812 research outputs found
The Matsubara-Fradkin Thermodynamical Quantization of Podolsky Electrodynamics
In this work we apply the Matsubara-Fradkin formalism and the Nakanishi's
auxiliary field method to the quantization of the Podolsky electrodynamics in
thermodynamic equilibrium. This approach allows us to write consistently the
path integral representation for the partition function of gauge theories in a
simple manner. Furthermore, we find the Dyson-Schwinger-Fradkin equations and
the Ward-Fradkin-Takahashi identities for the Podolsky theory. We also write
the most general form for the polarization tensor in thermodynamic equilibrium.Comment: Submitted to Physical Review
On the pathwidth of almost semicomplete digraphs
We call a digraph {\em -semicomplete} if each vertex of the digraph has at
most non-neighbors, where a non-neighbor of a vertex is a vertex such that there is no edge between and in either direction.
This notion generalizes that of semicomplete digraphs which are
-semicomplete and tournaments which are semicomplete and have no
anti-parallel pairs of edges. Our results in this paper are as follows. (1) We
give an algorithm which, given an -semicomplete digraph on vertices
and a positive integer , in time either
constructs a path-decomposition of of width at most or concludes
correctly that the pathwidth of is larger than . (2) We show that there
is a function such that every -semicomplete digraph of pathwidth
at least has a semicomplete subgraph of pathwidth at least .
One consequence of these results is that the problem of deciding if a fixed
digraph is topologically contained in a given -semicomplete digraph
admits a polynomial-time algorithm for fixed .Comment: 33pages, a shorter version to appear in ESA 201
Cooper pair tunneling in junctions of singlet quantum Hall states and superconductors
We propose tunnel junctions of a Hall bar and a superconducting lead, for
observing Cooper-pair tunneling into singlet fractional quantum Hall edge
states. These tunnel junctions provide a natural means of extracting precise
information of the spin polarization and the filling factor of the state. The
low energy regime of one of the set-ups is governed by a novel quantum
entangled fixed point.Comment: 4 pages, 1 figure (3 subfigures); new title and abstract; new
discussion of the quantum entangled fixed point; final manuscript as
publishe
Chern-Simons theory, exactly solvable models and free fermions at finite temperature
We show that matrix models in Chern-Simons theory admit an interpretation as
1D exactly solvable models, paralleling the relationship between the Gaussian
matrix model and the Calogero model. We compute the corresponding Hamiltonians,
ground-state wavefunctions and ground-state energies and point out that the
models can be interpreted as quasi-1D Coulomb plasmas. We also study the
relationship between Chern-Simons theory on and a system of N
one-dimensional fermions at finite temperature with harmonic confinement. In
particular we show that the Chern-Simons partition function can be described by
the density matrix of the free fermions in a very particular, crystalline,
configuration. For this, we both use the Brownian motion and the matrix model
description of Chern-Simons theory and find several common features with c=1
theory at finite temperature. Finally, using the exactly solvable model result,
we show that the finite temperature effect can be described with a specific
two-body interaction term in the Hamiltonian, with 1D Coulombic behavior at
large separations.Comment: 19 pages, v2: references adde
Gauge Fixing and BFV Quantization
Nonsingularity conditions are established for the BFV gauge-fixing fermion
which are sufficient for it to lead to the correct path integral for a theory
with constraints canonically quantized in the BFV approach. The conditions
ensure that anticommutator of this fermion with the BRST charge regularises the
path integral by regularising the trace over non-physical states in each ghost
sector. The results are applied to the quantization of a system which has a
Gribov problem, using a non-standard form of the gauge-fixing fermion.Comment: 14 page
Entanglement entropy of integer Quantum Hall states in polygonal domains
The entanglement entropy of the integer Quantum Hall states satisfies the
area law for smooth domains with a vanishing topological term. In this paper we
consider polygonal domains for which the area law acquires a constant term that
