Superconformal hypermultiplets

We present theories of N=2 hypermultiplets in four spacetime dimensions that are invariant under rigid or local superconformal symmetries. The target spaces of theories with rigid superconformal invariance are (4n)-dimensional {\it special} hyper-K\"ahler manifolds. Such manifolds can be described as cones over tri-Sasakian metrics and are locally the product of a flat four-dimensional space and a quaternionic manifold. The latter manifolds appear in the coupling of hypermultiplets to N=2 supergravity. We employ local sections of an Sp$(n)\times{\rm Sp}(1)$ bundle in the formulation of the Lagrangian and transformation rules, thus allowing for arbitrary coordinatizations of the hyper-K\"ahler and quaternionic manifolds

Geometry of N=4, d=1 nonlinear supermultiplet

We construct the general action for $N=4, d=1$ nonlinear supermultiplet including the most general interaction terms which depend on the arbitrary function $h$ obeying the Laplace equation on $S^3$. We find the bosonic field $B$ which depends on the components of nonlinear supermultiplet and transforms as a full time derivative under N=4 supersymmetry. The most general interaction is generated just by a Fayet-Iliopoulos term built from this auxiliary component. Being transformed through a full time derivative under $N=4, d=1$ supersymmetry, this auxiliary component $B$ may be dualized into a fourth scalar field giving rise to a four dimensional $N=4, d=1$ sigma-model. We analyzed the geometry in the bosonic sector and find that it is not a hyper-K\"ahler one. With a particular choice of the target space metric $g$ the geometry in the bosonic sector coincides with the one which appears in heterotic $(4,0)$ sigma-model in $d=2$.Comment: 9 pages, LaTeX file, PACS: 11.30.Pb, 03.65.-

Free energy surfaces from nonequilibrium processes without work measurement

Recent developments in statistical mechanics have allowed the estimation of equilibrium free energies from the statistics of work measurements during processes that drive the system out of equilibrium. Here a different class of processes is considered, wherein the system is prepared and released from a nonequilibrium state, and no external work is involved during its observation. For such ``clamp-and-release'' processes, a simple strategy for the estimation of equilibrium free energies is offered. The method is illustrated with numerical simulations, and analyzed in the context of tethered single-molecule experiments.Comment: 15 pages, 3 figures (1 color); accepted to J. Chem. Phy

Comment on "Wave functions for a Duffin-Kemmer-Petiau particle in a time-dependent potential"

It is shown that the paper "Wave functions for a Duffin-Kemmer-Petiau particle in a time-dependent potential", by Merad and Bensaid [J. Math. Phys. 48, 073515 (2007)] is not correct in using inadvertently a non-Hermitian Hamiltonian in a formalism that does require Hermitian Hamiltonians.Comment: 2 page