Higher Mechanics

Higher-order supersymmetric quantum mechanics

We review the higher-order supersymmetric quantum mechanics (H-SUSY QM), which involves differential intertwining operators of order greater than one. The iterations of first-order SUSY transformations are used to derive in a simple way the higher-order case. The second order technique is addressed directly, and through this approach unexpected possibilities for designing spectra are uncovered....

Higher Toda Mechanics and Spectral Curves

For each one of the Lie algebras gln and g̃ln, we constructed a family of integrable generalizations of the Toda chains characterized by two integers m+ and m−. The Lax matrices and the equations of motion are given explicitly, and the integrals of motion can be calculated in terms of the trace of powers of the Lax matrix L. For the case of m+ = m−, we find a symmetric reduction for each general...

Supersymmetric quantum mechanics based on higher excited states

We generalize the formalism and the techniques of the supersymmetric (susy) quantum mechanics to the cases where the superpotential is generated/defined by higher excited eigenstates. The generalization is technically almost straightforward but physically quite nontrivial since it yields an infinity of new classes of susy-partner potentials, whose spectra are exactly identical except for the lo...

Statistical Mechanics of Nucleosomes Constrained by Higher-Order Chromatin Structure.

Eukaryotic DNA is packaged into chromatin: one-dimensional arrays of nucleosomes separated by stretches of linker DNA are folded into 30-nm chromatin fibers which in turn form higher-order structures (Felsenfeld and Groudine in Nature 421:448, 2003). Each nucleosome, the fundamental unit of chromatin, has 147 base pairs (bp) of DNA wrapped around a histone octamer (Richmond and Davey in Nature ...

Higher Order Weight Functions in Fracture Mechanics of Multimaterials