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 $1$ 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 $\sqrt{}\sim 3\times 10^{-14}$ for scalar perturbations and $\sqrt{}\sim 7\times 10^{-18} (r/0.06)$ for tensor perturbations with a tensor-to-scalar ratio $r$.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 $V_{00} \simeq 2.6 \times 10^{-17}\, \Delta \chi (r/0.06)$ can be induced by chiral gravitational-wave (GW) background with tensor-to-scalar ratio $r$ and chirality parameter $\Delta\chi$ (which is $\pm1$ 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 $\sqrt{< V_{00}^2>} \simeq 1.5\times 10^{-18}\, (r/0.06)^{1/2}$ implying that the chirality parameter must be $\Delta \chi \gtrsim 0.12 (r/0.06)^{-1/2}$ 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 $SO(2) \otimes T(1)$, 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 ($10^4\,\mathrm{Mpc}^{-1}\lesssim k \lesssim10^5\,\mathrm{Mpc}^{-1}$) from the modification of the freeze-out value of the neutron-proton ratio at big-bang nucleosynthesis era. Around the freeze-out temperature $T\sim 0.5\,\mathrm{MeV}$, 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 $^4$He abundance, we obtain the constraint on the power spectrum of the curvature perturbations as $\Delta^2_\mathcal{R}\lesssim 0.018$ on $10^4\,\mathrm{Mpc}^{-1}\lesssim k \lesssim 10^5\,\mathrm{Mpc}^{-1}$.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-$V$ parameter in the standard $\Lambda$CDM cosmological model and show how it depends on redshift, or equivalently, the observed frequency.Comment: 5 pages, 2 figures; added reference