6,007 research outputs found
A History of Feynman's Sum over Histories in Quantum Mechanics
A history of Feynman's sum over histories is presented in brief. A focus is
placed on the progress of path-integration techniques for exactly
path-integrable problems in quantum mechanics.Comment: 3 pages, to appear in the proceedings of the 6th International
Conference on "Path-Integrals from peV to TeV", Florence, Italy, 199
Gravitational waves induced by scalar perturbations as probes of the small-scale primordial spectrum
Compared to primordial perturbations on large scales, roughly larger than
megaparsec, those on smaller scales are not severely constrained. We revisit
the issue of probing small-scale primordial perturbations using gravitational
waves (GWs), based on the fact that, when large-amplitude primordial
perturbations on small scales exist, GWs with relatively large amplitudes are
induced at second order in scalar perturbations, and these induced GWs can be
probed by both existing and planned gravitational-wave projects. We use
accurate methods to calculate these induced GWs and take into account
sensitivities of different experiments to induced GWs carefully, to report
existing and expected limits on the small-scale primordial spectrum.Comment: 10 pages, 6 figures, v3: minor changes, version accepted for
publication in PR
Circular polarization of the cosmic microwave background from vector and tensor perturbations
Circular polarization of the cosmic microwave background (CMB) can be induced
by Faraday conversion of the primordial linearly polarized radiation as it
propagates through a birefringent medium. Recent work has shown that the
dominant source of birefringence from primordial density perturbations is the
anisotropic background CMB. Here we extend prior work to allow for the
additional birefringence that may arise from primordial vector and tensor
perturbations. We derive the formulas for the power spectrum of the induced
circular polarization and apply those to the standard cosmology. We find the
root-variance of the induced circular polarization to be for scalar perturbations and for tensor perturbations with a tensor-to-scalar ratio .Comment: 15 pages, 2 figures, v2: minor changes, version accepted for
publication in PR
Chiral photons from chiral gravitational waves
We show that a parity-breaking uniform (averaged over all directions on the
sky) circular polarization of amplitude can be induced by chiral gravitational-wave (GW)
background with tensor-to-scalar ratio and chirality parameter
(which is for a maximally chiral background). We also show, however,
that a uniform circular polarization can arise from a realization of a
non-chiral GW background that spontaneously breaks parity. The magnitude of
this polarization is drawn from a distribution of root-variance implying that the
chirality parameter must be to
establish that the GW background is chiral. Although these values are too small
to be detected by any experiment in the foreseeable future, the calculation is
a proof of principle that cosmological parity breaking in the form of a chiral
gravitational-wave background can be imprinted in the chirality of the photons
in the cosmic microwave background. It also illustrates how a seemingly
parity-breaking cosmological signal can arise from parity-conserving physics.Comment: 5 pages, v2: minor changes, version accepted for publication in PR
Geometric spin manipulation in semiconductor quantum dots
We propose a method to flip the spin completely by an adiabatic transport of
quantum dots. We show that it is possible to flip the spin by inducing a
geometric phase on the spin state of a quantum dot. We estimate the geometric
spin flip time (approximately 2 pico-sec) which turned out to be much shorter
than the experimentally reported decoherence time (approx. 100 nano-sec) that
would provide an alternative means of fliping the spin before reaching
decoherence. It is important that both the Rashba coupling and the Dresselhaus
coupling are present for inducing a phase necessary for spin flip. If one of
them is absent, the induced phase is trivial and irrelevant for spin-flip.Comment: 4 pages, 3 figure
Super-radiant phase transition in superconducting circuit in thermal equilibrium
We propose a superconducting circuit that shows a super-radiant phase
transition (SRPT) in the thermal equilibrium. The existence of the SRPT is
confirmed analytically in the limit of an infinite number of artificial atoms.
We also perform numerical diagonalization of the Hamiltonian with a finite
number of atoms and observe an asymptotic behavior approaching the infinite
limit as the number of atoms increases. The SRPT can also be interpreted
intuitively in a classical analysis.Comment: 8 pages, 3 figure
Path integration in the field of a topological defect: the case of dispiration
The motion of a particle in the field of dispiration (due to a wedge
disclination and a screw dislocation) is studied by path integration. By
gauging , first, we derive the metric, curvature, and
torsion of the medium of dispiration. Then we carry out explicitly path
integration for the propagator of a particle moving in the non-Euclidean medium
under the influence of a scalar potential and a vector potential. We obtain
also the winding number representation of the propagator by taking the
non-trivial topological structure of the medium into account. We extract the
energy spectrum and the eigenfunctions from the propagator. Finally we make
some remarks for special cases. Particularly, paying attention to the
difference between the result of the path integration and the solution of
Schr\"odinger's equation in the case of disclination, we suggest that
Schr\"odinger equation may have to be modified by a curvature term
Revisiting constraints on small scale perturbations from big-bang nucleosynthesis
We revisit the constraints on the small scale density perturbations
() from the
modification of the freeze-out value of the neutron-proton ratio at big-bang
nucleosynthesis era. Around the freeze-out temperature , the universe can be divided into several local patches
which have different temperatures since any perturbation which enters the
horizon after the neutrino decoupling has not diffused yet. Taking account of
this situation, we calculate the freeze-out value in detail. We find that the
small scale perturbations decrease the n-p ratio in contrast to previous works.
With use of the latest observed He abundance, we obtain the constraint on
the power spectrum of the curvature perturbations as
on .Comment: 13 pages, 7 figures, PRD accepted version (DOI:
http://dx.doi.org/10.1103/PhysRevD.94.043527
Window function dependence of the novel mass function of primordial black holes
We investigate the ambiguity of the novel mass function of primordial black
holes, which has succeeded in identifying the black hole mass in a given
configuration of fluctuations, due to the choice of window function of smoothed
density fluctuations. We find that while the window function dependence of the
exponential factor in the novel mass function is the same as the one in the
conventional mass function around the top-hat scale, the dependences are
different on other scales, which leads to the narrower mass function in the
novel formulation for some window functions.Comment: 17 pages, 3 figure
Standard Model Prediction for Cosmological 21cm Circular Polarization
Before cosmic reionization, hydrogen atoms acquire a spin polarization
quadrupole through interaction with the anisotropic 21-cm radiation field. The
interaction of this quadrupole with anisotropies in the cosmic microwave
background (CMB) radiation field gives a net spin orientation to the hydrogen
atoms. The 21-cm radiation emitted by these spin-oriented hydrogen atoms is
circularly polarized. Here, we reformulate succinctly the derivation of the
expression for this circular polarization in terms of Cartesian (rather than
spherical) tensors. We then compute the angular power spectrum of the observed
Stokes- parameter in the standard CDM cosmological model and show
how it depends on redshift, or equivalently, the observed frequency.Comment: 5 pages, 2 figures; added reference
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