530 research outputs found

### Volume Dependence of Spectral Weights for Unstable Particles in a Solvable Model

Volume dependence of the spectral weight is usually used as a simple criteria
to distinguish single-particle states from multi-particle states in lattice QCD
calculations. Within a solvable model, the Lee model, we show that this
criteria is in principle only valid for a stable particle or a narrow
resonance. If the resonance being studied is broad, then the volume dependence
of the corresponding spectral weight resembles that of a multi-particle state
instead of a single-particle one. For an unstable $V$-particle in the Lee
model, the transition from single-particle to multi-particle volume dependence
is governed by the ratio of its physical width to the typical level spacing in
the finite volume. We estimate this ratio for practical lattice QCD simulations
and find that, for most cases, the resonance studied in lattice QCD simulations
still resembles the single particle behavior.Comment: 15 pages, no figures. Title modified. Version to appear on Phys. Rev.

### Antilinear spectral symmetry and the vortex zero-modes in topological insulators and graphene

We construct the general extension of the four-dimensional Jackiw-Rossi-Dirac
Hamiltonian that preserves the antilinear reflection symmetry between the
positive and negative energy eigenstates. Among other systems, the resulting
Hamiltonian describes the s-wave superconducting vortex at the surface of the
topological insulator, at a finite chemical potential, and in the presence of
both Zeeman and orbital couplings to the external magnetic field. Here we find
that the bound zero-mode exists only when the Zeeman term is below a critical
value. Other physical realizations pertaining to graphene are considered, and
some novel zero-energy wave functions are analytically computed.Comment: 6 revtex pages; typos corrected, published versio

### Probability in relativistic quantum mechanics and foliation of spacetime

The conserved probability densities (attributed to the conserved currents
derived from relativistic wave equations) should be non-negative and the
integral of them over an entire hypersurface should be equal to one. To satisfy
these requirements in a covariant manner, the foliation of spacetime must be
such that each integral curve of the current crosses each hypersurface of the
foliation once and only once. In some cases, it is necessary to use
hypersurfaces that are not spacelike everywhere. The generalization to the
many-particle case is also possible.Comment: 9 pages, 3 figures, revised, new references, to appear in Int. J.
Mod. Phys.

### Fading Gravity and Self-Inflation

We study the cosmology of a toy modified theory of gravity in which gravity
shuts off at short distances, as in the fat graviton scenario of Sundrum. In
the weak-field limit, the theory is perturbatively local, ghost-free and
unitary, although likely suffers from non-perturbative instabilities. We derive
novel self-inflationary solutions from the vacuum equations of the theory,
without invoking scalar fields or other forms of stress energy. The modified
perturbation equation expressed in terms of the Newtonian potential closely
resembles its counterpart for inflaton fluctuations. The resulting scalar
spectrum is therefore slightly red, akin to the simplest scalar-driven
inflationary models. A key difference, however, is that the gravitational wave
spectrum is generically not scale invariant. In particular the tensor spectrum
can have a blue tilt, a distinguishing feature from standard inflation.Comment: 35 pages, 4 figures. v3: version to appear in Phys. Rev.

### A Note on a Particle-Antiparticle Interaction

We develop an iso spin like formulation with particles and their anti
particle counterparts. This leads to a new shortlived interaction between them,
valid at very high energies and mediated by massive particles. We point out
that evidence for this is already suggested by the very recent observations by
the CDF team at Fermi Lab.Comment: 8 pages latex; Int.J.Mod.Phys E, 201

### Might EPR particles communicate through a wormhole?

We consider the two-particle wave function of an Einstein-Podolsky-Rosen
system, given by a two dimensional relativistic scalar field model. The Bohm-de
Broglie interpretation is applied and the quantum potential is viewed as
modifying the Minkowski geometry. In this way an effective metric, which is
analogous to a black hole metric in some limited region, is obtained in one
case and a particular metric with singularities appears in the other case,
opening the possibility, following Holland, of interpreting the EPR
correlations as being originated by an effective wormhole geometry, through
which the physical signals can propagate.Comment: Corrected version, to appears in EP

### Gauge-Invariant Approach to Meson Photoproduction Including the Final-State Interaction

A gauge-invariant formalism is presented for the practical treatment of
photo- and electroproduction of pseudoscalar mesons off nucleons that allows an
explicit incorporation of hadronic final-state interactions. The
semi-phenomenological approach is based on a field theory developed by one of
the authors. It generalizes an earlier approach by allowing for systematic
improvement of approximations in a controlled manner. The practical feasibility
is illustrated by applying the lowest-order result to the photoproduction of
both neutral and charged pions.Comment: Plenary talk given at the N*2005 Workshop (Oct. 2005, Tallahassee,
FL); to appear in the Proceedings (to be publ. by WorldScientific

### On the Relationship between Resolution Enhancement and Multiphoton Absorption Rate in Quantum Lithography

The proposal of quantum lithography [Boto et al., Phys. Rev. Lett. 85, 2733
(2000)] is studied via a rigorous formalism. It is shown that, contrary to Boto
et al.'s heuristic claim, the multiphoton absorption rate of a ``NOON'' quantum
state is actually lower than that of a classical state with otherwise identical
parameters. The proof-of-concept experiment of quantum lithography [D'Angelo et
al., Phys. Rev. Lett. 87, 013602 (2001)] is also analyzed in terms of the
proposed formalism, and the experiment is shown to have a reduced multiphoton
absorption rate in order to emulate quantum lithography accurately. Finally,
quantum lithography by the use of a jointly Gaussian quantum state of light is
investigated, in order to illustrate the trade-off between resolution
enhancement and multiphoton absorption rate.Comment: 14 pages, 7 figures, submitted, v2: rewritten in response to
referees' comments, v3: rewritten and extended, v4: accepted by Physical
Review

### Relativistic diffusive motion in random electromagnetic fields

We show that the relativistic dynamics in a Gaussian random electromagnetic
field can be approximated by the relativistic diffusion of Schay and Dudley.
Lorentz invariant dynamics in the proper time leads to the diffusion in the
proper time. The dynamics in the laboratory time gives the diffusive transport
equation corresponding to the Juettner equilibrium at the inverse temperature
\beta^{-1}=mc^{2}. The diffusion constant is expressed by the field strength
correlation function (Kubo's formula).Comment: the version published in JP

### Vortex Loops and Majoranas

We investigate the role that vortex loops play in characterizing eigenstates
of interacting Majoranas. We first give some general results, and then we focus
on ladder Hamiltonian examples to test further ideas. Two methods yield exact
results: i.) We utilize the mapping of spin Hamiltonians to quartic
interactions of Majoranas and show under certain conditions the spectra of
these two examples coincide. ii) In cases with reflection-symmetric
Hamiltonians, we use reflection positivity for Majoranas to characterize
vortices. Aside from these exact results, two additional methods suggest wider
applicability of these results: iii.) Numerical evidence suggests similar
behavior for certain systems without reflection symmetry. iv.) A perturbative
analysis also suggests similar behavior without the assumption of reflection
symmetry.Comment: 28 page

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