69 research outputs found
Pauli equation and the method of supersymmetric factorization
We consider different variants of factorization of a 2x2 matrix
Schroedinger/Pauli operator in two spatial dimensions. They allow to relate its
spectrum to the sum of spectra of two scalar Schroedinger operators, in a
manner similar to one-dimensional Darboux transformations. We consider both the
case when such factorization is reduced to the ordinary 2-dimensional SUSY QM
quasifactorization and a more general case which involves covariant
derivatives. The admissible classes of electromagnetic fields are described and
some illustrative examples are given.Comment: 18 pages, Late
Multiparticle SUSY quantum mechanics and the representations of permutation group
The method of multidimensional SUSY Quantum Mechanics is applied to the
investigation of supersymmetrical N-particle systems on a line for the case of
separable center-of-mass motion. New decompositions of the superhamiltonian
into block-diagonal form with elementary matrix components are constructed.
Matrices of coefficients of these minimal blocks are shown to coincide with
matrices of irreducible representations of permutations group S_N, which
correspond to the Young tableaux (N-M,1^M). The connections with known
generalizations of N-particle Calogero and Sutherland models are established.Comment: 20 pages, Latex,no figure
COMPUTER SIMULATION OF LOCAL MOBILITY IN DENDRIMERS WITH ASYMMETRIC BRANCHING BY BROWNIAN DYNAMICS METHOD
The Brownian dynamics method has been used to study the effect of the branching asymmetry on the local orientational mobility of segments and bonds in dendrimers in good solvent. âCoarse-grainedâ models of flexible dendrimers with different branching symmetry but with the same average segment length were considered. The frequency dependences of the rate of the spin-lattice relaxation nuclear magnetic resonance (NMR) [1/T1H(H)] for segments or bonds located at different distances from terminal monomers were calculated. After the exclusion of the contribution of the overall dendrimer rotation the position of the maxima of the frequency dependences [1/T1H(ÏH)] for different segments with the same length doesnât depend on their location inside a dendrimer both for phantom models and for models with excluded volume interactions. This effect doesnât depend also on the branching symmetry, but the position of the maximum [1/T1H(ÏH))] is determined by the segment length. For bonds inside segments the positions of the maximum [1/T1H(ÏH)] coincide for all models considered. Therefore, the obtained earlier conclusion about the weak influence of the excluded volume interactions on the local dynamics in the flexible symmetric dendrimers can be generalized for dendrimers with an asymmetric branching
Equivalence of the super Lax and local Dunkl operators for Calogero-like models
Following Shastry and Sutherland I construct the super Lax operators for the
Calogero model in the oscillator potential. These operators can be used for the
derivation of the eigenfunctions and integrals of motion of the Calogero model
and its supersymmetric version. They allow to infer several relations involving
the Lax matrices for this model in a fast way. It is shown that the super Lax
operators for the Calogero and Sutherland models can be expressed in terms of
the supercharges and so called local Dunkl operators constructed in our recent
paper with M. Ioffe. Several important relations involving Lax matrices and
Hamiltonians of the Calogero and Sutherland models are easily derived from the
properties of Dunkl operators.Comment: 25 pages, Latex, no figures. Accepted for publication in: Jounal of
Physics A: Mathematical and Genera
Higher Order Matrix SUSY Transformations in Two-Dimensional Quantum Mechanics
The iteration procedure of supersymmetric transformations for the
two-dimensional Schroedinger operator is implemented by means of the matrix
form of factorization in terms of matrix 2x2 supercharges. Two different types
of iterations are investigated in detail. The particular case of diagonal
initial Hamiltonian is considered, and the existence of solutions is
demonstrated. Explicit examples illustrate the construction.Comment: 15
Nature of Viscoelasticity in Lamellar Block Copolymers: Contraction Correlated to Strain Localization
Intertwining Relations for the Matrix Calogero-like Models: Supersymmetry and Shape Invariance
Intertwining relations for -particle Calogero-like models with internal
degrees of freedom are investigated. Starting from the well known
Dunkl-Polychronakos operators, we construct new kind of local (without exchange
operation) differential operators. These operators intertwine the matrix
Hamiltonians corresponding to irreducible representations of the permutation
group . In particular cases, this method allows to construct a new class
of exactly solvable Dirac-like equations and a new class of matrix models with
shape invariance. The connection with approach of multidimensional
supersymmetric quantum mechanics is established.Comment: 24 p.
Dipolar and chain-linking effects on the rheology of grafted chains in a nanopore under shear at different grafting densities
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