9,666 research outputs found
Universal deformation rings of modules for algebras of dihedral type of polynomial growth
Let k be an algebraically closed field, and let \Lambda\ be an algebra of
dihedral type of polynomial growth as classified by Erdmann and Skowro\'{n}ski.
We describe all finitely generated \Lambda-modules V whose stable endomorphism
rings are isomorphic to k and determine their universal deformation rings
R(\Lambda,V). We prove that only three isomorphism types occur for
R(\Lambda,V): k, k[[t]]/(t^2) and k[[t]].Comment: 11 pages, 2 figure
Generation of two-photon states with arbitrary degree of entanglement via nonlinear crystal superlattices
We demonstrate a general method of engineering the joint quantum state of
photon pairs produced in spontaneous parametric downconversion (PDC). The
method makes use of a superlattice structure of nonlinear and linear materials,
in conjunction with a broadband pump, to manipulate the group delays of the
signal and idler photons relative to the pump pulse, and realizes a joint
spectral amplitude with arbitrary degree of entanglement for the generated
pairs. This method of group delay engineering has the potential of synthesizing
a broad range of states including factorizable states crucial for quantum
networking and states optimized for Hong-Ou-Mandel interferometry. Experimental
results for the latter case are presented, illustrating the principles of this
approach.Comment: 4 pages, 4 figures, accepted Phys. Rev. Let
Collective motion of active Brownian particles in one dimension
We analyze a model of active Brownian particles with non-linear friction and
velocity coupling in one spatial dimension. The model exhibits two modes of
motion observed in biological swarms: A disordered phase with vanishing mean
velocity and an ordered phase with finite mean velocity. Starting from the
microscopic Langevin equations, we derive mean-field equations of the
collective dynamics. We identify the fixed points of the mean-field equations
corresponding to the two modes and analyze their stability with respect to the
model parameters. Finally, we compare our analytical findings with numerical
simulations of the microscopic model.Comment: submitted to Eur. Phys J. Special Topic
Stability of adhesion clusters under constant force
We solve the stochastic equations for a cluster of parallel bonds with shared
constant loading, rebinding and the completely dissociated state as an
absorbing boundary. In the small force regime, cluster lifetime grows only
logarithmically with bond number for weak rebinding, but exponentially for
strong rebinding. Therefore rebinding is essential to ensure physiological
lifetimes. The number of bonds decays exponentially with time for most cases,
but in the intermediate force regime, a small increase in loading can lead to
much faster decay. This effect might be used by cell-matrix adhesions to induce
signaling events through cytoskeletal loading.Comment: Revtex, 4 pages, 4 Postscript files include
Support varieties for selfinjective algebras
Support varieties for any finite dimensional algebra over a field were
introduced by Snashall-Solberg using graded subalgebras of the Hochschild
cohomology. We mainly study these varieties for selfinjective algebras under
appropriate finite generation hypotheses. Then many of the standard results
from the theory of support varieties for finite groups generalize to this
situation. In particular, the complexity of the module equals the dimension of
its corresponding variety, all closed homogeneous varieties occur as the
variety of some module, the variety of an indecomposable module is connected,
periodic modules are lines and for symmetric algebras a generalization of
Webb's theorem is true
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