88,373 research outputs found
Fluctuations of the vacuum energy density of quantum fields in curved spacetime via generalized zeta functions
For quantum fields on a curved spacetime with an Euclidean section, we derive
a general expression for the stress energy tensor two-point function in terms
of the effective action. The renormalized two-point function is given in terms
of the second variation of the Mellin transform of the trace of the heat kernel
for the quantum fields. For systems for which a spectral decomposition of the
wave opearator is possible, we give an exact expression for this two-point
function. Explicit examples of the variance to the mean ratio of the vacuum energy density of a
massless scalar field are computed for the spatial topologies of and , with results of , and
respectively. The large variance signifies the importance
of quantum fluctuations and has important implications for the validity of
semiclassical gravity theories at sub-Planckian scales. The method presented
here can facilitate the calculation of stress-energy fluctuations for quantum
fields useful for the analysis of fluctuation effects and critical phenomena in
problems ranging from atom optics and mesoscopic physics to early universe and
black hole physics.Comment: Uses revte
Gather-Excite: Exploiting Feature Context in Convolutional Neural Networks
While the use of bottom-up local operators in convolutional neural networks
(CNNs) matches well some of the statistics of natural images, it may also
prevent such models from capturing contextual long-range feature interactions.
In this work, we propose a simple, lightweight approach for better context
exploitation in CNNs. We do so by introducing a pair of operators: gather,
which efficiently aggregates feature responses from a large spatial extent, and
excite, which redistributes the pooled information to local features. The
operators are cheap, both in terms of number of added parameters and
computational complexity, and can be integrated directly in existing
architectures to improve their performance. Experiments on several datasets
show that gather-excite can bring benefits comparable to increasing the depth
of a CNN at a fraction of the cost. For example, we find ResNet-50 with
gather-excite operators is able to outperform its 101-layer counterpart on
ImageNet with no additional learnable parameters. We also propose a parametric
gather-excite operator pair which yields further performance gains, relate it
to the recently-introduced Squeeze-and-Excitation Networks, and analyse the
effects of these changes to the CNN feature activation statistics.Comment: NeurIPS 201
Phase dynamics of inductively coupled intrinsic Josephson junctions and terahertz electromagnetic radiation
The Josephson effects associated with quantum tunneling of Cooper pairs
manifest as nonlinear relations between the superconductivity phase difference
and the bias current and voltage. Many novel phenomena appear, such as Shapiro
steps in dc cuurent-voltage (IV) characteristics of a Josephson junction under
microwave shining, which can be used as a voltage standard. Inversely, the
Josephson effects provide a unique way to generate high-frequency
electromagnetic (EM) radiation by dc bias voltage. The discovery of cuprate
high-Tc superconductors accelerated the effort to develop novel source of EM
waves based on a stack of atomically dense-packed intrinsic Josephson junctions
(IJJs), since the large superconductivity gap covers the whole terahertz
frequency band. Very recently, strong and coherent terahertz radiations have
been successfully generated from a mesa structure of
single crystal which works both as the source
of energy gain and as the cavity for resonance. It is then found theoretically
that, due to huge inductive coupling of IJJs produced by the nanometer junction
separation and the large London penetration depth of order of of
the material, a novel dynamic state is stabilized in the coupled sine-Gordon
system, in which kinks in phase differences are developed responding
to the standing wave of Josephson plasma and are stacked alternatively in the
c-axis. This novel solution of the inductively coupled sine-Gordon equations
captures the important features of experimental observations. The theory
predicts an optimal radiation power larger than the one available to date by
orders of magnitude, and thus suggests the technological relevance of the
phenomena.Comment: review article (69 pages, 30 figures
Decoherence in Quantum Gravity: Issues and Critiques
An increasing number of papers have appeared in recent years on decoherence
in quantum gravity at the Planck energy. We discuss the meaning of decoherence
in quantum gravity starting from the common notion that quantum gravity is a
theory for the microscopic structures of spacetime, and invoking some generic
features of quantum decoherence from the open systems viewpoint. We dwell on a
range of issues bearing on this process including the relation between
statistical and quantum, noise from effective field theory, the meaning of
stochasticity, the origin of non-unitarity and the nature of nonlocality in
this and related contexts. To expound these issues we critique on two
representative theories: One claims that decoherence in quantum gravity scale
leads to the violation of CPT symmetry at sub-Planckian energy which is used to
explain today's particle phenomenology. The other uses this process in place
with the Brownian motion model to prove that spacetime foam behaves like a
thermal bath.Comment: 25 pages, proceedings of DICE06 (Piombino
Noise Kernel in Stochastic Gravity and Stress Energy Bi-Tensor of Quantum Fields in Curved Spacetimes
The noise kernel is the vacuum expectation value of the (operator-valued)
stress-energy bi-tensor which describes the fluctuations of a quantum field in
curved spacetimes. It plays the role in stochastic semiclassical gravity based
on the Einstein-Langevin equation similar to the expectation value of the
stress-energy tensor in semiclassical gravity based on the semiclassical
Einstein equation. According to the stochastic gravity program, this two point
function (and by extension the higher order correlations in a hierarchy) of the
stress energy tensor possesses precious statistical mechanical information of
quantum fields in curved spacetime and, by the self-consistency required of
Einstein's equation, provides a probe into the coherence properties of the
gravity sector (as measured by the higher order correlation functions of
gravitons) and the quantum nature of spacetime. It reflects the low and medium
energy (referring to Planck energy as high energy) behavior of any viable
theory of quantum gravity, including string theory. It is also useful for
calculating quantum fluctuations of fields in modern theories of structure
formation and for backreaction problems in cosmological and black holes
spacetimes.
We discuss the properties of this bi-tensor with the method of
point-separation, and derive a regularized expression of the noise-kernel for a
scalar field in general curved spacetimes. One collorary of our finding is that
for a massless conformal field the trace of the noise kernel identically
vanishes. We outline how the general framework and results derived here can be
used for the calculation of noise kernels for Robertson-Walker and
Schwarzschild spacetimes.Comment: 22 Pages, RevTeX; version accepted for publication in PR
Macroscopic Quantum Phenomena from the Correlation, Coupling and Criticality Perspectives
In this sequel paper we explore how macroscopic quantum phenomena can be
measured or understood from the behavior of quantum correlations which exist in
a quantum system of many particles or components and how the interaction
strengths change with energy or scale, under ordinary situations and when the
system is near its critical point. We use the nPI (master) effective action
related to the Boltzmann-BBGKY / Schwinger-Dyson hierarchy of equations as a
tool for systemizing the contributions of higher order correlation functions to
the dynamics of lower order correlation functions. Together with the large N
expansion discussed in our first paper(MQP1) we explore 1) the conditions
whereby an H-theorem is obtained, which can be viewed as a signifier of the
emergence of macroscopic behavior in the system. We give two more examples from
past work: 2) the nonequilibrium dynamics of N atoms in an optical lattice
under the large (field components), 2PI and second order perturbative
expansions, illustrating how N and enter in these three aspects of
quantum correlations, coherence and coupling strength. 3) the behavior of an
interacting quantum system near its critical point, the effects of quantum and
thermal fluctuations and the conditions under which the system manifests
infrared dimensional reduction. We also discuss how the effective field theory
concept bears on macroscopic quantum phenomena: the running of the coupling
parameters with energy or scale imparts a dynamical-dependent and an
interaction-sensitive definition of `macroscopia'.Comment: For IARD 2010 meeting, Hualien, Taiwan. Proceedings to appear in J.
Physics (Conf. Series
- …