29,699 research outputs found
Anomalous diffusion in quantum Brownian motion with colored noise
Anomalous diffusion is discussed in the context of quantum Brownian motion
with colored noise. It is shown that earlier results follow simply and directly
from the fluctuation-dissipation theorem. The limits on the long-time
dependence of anomalous diffusion are shown to be a consequence of the second
law of thermodynamics. The special case of an electron interacting with the
radiation field is discussed in detail. We apply our results to wave-packet
spreading
Decoherence and Recoherence in Model Quantum Systems
We discuss the various manifestations of quantum decoherence in the forms of
dephasing, entanglement with the environment, and revelation of "which-path"
information. As a specific example, we consider an electron interference
experiment. The coupling of the coherent electrons to the quantized
electromagnetic field illustrates all of these versions of decoherence. This
decoherence has two equivalent interpretations, in terms of photon emission or
in terms of Aharonov-Bohm phase fluctuations. We consider the case when the
coherent electrons are coupled to photons in a squeezed vacuum state. The
time-averaged result is increased decoherence. However, if only electrons which
are emitted during selected periods are counted, the decoherence can be
suppressed below the level for the photon vacuum. This is the phenomenon of
recoherence. This effect is closely related to the quantum violations of the
weak energy condition, and is restricted by similar inequalities. We give some
estimates of the magnitude of the recoherence effect and discuss prospects for
observing it in an electron interferometry experiment.Comment: 8 pages, 3 figures, talk presented at the 7th Friedmann Seminar, Joao
Pessoa, Brazil, July 200
Simulating Impacts of Extreme Weather Events on Urban Transport Infrastructure in the UK
Urban areas face many risks from future climate change and their infrastructure will be placed under more pressure
due to changes in climate extremes. Using the Tyndall Centre Urban Integrated Assessment Framework, this paper
describes a methodology used to assess the impacts of future climate extremes on transport infrastructure in
London. Utilising high-resolution projections for future climate in the UK, alongside stochastic weather generators
for downscaling, urban temperature and flooding models are used to provide information on the likelihood of future
extremes. These are then coupled with spatial network models of urban transport infrastructure and, using thresholds
to define the point at which systems cease to function normally, disruption to the networks can be simulated.
Results are shown for both extreme heat and urban surface water flooding events and the impacts on the travelling
population, in terms of both disruption time and monetary cost
Cosmological and Black Hole Horizon Fluctuations
The quantum fluctuations of horizons in Robertson-Walker universes and in the
Schwarzschild spacetime are discussed. The source of the metric fluctuations is
taken to be quantum linear perturbations of the gravitational field. Lightcone
fluctuations arise when the retarded Green's function for a massless field is
averaged over these metric fluctuations. This averaging replaces the
delta-function on the classical lightcone with a Gaussian function, the width
of which is a measure of the scale of the lightcone fluctuations. Horizon
fluctuations are taken to be measured in the frame of a geodesic observer
falling through the horizon. In the case of an expanding universe, this is a
comoving observer either entering or leaving the horizon of another observer.
In the black hole case, we take this observer to be one who falls freely from
rest at infinity. We find that cosmological horizon fluctuations are typically
characterized by the Planck length. However, black hole horizon fluctuations in
this model are much smaller than Planck dimensions for black holes whose mass
exceeds the Planck mass. Furthermore, we find black hole horizon fluctuations
which are sufficiently small as not to invalidate the semiclassical derivation
of the Hawking process.Comment: 22 pages, Latex, 4 figures, uses eps
Two-loop effective potential for a general renormalizable theory and softly broken supersymmetry
I compute the two-loop effective potential in the Landau gauge for a general
renormalizable field theory in four dimensions. Results are presented for the
\bar{MS} renormalization scheme based on dimensional regularization, and for
the \bar{DR} and \bar{DR}' schemes based on regularization by dimensional
reduction. The last of these is appropriate for models with softly broken
supersymmetry, such as the Minimal Supersymmetric Standard Model. I find the
parameter redefinition which relates the \bar{DR} and \bar{DR}' schemes at
two-loop order. I also discuss the renormalization group invariance of the
two-loop effective potential, and compute the anomalous dimensions for scalars
and the beta function for the vacuum energy at two-loop order in softly broken
supersymmetry. Several illustrative examples and consistency checks are
included.Comment: 38 pages. Typos in equations (3.5), (3.11), and (6.3) are fixed.
