21 research outputs found
Zero modes of various graphene confiurations from the index theorem
In this article we consider a graphene sheet that is folded in various compact geometries with arbitrary topology described by a certain genus, g. While
the Hamiltonian of these systems is defined on a lattice one can take the continuous limit. The obtained Dirac-like Hamiltonian describes well the low energy modes of
the initial system. Starting from first principles we derive an index theorem that corresponds to this Hamiltonian. This theorem relates the zero energy modes of
the graphene sheet with the topology of the compact lattice. For g = 0 and g = 1 these results coincide with the analytical and numerical studies performed for
fullerene molecules and carbon nanotubes while for higher values of g they give predictions for more complicated molecules
Instantons in Four-Fermi Term Broken SUSY with General Potential
It is shown how to solve the Euclidean equations of motion of a point
particle in a general potential and in the presence of a four-Fermi term. The
classical action in this theory depends explicitly on a set of four fermionic
collective coordinates. The corrections to the classical action due to the
presence of fermions are of topological nature in the sense that they depend
only on the values of the fields at the boundary points .
As an application, the Sine-Gordon model with a four-Fermi term is solved
explicitly and the corrections to the classical action are computed.Comment: 8 page
Closed Bosonic String Partition Function in Time Independent Exact PP-Wave Background
The modular invariance of the one-loop partition function of the closed
bosonic string in four dimensions in the presence of certain homogeneous exact
pp-wave backgrounds is studied. In the absence of an axion field the partition
function is found to be modular invariant. In the presence of an axion field
modular invariace is broken. This can be attributed to the light-cone gauge
which breaks the symmetry in the -, -directions. Recovery of this
broken modular invariance suggests the introduction of twists in the
world-sheet directions. However, one needs to go beyond the light-cone gauge to
introduce such twists.Comment: 17 pages, added reference
The -value Equation and Wigner Distributions in Noncommutative Heisenberg algebras
We consider the quantum mechanical equivalence of the Seiberg-Witten map in
the context of the Weyl-Wigner-Groenewold-Moyal phase-space formalism in order
to construct a quantum mechanics over noncommutative Heisenberg algebras. The
formalism is then applied to the exactly soluble Landau and harmonic oscillator
problems in the 2-dimensional noncommutative phase-space plane, in order to
derive their correct energy spectra and corresponding Wigner distributions. We
compare our results with others that have previously appeared in the
literature.Comment: 19 page
Effective stress-energy tensors, self-force, and broken symmetry
Deriving the motion of a compact mass or charge can be complicated by the
presence of large self-fields. Simplifications are known to arise when these
fields are split into two parts in the so-called Detweiler-Whiting
decomposition. One component satisfies vacuum field equations, while the other
does not. The force and torque exerted by the (often ignored) inhomogeneous
"S-type" portion is analyzed here for extended scalar charges in curved
spacetimes. If the geometry is sufficiently smooth, it is found to introduce
effective shifts in all multipole moments of the body's stress-energy tensor.
This greatly expands the validity of statements that the homogeneous R field
determines the self-force and self-torque up to renormalization effects. The
forces and torques exerted by the S field directly measure the degree to which
a spacetime fails to admit Killing vectors inside the body. A number of
mathematical results related to the use of generalized Killing fields are
therefore derived, and may be of wider interest. As an example of their
application, the effective shift in the quadrupole moment of a charge's
stress-energy tensor is explicitly computed to lowest nontrivial order.Comment: 22 pages, fixed typos and simplified discussio
Brownian motion meets Riemann curvature
The general covariance of the diffusion equation is exploited in order to
explore the curvature effects appearing on brownian motion over a d-dimensional
curved manifold. We use the local frame defined by the so called Riemann normal
coordinates to derive a general formula for the mean-square geodesic distance
(MSD) at the short-time regime. This formula is written in terms of
invariants that depend on the Riemann curvature tensor. We study the
n-dimensional sphere case to validate these results. We also show that the
diffusion for positive constant curvature is slower than the diffusion in a
plane space, while the diffusion for negative constant curvature turns out to
be faster. Finally the two-dimensional case is emphasized, as it is relevant
for the single particle diffusion on biomembranes.Comment: 16 pages and 3 figure
Locally Weyl invariant massless bosonic and fermionic spin-1/2 action in the and space-times
We search for a real bosonic and fermionic action in four dimensions which
both remain invariant under local Weyl transformations in the presence of
non-metricity and contortion tensor. In the presence of the non-metricity
tensor the investigation is extended to Weyl space-time while when
the torsion is encountered we are restricted to the Riemann-Cartan
space-time. Our results hold for a subgroup of the Weyl-Cartan
space-time and we also calculate extra contributions to the conformal gravity.Comment: 16 page
The weakly coupled fractional one-dimensional Schr\"{o}dinger operator with index
We study fundamental properties of the fractional, one-dimensional Weyl
operator densely defined on the Hilbert space
and determine the asymptotic behaviour of
both the free Green's function and its variation with respect to energy for
bound states. In the sequel we specify the Birman-Schwinger representation for
the Schr\"{o}dinger operator
and extract the finite-rank portion which is essential for the asymptotic
expansion of the ground state. Finally, we determine necessary and sufficient
conditions for there to be a bound state for small coupling constant .Comment: 16 pages, 1 figur
The Noncommutative Harmonic Oscillator based in Simplectic Representation of Galilei Group
In this work we study symplectic unitary representations for the Galilei
group. As a consequence the Schr\"odinger equation is derived in phase space.
The formalism is based on the non-commutative structure of the star-product,
and using the group theory approach as a guide a physical consistent theory in
phase space is constructed. The state is described by a quasi-probability
amplitude that is in association with the Wigner function. The 3D harmonic
oscillator and the noncommutative oscillator are studied in phase space as an
application, and the Wigner function associated to both cases are determined.Comment: 7 pages,no figure