733 research outputs found
Second-order critical lines of spin-S Ising models in a splitting field with Grassmann techniques
We propose a method to study the second-order critical lines of classical
spin- Ising models on two-dimensional lattices in a crystal or splitting
field, using an exact expression for the bare mass of the underlying field
theory. Introducing a set of anticommuting variables to represent the partition
function, we derive an exact and compact expression for the bare mass of the
model including all local multi-fermions interactions. By extension of the
Ising and Blume-Capel models, we extract the free energy singularities in the
low momentum limit corresponding to a vanishing bare mass. The loci of these
singularities define the critical lines depending on the spin S, in good
agreement with previous numerical estimations. This scheme appears to be
general enough to be applied in a variety of classical Hamiltonians
A Generalization of the Bargmann-Fock Representation to Supersymmetry by Holomorphic Differential Geometry
In the Bargmann-Fock representation the coordinates act as bosonic
creation operators while the partial derivatives act as
annihilation operators on holomorphic -forms as states of a -dimensional
bosonic oscillator. Considering also -forms and further geometrical objects
as the exterior derivative and Lie derivatives on a holomorphic , we
end up with an analogous representation for the -dimensional supersymmetric
oscillator. In particular, the supersymmetry multiplet structure of the Hilbert
space corresponds to the cohomology of the exterior derivative. In addition, a
1-complex parameter group emerges naturally and contains both time evolution
and a homotopy related to cohomology. Emphasis is on calculus.Comment: 11 pages, LaTe
Dynamics of a thin shell in the Reissner-Nordstrom metric
We describe the dynamics of a thin spherically symmetric gravitating shell in
the Reissner-Nordstrom metric of the electrically charged black hole. The
energy-momentum tensor of electrically neutral shell is modelled by the perfect
fluid with a polytropic equation of state. The motion of a shell is described
fully analytically in the particular case of the dust equation of state. We
construct the Carter-Penrose diagrams for the global geometry of the eternal
black hole, which illustrate all possible types of solutions for moving shell.
It is shown that for some specific range of initial parameters there are
possible the stable oscillating motion of the shell transferring it
consecutively in infinite series of internal universes. We demonstrate also
that this oscillating type of motion is possible for an arbitrary polytropic
equation of state on the shell.Comment: 17 pages, 7 figure
On Hubbard-Stratonovich Transformations over Hyperbolic Domains
We discuss and prove validity of the Hubbard-Stratonovich (HS) identities
over hyperbolic domains which are used frequently in the studies on disordered
systems and random matrices. We also introduce a counterpart of the HS identity
arising in disordered systems with "chiral" symmetry. Apart from this we
outline a way of deriving the nonlinear -model from the gauge-invariant
Wegner orbital model avoiding the use of the HS transformations.Comment: More accurate proofs are given; a few misprints are corrected; a
misleading reference and a footnote in the end of section 2.2 are remove
Hawking Radiation as Quantum Tunneling in Rindler Coordinate
We substantiate the Hawking radiation as quantum tunneling of fields or
particles crossing the horizon by using the Rindler coordinate. The thermal
spectrum detected by an accelerated particle is interpreted as quantum
tunneling in the Rindler spacetime. Representing the spacetime near the horizon
locally as a Rindler spacetime, we find the emission rate by tunneling, which
is expressed as a contour integral and gives the correct Boltzmann factor. We
apply the method to non-extremal black holes such as a Schwarzschild black
hole, a non-extremal Reissner-Nordstr\"{o}m black hole, a charged Kerr black
hole, de Sitter space, and a Schwarzschild-anti de Sitter black hole.Comment: LaTex 19 pages, no figure; references added and replaced by the
version accepted in JHE
On representations of super coalgebras
The general structure of the representation theory of a -graded
coalgebra is discussed. The result contains the structure of Fourier analysis
on compact supergroups and quantisations thereof as a special case. The general
linear supergroups serve as an explicit illustration and the simplest example
is carried out in detail.Comment: 18 pages, LaTeX, KCL-TH-94-
Toward peripheral nerve mechanical characterization using Brillouin imaging spectroscopy
SIGNIFICANCE: Peripheral nerves are viscoelastic tissues with unique elastic characteristics. Imaging of peripheral nerve elasticity is important in medicine, particularly in the context of nerve injury and repair. Elasticity imaging techniques provide information about the mechanical properties of peripheral nerves, which can be useful in identifying areas of nerve damage or compression, as well as assessing the success of nerve repair procedures.
AIM: We aim to assess the feasibility of Brillouin microspectroscopy for peripheral nerve imaging of elasticity, with the ultimate goal of developing a new diagnostic tool for peripheral nerve injury
APPROACH: Viscoelastic properties of the peripheral nerve were evaluated with Brillouin imaging spectroscopy.
RESULTS: An external stress exerted on the fixed nerve resulted in a Brillouin shift. Quantification of the shift enabled correlation of the Brillouin parameters with nerve elastic properties.
CONCLUSIONS: Brillouin microscopy provides sufficient sensitivity to assess viscoelastic properties of peripheral nerves
Fermions and Loops on Graphs. II. Monomer-Dimer Model as Series of Determinants
We continue the discussion of the fermion models on graphs that started in
the first paper of the series. Here we introduce a Graphical Gauge Model (GGM)
and show that : (a) it can be stated as an average/sum of a determinant defined
on the graph over (binary) gauge field; (b) it is equivalent
to the Monomer-Dimer (MD) model on the graph; (c) the partition function of the
model allows an explicit expression in terms of a series over disjoint directed
cycles, where each term is a product of local contributions along the cycle and
the determinant of a matrix defined on the remainder of the graph (excluding
the cycle). We also establish a relation between the MD model on the graph and
the determinant series, discussed in the first paper, however, considered using
simple non-Belief-Propagation choice of the gauge. We conclude with a
discussion of possible analytic and algorithmic consequences of these results,
as well as related questions and challenges.Comment: 11 pages, 2 figures; misprints correcte
On the construction of generalized Grassmann representatives of state vectors
Generalized -graded Grassmann variables are used to label coherent
states related to the nilpotent representation of the q-oscillator of
Biedenharn and Macfarlane when the deformation parameter is a root of unity.
These states are then used to construct generalized Grassmann representatives
of state vectors.Comment: 8 page
Charged Particle with Magnetic Moment in the Aharonov-Bohm Potential
We considered a charged quantum mechanical particle with spin
and gyromagnetic ratio in the field af a magnetic string. Whereas the
interaction of the charge with the string is the well kown Aharonov-Bohm effect
and the contribution of magnetic moment associated with the spin in the case
is known to yield an additional scattering and zero modes (one for each
flux quantum), an anomaly of the magnetic moment (i.e. ) leads to bound
states. We considered two methods for treating the case . \\ The first is
the method of self adjoint extension of the corresponding Hamilton operator. It
yields one bound state as well as additional scattering. In the second we
consider three exactly solvable models for finite flux tubes and take the limit
of shrinking its radius to zero. For finite radius, there are bound
states ( is the number of flux quanta in the tube).\\ For the bound
state energies tend to infinity so that this limit is not physical unless along with . Thereby only for fluxes less than unity the results of
the method of self adjoint extension are reproduced whereas for larger fluxes
bound states exist and we conclude that this method is not applicable.\\ We
discuss the physically interesting case of small but finite radius whereby the
natural scale is given by the anomaly of the magnetic moment of the electron
.Comment: 16 pages, Latex, NTZ-93-0
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