1,366 research outputs found
New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
Integrable N-particle systems have an important property that the associated
Seiberg-Witten prepotentials satisfy the WDVV equations. However, this does not
apply to the most interesting class of elliptic and double-elliptic systems.
Studying the commutativity conjecture for theta-functions on the families of
associated spectral curves, we derive some other non-linear equations for the
perturbative Seiberg-Witten prepotential, which turn out to have exactly the
double-elliptic system as their generic solution. In contrast with the WDVV
equations, the new equations acquire non-perturbative corrections which are
straightforwardly deducible from the commutativity conditions. We obtain such
corrections in the first non-trivial case of N=3 and describe the structure of
non-perturbative solutions as expansions in powers of the flat moduli with
coefficients that are (quasi)modular forms of the elliptic parameter.Comment: 25 page
Fluctuation Induced Forces in Non-equilibrium (Diffusive) Dynamics
Thermal fluctuations in non-equilibrium steady states generically lead to
power law decay of correlations for conserved quantities. Embedded bodies which
constrain fluctuations in turn experience fluctuation induced forces. We
compute these forces for the simple case of parallel slabs in a driven
diffusive system. The force falls off with slab separation as (at
temperature , and in all spatial dimensions), but can be attractive or
repulsive. Unlike the equilibrium Casimir force, the force amplitude is
non-universal and explicitly depends on dynamics. The techniques introduced can
be generalized to study pressure and fluctuation induced forces in a broad
class of non-equilibrium systems.Comment: 5 pages, 2 figure
Acquisition and Spread of Antimicrobial Resistance : A tet(X) Case Study
Peer reviewedPublisher PD
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