only depends on the angles of the vertices and we give a general expression for
it. We study also the dependence of the entanglement spectrum on the geometry
and give it a simple physical interpretation.Comment: 8 pages, 6 figure
Holomorphic Factorization and Renormalization Group in Closed String Theory
The prescription of Kawai, Lewellen and Tye for writing the closed string
tree amplitudes as sums of products of open string tree amplitudes, is applied
to the world sheet renormalization group equation. The main point is that
regularization of the Minkowski (rather than Euclidean) world sheet theory
allows factorization into left-moving and right-moving sectors to be
maintained. Explicit calculations are done for the tachyon and the
(gauge-fixed) graviton.Comment: 19 pages, Latex File, 9 figure
A (1,2) Heterotic String with Gauge Symmetry
We construct a (1,2) heterotic string with gauge symmetry and determine its
particle spectrum. This theory has a local N=1 worldsheet supersymmetry for
left movers and a local N=2 worldsheet supersymmetry for right movers and
describes particles in either two or three space-time dimensions. We show that
fermionizing the bosons of the compactified N=1 space leads to a particle
spectrum which has nonabelian gauge symmetry. The fermionic formulation of the
theory corresponds to a dimensional reduction of self dual Yang Mills. We also
give a worldsheet action for the theory and calculate the one-loop path
integral.Comment: 17 pages, added reference
Relativistic calculations of the K-K charge transfer and K-vacancy production probabilities in low-energy ion-atom collisions
The previously developed technique for evaluation of charge-transfer and
electron-excitation processes in low-energy heavy-ion collisions [I.I. Tupitsyn
et al., Phys. Rev. A 82, 042701(2010)] is extended to collisions of ions with
neutral atoms. The method employs the active electron approximation, in which
only the active electron participates in the charge transfer and excitation
processes while the passive electrons provide the screening DFT potential. The
time-dependent Dirac wave function of the active electron is represented as a
linear combination of atomic-like Dirac-Fock-Sturm orbitals, localized at the
ions (atoms). The screening DFT potential is calculated using the overlapping
densities of each ions (atoms), derived from the atomic orbitals of the passive
electrons. The atomic orbitals are generated by solving numerically the
one-center Dirac-Fock and Dirac-Fock-Sturm equations by means of a
finite-difference approach with the potential taken as the sum of the exact
reference ion (atom) Dirac-Fock potential and of the Coulomb potential from the
other ion within the monopole approximation. The method developed is used to
calculate the K-K charge transfer and K-vacancy production probabilties for the
Ne -- F collisions at the F projectile
energies 130 keV/u and 230 keV/u. The obtained results are compared with
experimental data and other theoretical calculations. The K-K charge transfer
and K-vacancy production probabilities are also calculated for the Xe --
Xe collision.Comment: 16 pages, 4 figure
Bilayers of Chiral Spin States
We study the behavior of two planes of Quantum Heisenberg Antiferromagnet in
the regime in which a Chiral Spin Liquid is stabilized in each plane. The
planes are coupled by an exchange interaction of strength . We show that
in the regime of small (for both ferromagnetic {\it and}
antiferromagnetic coupling), the system dynamically selects an
\underline{antiferromagnetic} ordering of the ground state {\it chiralities} of
the planes. For the case of an antiferromagnetic interaction between the
planes, we find that, at some critical value of the inter-layer
coupling, there is a phase transition to a valence-bond state on the interlayer
links. We derive an effective Landau-Ginzburg theory for this phase transition.
It contains two gauge fields coupled to the order parameter field. We
study the low energy spectrum of each phase. In the condensed phase an
``anti-Higgs-Anderson" mechanism occurs. It effectively restores time-reversal
invariance by rendering massless one of the gauge fields while the other field
locks the chiral degrees of freedom locally. There is no phase transition for
ferromagnetic couplings.Comment: to appear in Phys. Rev. B; shortened version; several typos correcte
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