2,078 research outputs found
Clustering of fermionic truncated expectation values via functional integration
I give a simple proof that the correlation functions of many-fermion systems
have a convergent functional Grassmann integral representation, and use this
representation to show that the cumulants of fermionic quantum statistical
mechanics satisfy l^1-clustering estimates
Constructive Field Theory and Applications: Perspectives and Open Problems
In this paper we review many interesting open problems in mathematical
physics which may be attacked with the help of tools from constructive field
theory. They could give work for future mathematical physicists trained with
the constructive methods well within the 21st century
The Global Renormalization Group Trajectory in a Critical Supersymmetric Field Theory on the Lattice Z^3
We consider an Euclidean supersymmetric field theory in given by a
supersymmetric perturbation of an underlying massless Gaussian measure
on scalar bosonic and Grassmann fields with covariance the Green's function of
a (stable) L\'evy random walk in . The Green's function depends on the
L\'evy-Khintchine parameter with . For
the interaction is marginal. We prove for
sufficiently small and initial
parameters held in an appropriate domain the existence of a global
renormalization group trajectory uniformly bounded on all renormalization group
scales and therefore on lattices which become arbitrarily fine. At the same
time we establish the existence of the critical (stable) manifold. The
interactions are uniformly bounded away from zero on all scales and therefore
we are constructing a non-Gaussian supersymmetric field theory on all scales.
The interest of this theory comes from the easily established fact that the
Green's function of a (weakly) self-avoiding L\'evy walk in is a second
moment (two point correlation function) of the supersymmetric measure governing
this model. The control of the renormalization group trajectory is a
preparation for the study of the asymptotics of this Green's function. The
rigorous control of the critical renormalization group trajectory is a
preparation for the study of the critical exponents of the (weakly)
self-avoiding L\'evy walk in .Comment: 82 pages, Tex with macros supplied. Revision includes 1. redefinition
of norms involving fermions to ensure uniqueness. 2. change in the definition
of lattice blocks and lattice polymer activities. 3. Some proofs have been
reworked. 4. New lemmas 5.4A, 5.14A, and new Theorem 6.6. 5.Typos
corrected.This is the version to appear in Journal of Statistical Physic
The Development of the Teacher as a Professional in an Alternative Teacher Education Program
Recruitment and retention strategies are a growing concern for Catholic educational leaders. This article offers a glimpse into the dynamics of a leading teacher recruitment effort, the Alliance for Catholic Education (ACE) sponsored by the University of Notre Dame. After surveying the first two cohorts who taught in Catholic schools through ACE, the authors uncover significant and meaningful components of this alternative teacher preparation program with a view to challenging traditional teacher education efforts and preservice requirements
An Efficient Algorithm for Enumerating Chordless Cycles and Chordless Paths
A chordless cycle (induced cycle) of a graph is a cycle without any
chord, meaning that there is no edge outside the cycle connecting two vertices
of the cycle. A chordless path is defined similarly. In this paper, we consider
the problems of enumerating chordless cycles/paths of a given graph
and propose algorithms taking time for each chordless cycle/path. In
the existing studies, the problems had not been deeply studied in the
theoretical computer science area, and no output polynomial time algorithm has
been proposed. Our experiments showed that the computation time of our
algorithms is constant per chordless cycle/path for non-dense random graphs and
real-world graphs. They also show that the number of chordless cycles is much
smaller than the number of cycles. We applied the algorithm to prediction of
NMR (Nuclear Magnetic Resonance) spectra, and increased the accuracy of the
prediction
Sparse Kneser graphs are Hamiltonian
For integers k≥1 and n≥2k+1, the Kneser graph K(n,k) is the graph whose vertices are the k-element subsets of {1,…,n} and whose edges connect pairs of subsets that are disjoint. The Kneser graphs of the form K(2k+1,k) are also known as the odd graphs. We settle an old problem due to Meredith, Lloyd, and Biggs from the 1970s, proving that for every k≥3, the odd graph K(2k+1,k) has a Hamilton cycle. This and a known conditional result due to Johnson imply that all Kneser graphs of the form K(2k+2a,k) with k≥3 and a≥0 have a Hamilton cycle. We also prove that K(2k+1,k) has at least 22k−6 distinct Hamilton cycles for k≥6. Our proofs are based on a reduction of the Hamiltonicity problem in the odd graph to the problem of finding a spanning tree in a suitably defined hypergraph on Dyck words
Quantum Transport in a Nanosize Silicon-on-Insulator Metal-Oxide-Semiconductor
An approach is developed for the determination of the current flowing through
a nanosize silicon-on-insulator (SOI) metal-oxide-semiconductor field-effect
transistors (MOSFET). The quantum mechanical features of the electron transport
are extracted from the numerical solution of the quantum Liouville equation in
the Wigner function representation. Accounting for electron scattering due to
ionized impurities, acoustic phonons and surface roughness at the Si/SiO2
interface, device characteristics are obtained as a function of a channel
length. From the Wigner function distributions, the coexistence of the
diffusive and the ballistic transport naturally emerges. It is shown that the
scattering mechanisms tend to reduce the ballistic component of the transport.
The ballistic component increases with decreasing the channel length.Comment: 21 pages, 8 figures, E-mail addresses: [email protected]
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