10,180 research outputs found
Semiclassical Resolvent Estimates and Wave Decay in Low Regularity
In this thesis, we prove weighted resolvent upper bounds for semiclassical Schršodinger operators. These upper bounds hold in the semiclassical limit. First, we consider operators in dimension two when the potential is Lipschitz with long range decay. We prove that the resolvent norm grows at most exponentially in the inverse semiclassical parameter, while near infinity it grows at most linearly. Both of these bounds are optimal. Second, we work in any dimension and require that the potential belong to Lâ and have compact support. Again, we find that the weighted resolvent norm grows at most exponentially, but this time with an additional loss in the exponent. Finally, we apply the resolvent bounds to prove two logarithmic local energy decay rates for the wave equation, one when the wavespeed is a compactly supported Lipschitz perturbation of unity, and the other when the wavespeed is a compactly supported Lâ perturbation of unity
Mode-Locked Two-Photon States
The concept of mode locking in laser is applied to a two-photon state with
frequency entanglement. Cavity enhanced parametric down-conversion is found to
produce exactly such a state. The mode-locked two-photon state exhibits a
comb-like correlation function. An unbalanced Hong-Ou-Mandel type
interferometer is used to measure the correlation function. A revival of the
typical interference dip is observed. We will discuss schemes for engineering
of quantum states in time domain.Comment: 4 pages, 5 figure
Frequency-Domain Coherent Control of Femtosecond Two-Photon Absorption: Intermediate-Field vs. Weak-Field Regime
Coherent control of femtosecond two-photon absorption in the
intermediate-field regime is analyzed in detail in the powerful frequency
domain using an extended 4th-order perturbative description. The corresponding
absorption is coherently induced by the weak-field non-resonant two-photon
transitions as well as by four-photon transitions involving three absorbed
photons and one emitted photons. The interferences between these two groups of
transitions lead to a difference between the intermediate-field and weak-field
absorption dynamics. The corresponding interference nature (constructive or
destructive) strongly depends on the detuning direction of the pulse spectrum
from half the two-photon transition frequency. The model system of the study is
atomic sodium, for which both experimental and theoretical results are
obtained. The detailed understanding obtained here serves as a basis for
coherent control with rationally-shaped femtosecond pulses in a regime of
sizable absorption yields.Comment: 25 pages, 5 figure
Quantum tomography as normalization of incompatible observations
Quantum states are successfully reconstructed using the maximum likelihood
estimation on the subspace where the measured projectors reproduce the identity
operator. Reconstruction corresponds to normalization of incompatible
observations. The proposed approach handles the noisy data corresponding to
realistic incomplete observation with finite resolution.Comment: RevTeX, 4 pages, 3 figure
Model-based Cognitive Neuroscience: Multifield Mechanistic Integration in Practice
Autonomist accounts of cognitive science suggest that cognitive model building and theory construction (can or should) proceed independently of findings in neuroscience. Common functionalist justifications of autonomy rely on there being relatively few constraints between neural structure and cognitive function (e.g., Weiskopf, 2011). In contrast, an integrative mechanistic perspective stresses the mutual constraining of structure and function (e.g., Piccinini & Craver, 2011; Povich, 2015). In this paper, I show how model-based cognitive neuroscience (MBCN) epitomizes the integrative mechanistic perspective and concentrates the most revolutionary elements of the cognitive neuroscience revolution (Boone & Piccinini, 2016). I also show how the prominent subset account of functional realization supports the integrative mechanistic perspective I take on MBCN and use it to clarify the intralevel and interlevel components of integration
Iterative algorithm for reconstruction of entangled states
An iterative algorithm for the reconstruction of an unknown quantum state
from the results of incompatible measurements is proposed. It consists of
Expectation-Maximization step followed by a unitary transformation of the
eigenbasis of the density matrix. The procedure has been applied to the
reconstruction of the entangled pair of photons.Comment: 4 pages, no figures, some formulations changed, a minor mistake
correcte
Investigation of the field-induced ferromagnetic phase transition in spin polarized neutron matter: a lowest order constrained variational approach
In this paper, the lowest order constrained variational (LOCV) method has
been used to investigate the magnetic properties of spin polarized neutron
matter in the presence of strong magnetic field at zero temperature employing
potential. Our results indicate that a ferromagnetic phase transition
is induced by a strong magnetic field with strength greater than ,
leading to a partial spin polarization of the neutron matter. It is also shown
that the equation of state of neutron matter in the presence of magnetic field
is stiffer than the case in absence of magnetic field.Comment: 23 pages, 9 figures Phys. Rev. C (2011) in pres
Reducing the weak lensing noise for the gravitational wave Hubble diagram using the non-Gaussianity of the magnification distribution
Gravitational wave sources are a promising cosmological standard candle
because their intrinsic luminosities are determined by fundamental physics (and
are insensitive to dust extinction). They are, however, affected by weak
lensing magnification due to the gravitational lensing from structures along
the line of sight. This lensing is a source of uncertainty in the distance
determination, even in the limit of perfect standard candle measurements. It is
commonly believed that the uncertainty in the distance to an ensemble of
gravitational wave sources is limited by the standard deviation of the lensing
magnification distribution divided by the square root of the number of sources.
Here we show that by exploiting the non-Gaussian nature of the lensing
magnification distribution, we can improve this distance determination,
typically by a factor of 2--3; we provide a fitting formula for the effective
distance accuracy as a function of redshift for sources where the lensing noise
dominates.Comment: matches PRD accepted version (expanded description of the
cosmological parameter space + minor changes
Spatial field correlation, the building block of mesoscopic fluctuations
The absence of self averaging in mesoscopic systems is a consequence of
long-range intensity correlation. Microwave measurements suggest and
diagrammatic calculations confirm that the correlation function of the
normalized intensity with displacement of the source and detector,
and , respectively, can be expressed as the sum of three terms, with
distinctive spatial dependences. Each term involves only the sum or the product
of the square of the field correlation function, . The
leading-order term is the product, the next term is proportional to the sum.
The third term is proportional to .Comment: Submitted to PR
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