28,873 research outputs found
Gravitation as Anholonomy
A gravitational field can be seen as the anholonomy of the tetrad fields.
This is more explicit in the teleparallel approach, in which the gravitational
field-strength is the torsion of the ensuing Weitzenboeck connection. In a
tetrad frame, that torsion is just the anholonomy of that frame. The infinitely
many tetrad fields taking the Lorentz metric into a given Riemannian metric
differ by point-dependent Lorentz transformations. Inertial frames constitute a
smaller infinity of them, differing by fixed-point Lorentz transformations.
Holonomic tetrads take the Lorentz metric into itself, and correspond to
Minkowski flat spacetime. An accelerated frame is necessarily anholonomic and
sees the electromagnetic field strength with an additional term.Comment: RevTeX4, 10 pages, no figures. To appear in Gen. Rel. Gra
The Equivalence Principle Revisited
A precise formulation of the strong Equivalence Principle is essential to the
understanding of the relationship between gravitation and quantum mechanics.
The relevant aspects are reviewed in a context including General Relativity,
but allowing for the presence of torsion. For the sake of brevity, a concise
statement is proposed for the Principle: "An ideal observer immersed in a
gravitational field can choose a reference frame in which gravitation goes
unnoticed". This statement is given a clear mathematical meaning through an
accurate discussion of its terms. It holds for ideal observers (time-like
smooth non-intersecting curves), but not for real, spatially extended
observers. Analogous results hold for gauge fields. The difference between
gravitation and the other fundamental interactions comes from their distinct
roles in the equation of force.Comment: RevTeX, 18 pages, no figures, to appear in Foundations of Physic
Boundary versus bulk behavior of time-dependent correlation functions in one-dimensional quantum systems
We study the influence of reflective boundaries on time-dependent responses
of one-dimensional quantum fluids at zero temperature beyond the low-energy
approximation. Our analysis is based on an extension of effective mobile
impurity models for nonlinear Luttinger liquids to the case of open boundary
conditions. For integrable models, we show that boundary autocorrelations
oscillate as a function of time with the same frequency as the corresponding
bulk autocorrelations. This frequency can be identified as the band edge of
elementary excitations. The amplitude of the oscillations decays as a power law
with distinct exponents at the boundary and in the bulk, but boundary and bulk
exponents are determined by the same coupling constant in the mobile impurity
model. For nonintegrable models, we argue that the power-law decay of the
oscillations is generic for autocorrelations in the bulk, but turns into an
exponential decay at the boundary. Moreover, there is in general a nonuniversal
shift of the boundary frequency in comparison with the band edge of bulk
excitations. The predictions of our effective field theory are compared with
numerical results obtained by time-dependent density matrix renormalization
group (tDMRG) for both integrable and nonintegrable critical spin- chains
with , and .Comment: 20 pages, 12 figure
Gravitomagnetic Moments of the Fundamental Fields
The quadratic form of the Dirac equation in a Riemann spacetime yields a
gravitational gyromagnetic ratio \kappa_S = 2 for the interaction of a Dirac
spinor with curvature. A gravitational gyromagnetic ratio \kappa_S = 1 is also
found for the interaction of a vector field with curvature. It is shown that
the Dirac equation in a curved background can be obtained as the square--root
of the corresponding vector field equation only if the gravitational
gyromagnetic ratios are properly taken into account.Comment: 8 pages, RevTeX Style, no figures, changed presentation -- now
restricted to fields of spin 0, 1/2 and 1 -- some references adde
Connectivity-Driven Coherence in Complex Networks
We study the emergence of coherence in complex networks of mutually coupled
non-identical elements. We uncover the precise dependence of the dynamical
coherence on the network connectivity, on the isolated dynamics of the elements
and the coupling function. These findings predict that in random graphs, the
enhancement of coherence is proportional to the mean degree. In locally
connected networks, coherence is no longer controlled by the mean degree, but
rather on how the mean degree scales with the network size. In these networks,
even when the coherence is absent, adding a fraction s of random connections
leads to an enhancement of coherence proportional to s. Our results provide a
way to control the emergent properties by the manipulation of the dynamics of
the elements and the network connectivity.Comment: 4 pages, 2 figure
Orbital multicriticality in spin gapped quasi-1D antiferromagnets
Motivated by the quasi-1D antiferromagnet CaVO, we explore
spin-orbital systems in which the spin modes are gapped but orbitals are near a
macroscopically degenerate classical transition. Within a simplified model we
show that gapless orbital liquid phases possessing power-law correlations may
occur without the strict condition of a continuous orbital symmetry. For the
model proposed for CaVO, we find that an orbital phase with coexisting
order parameters emerges from a multicritical point. The effective orbital
model consists of zigzag-coupled transverse field Ising chains. The
corresponding global phase diagram is constructed using field theory methods
and analyzed near the multicritical point with the aid of an exact solution of
a zigzag XXZ model.Comment: 9 page
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