4,660 research outputs found
Interplay between nanometer-scale strain variations and externally applied strain in graphene
We present a molecular modeling study analyzing nanometer-scale strain
variations in graphene as a function of externally applied tensile strain. We
consider two different mechanisms that could underlie nanometer-scale strain
variations: static perturbations from lattice imperfections of an underlying
substrate and thermal fluctuations. For both cases we observe a decrease in the
out-of-plane atomic displacements with increasing strain, which is accompanied
by an increase in the in-plane displacements. Reflecting the non-linear elastic
properties of graphene, both trends together yield a non-monotonic variation of
the total displacements with increasing tensile strain. This variation allows
to test the role of nanometer-scale strain variations in limiting the carrier
mobility of high-quality graphene samples
Renormalization group improved gravitational actions: a Brans-Dicke approach
A new framework for exploiting information about the renormalization group
(RG) behavior of gravity in a dynamical context is discussed. The
Einstein-Hilbert action is RG-improved by replacing Newton's constant and the
cosmological constant by scalar functions in the corresponding Lagrangian
density. The position dependence of and is governed by a RG
equation together with an appropriate identification of RG scales with points
in spacetime. The dynamics of the fields and does not admit a
Lagrangian description in general. Within the Lagrangian formalism for the
gravitational field they have the status of externally prescribed
``background'' fields. The metric satisfies an effective Einstein equation
similar to that of Brans-Dicke theory. Its consistency imposes severe
constraints on allowed backgrounds. In the new RG-framework, and
carry energy and momentum. It is tested in the setting of homogeneous-isotropic
cosmology and is compared to alternative approaches where the fields and
do not carry gravitating 4-momentum. The fixed point regime of the
underlying RG flow is studied in detail.Comment: LaTeX, 72 pages, no figure
The Response Field and the Saddle Points of Quantum Mechanical Path Integrals
In quantum statistical mechanics, Moyal's equation governs the time evolution
of Wigner functions and of more general Weyl symbols that represent the density
matrix of arbitrary mixed states. A formal solution to Moyal's equation is
given by Marinov's path integral. In this paper we demonstrate that this path
integral can be regarded as the natural link between several conceptual,
geometric, and dynamical issues in quantum mechanics. A unifying perspective is
achieved by highlighting the pivotal role which the response field, one of the
integration variables in Marinov's integral, plays for pure states even. The
discussion focuses on how the integral's semiclassical approximation relates to
its strictly classical limit; unlike for Feynman type path integrals, the
latter is well defined in the Marinov case. The topics covered include a random
force representation of Marinov's integral based upon the concept of "Airy
averaging", a related discussion of positivity-violating Wigner functions
describing tunneling processes, and the role of the response field in
maintaining quantum coherence and enabling interference phenomena. The double
slit experiment for electrons and the Bohm-Aharonov effect are analyzed as
illustrative examples. Furthermore, a surprising relationship between the
instantons of the Marinov path integral over an analytically continued ("Wick
rotated") response field, and the complex instantons of Feynman-type integrals
is found. The latter play a prominent role in recent work towards a
Picard-Lefschetz theory applicable to oscillatory path integrals and the
resurgence program.Comment: 58 page
A Spherical Plasma Dynamo Experiment
We propose a plasma experiment to be used to investigate fundamental
properties of astrophysical dynamos. The highly conducting, fast-flowing plasma
will allow experimenters to explore systems with magnetic Reynolds numbers an
order of magnitude larger than those accessible with liquid-metal experiments.
