both the continuous system and the discrete model are shown to possess a generalized time-reversal symmetry in addition to the known generalized parity. The impact of the driving force on the spectrum of the Floquet operator is studied. In particular, the occurrence of degenerate quasienergies causing coherent destruction of tunneling is discussed—to a large extent analytically—for arbitrary driving frequencies and barrier heights
Baker - Campbell - Hausdorff relation for special unitary groups SU(N)
Multiplication of two elements of the special unitary group SU(N) determines uniquely a third group element. A BAker-Campbell-Hausdorff relation is derived which expresses the group parameters of the product (written as an exponential) in terms of the parameters of the exponential factors. This requires the eigen- values of three (N-by-N) matrices. Consequently, the relation can be stated analytically up to N=4, in principle. Similarity transformations encoding the time evolution of quantum mechanical observables, for example, can be worked out by the same means
Thermally Activated Resonant Magnetization Tunneling in Molecular Magnets: Mn_12Ac and others
The dynamical theory of thermally activated resonant magnetization tunneling
in uniaxially anisotropic magnetic molecules such as Mn_12Ac (S=10) is
developed.The observed slow dynamics of the system is described by master
equations for the populations of spin levels.The latter are obtained by the
adiabatic elimination of fast degrees of freedom from the density matrix
equation with the help of the perturbation theory developed earlier for the
tunneling level splitting [D. A. Garanin, J. Phys. A, 24, L61 (1991)]. There
exists a temperature range (thermally activated tunneling) where the escape
rate follows the Arrhenius law, but has a nonmonotonic dependence on the bias
field due to tunneling at the top of the barrier. At lower temperatures this
regime crosses over to the non-Arrhenius law (thermally assisted tunneling).
The transition between the two regimes can be first or second order, depending
on the transverse field, which can be tested in experiments. In both regimes
the resonant maxima of the rate occur when spin levels in the two potential
wells match at certain field values. In the thermally activated regime at low
dissipation each resonance has a multitower self-similar structure with
progressively narrowing peaks mounting on top of each other.Comment: 18 pages, 8 figure