Explicit claim of renormalization group invariance in the general case of
softly-broken supersymmetry is added. Additional discussion of cases of
multiple simple or U(1) groups. Equations in Appendix B rewritten in a more
useful for
Chains of large gaps between primes
Let denote the -th prime, and for any and sufficiently
large , define the quantity which measures the occurrence of
chains of consecutive large gaps of primes. Recently, with Green and
Konyagin, the authors showed that for sufficiently large . In this
note, we combine the arguments in that paper with the Maier matrix method to
show that for any fixed and sufficiently large . The
implied constant is effective and independent of .Comment: 16 pages, no figure
Exponential Divergence and Long Time Relaxation in Chaotic Quantum Dynamics
Phase space representations of the dynamics of the quantal and classical cat
map are used to explore quantum--classical correspondence in a K-system: as
, the classical chaotic behavior is shown to emerge smoothly and
exactly. The quantum dynamics near the classical limit displays both
exponential separation of adjacent distributions and long time relaxation, two
characteristic features of classical chaotic motion.Comment: 10 pages, ReVTeX, to appear in Phys. Rev. Lett. 13 figures NOT
included. Available either as LARGE (uuencoded gzipped) postscript files or
hard-copies from [email protected]
Quantum Inequalities and Singular Energy Densities
There has been much recent work on quantum inequalities to constrain negative
energy. These are uncertainty principle-type restrictions on the magnitude and
duration of negative energy densities or fluxes. We consider several examples
of apparent failures of the quantum inequalities, which involve passage of an
observer through regions where the negative energy density becomes singular. We
argue that this type of situation requires one to formulate quantum
inequalities using sampling functions with compact support. We discuss such
inequalities, and argue that they remain valid even in the presence of singular
energy densities.Comment: 18 pages, LaTex, 2 figures, uses eps
Light-cone fluctuations and the renormalized stress tensor of a massless scalar field
We investigate the effects of light-cone fluctuations over the renormalized
vacuum expectation value of the stress-energy tensor of a real massless
minimally coupled scalar field defined in a ()-dimensional flat space-time
with topology . For modeling the influence of
light-cone fluctuations over the quantum field, we consider a random
Klein-Gordon equation. We study the case of centered Gaussian processes. After
taking into account all the realizations of the random processes, we present
the correction caused by random fluctuations. The averaged renormalized vacuum
expectation value of the stress-energy associated with the scalar field is
presented
A general worldline quantum inequality
Worldline quantum inequalities provide lower bounds on weighted averages of
the renormalised energy density of a quantum field along the worldline of an
observer. In the context of real, linear scalar field theory on an arbitrary
globally hyperbolic spacetime, we establish a worldline quantum inequality on
the normal ordered energy density, valid for arbitrary smooth timelike
trajectories of the observer, arbitrary smooth compactly supported weight
functions and arbitrary Hadamard quantum states. Normal ordering is performed
relative to an arbitrary choice of Hadamard reference state. The inequality
obtained generalises a previous result derived for static trajectories in a
static spacetime. The underlying argument is straightforward and is made
rigorous using the techniques of microlocal analysis. In particular, an
important role is played by the characterisation of Hadamard states in terms of
the microlocal spectral condition. We also give a compact form of our result
for stationary trajectories in a stationary spacetime.Comment: 19pp, LaTeX2e. The statement of the main result is changed slightly.
Several typos fixed, references added. To appear in Class Quantum Gra
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