The plasma is confined using a ring-cusp strategy and subject to a toroidal
differentially rotating outer boundary condition. As proof of principle, we
present magnetohydrodynamic simulations of the proposed experiment. When a von
K\'arm\'an-type boundary condition is specified, and the magnetic Reynolds
number is large enough, dynamo action is observed. At different values of the
magnetic Prandtl and Reynolds numbers the simulations demonstrate either
laminar or turbulent dynamo action
Running Gauge Coupling in Asymptotically Safe Quantum Gravity
We investigate the non-perturbative renormalization group behavior of the
gauge coupling constant using a truncated form of the functional flow equation
for the effective average action of the Yang-Mills-gravity system. We find a
non-zero quantum gravity correction to the standard Yang-Mills beta function
which has the same sign as the gauge boson contribution. Our results fit into
the picture according to which Quantum Einstein Gravity (QEG) is asymptotically
safe, with a vanishing gauge coupling constant at the non-trivial fixed point.Comment: 27 page
The role of Background Independence for Asymptotic Safety in Quantum Einstein Gravity
We discuss various basic conceptual issues related to coarse graining flows
in quantum gravity. In particular the requirement of background independence is
shown to lead to renormalization group (RG) flows which are significantly
different from their analogs on a rigid background spacetime. The importance of
these findings for the asymptotic safety approach to Quantum Einstein Gravity
(QEG) is demonstrated in a simplified setting where only the conformal factor
is quantized. We identify background independence as a (the ?) key prerequisite
for the existence of a non-Gaussian RG fixed point and the renormalizability of
QEG.Comment: 2 figures. Talk given by M.R. at the WE-Heraeus-Seminar "Quantum
Gravity: Challenges and Perspectives", Bad Honnef, April 14-16, 2008; to
appear in General Relativity and Gravitatio
Monitoring of crack growth in Ti-Al-4v alloy by the stress wave analysis technique
Stress wave analysis techniques for monitoring crack growth in Ti-6Al-4V alloy pressure vessel wall
Spinor gravity and diffeomorphism invariance on the lattice
The key ingredient for lattice regularized quantum gravity is diffeomorphism
symmetry. We formulate a lattice functional integral for quantum gravity in
terms of fermions. This allows for a diffeomorphism invariant functional
measure and avoids problems of boundedness of the action. We discuss the
concept of lattice diffeomorphism invariance. This is realized if the action
does not depend on the positioning of abstract lattice points on a continuous
manifold. Our formulation of lattice spinor gravity also realizes local Lorentz
symmetry. Furthermore, the Lorentz transformations are generalized such that
the functional integral describes simultaneously euclidean and Minkowski
signature. The difference between space and time arises as a dynamical effect
due to the expectation value of a collective metric field. The quantum
effective action for the metric is diffeomorphism invariant. Realistic gravity
can be obtained if this effective action admits a derivative expansion for long
wavelengths.Comment: 13 pages, proceedings 6th Aegean Summer School, Naxos 201
Quantum Einstein Gravity
We give a pedagogical introduction to the basic ideas and concepts of the
Asymptotic Safety program in Quantum Einstein Gravity. Using the continuum
approach based upon the effective average action, we summarize the state of the
art of the field with a particular focus on the evidence supporting the
existence of the non-trivial renormalization group fixed point at the heart of
the construction. As an application, the multifractal structure of the emerging
space-times is discussed in detail. In particular, we compare the continuum
prediction for their spectral dimension with Monte Carlo data from the Causal
Dynamical Triangulation approach.Comment: 87 pages, 13 figures, review article prepared for the New Journal of
Physics focus issue on Quantum Einstein Gravit
Renormalization Group Flow in Scalar-Tensor Theories. II
We study the UV behaviour of actions including integer powers of scalar
curvature and even powers of scalar fields with Functional Renormalization
Group techniques. We find UV fixed points where the gravitational couplings
have non-trivial values while the matter ones are Gaussian. We prove several
properties of the linearized flow at such a fixed point in arbitrary dimensions
in the one-loop approximation and find recursive relations among the critical
exponents. We illustrate these results in explicit calculations in for
actions including up to four powers of scalar curvature and two powers of the
scalar field. In this setting we notice that the same recursive properties
among the critical exponents, which were proven at one-loop order, still hold,
in such a way that the UV critical surface is found to be five dimensional. We
then search for the same type of fixed point in a scalar theory with minimal
coupling to gravity in including up to eight powers of scalar curvature.
Assuming that the recursive properties of the critical exponents still hold,
one would conclude that the UV critical surface of these theories is five
dimensional.Comment: 14 pages. v.2: Minor changes, some references adde
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