Schroedinger semigroups for vector fields

Journal Article · Fri Mar 01 00:00:00 EST 1985 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526631· OSTI ID:6105648

Osborn, T A; Corns, R A; Fujiwara, Y

Suppose H is the Hamiltonian that generates time evolution in an N-body, spin-dependent, nonrelativistic quantum system. If r is the total number of independent spin components and the particles move in three dimensions, then the Hamiltonian H is an r x r matrix operator given by the sum of the negative Laplacian -..delta../sub x/ on the (d = 3N)-dimensional Euclidean space R/sup d/ plus a Hermitian local matrix potential W(x). Uniform higher-order asymptotic expansions are derived for the time-evolution kernel, the heat kernel, and the resolvent kernel. These expansions are, respectively, for short times, high temperatures, and high energies. Explicit formulas for the matrix-valued coefficient functions entering the asymptotic expansions are determined. All the asymptotic expansions are accompanied by bounds for their respective error terms. These results are obtained for the class of potentials defined as the Fourier image of bounded complex-valued matrix measures. This class is suitable for the N-body problem since interactions of this type do not necessarily decrease as Vertical BarxVertical Bar..-->..infinity. Furthermore, this Fourier image class also contains periodic, almost periodic, and continuous random potentials. The method employed is based upon a constructive series representation of the kernels that define the analytic semigroup )e/sup -z/HVertical BarRe z>0).

• Research Organization: Univ. of Maryland, College Park, MD (United States). Dept. of Physics and Astronomy
• OSTI ID: 6105648
• Journal Information: J. Math. Phys. (N.Y.); (United States), Vol. 26:3
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
VECTOR FIELDS
GROUP THEORY
EUCLIDEAN SPACE
FOURIER TRANSFORMATION
HAMILTONIANS
KERNELS
MANY-BODY PROBLEM
MATRICES
PARTICLES
POTENTIALS
QUANTUM OPERATORS
SERIES EXPANSION
SPIN
VECTORS
ANGULAR MOMENTUM
INTEGRAL TRANSFORMATIONS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
PARTICLE PROPERTIES
RIEMANN SPACE
SPACE
TENSORS
TRANSFORMATIONS
645400* - High Energy Physics- Field Theory