No Intrinsic Decoherence of Inflationary Cosmological Perturbations

After a brief summary of the four main veins in the treatment of decoherence and quantum to classical transition in cosmology since the 1980s, we focus on one of these veins in the study of quantum decoherence of cosmological perturbations in inflationary universe, the case when it does not rely on any environment. This is what ‘intrinsic’ in the title refers to—a closed quantum system, consisting of a quantum field which drives inflation. The question is whether its quantum perturbations, which interact with the density contrast giving rise to structures in the universe, decohere with an inflationary expansion of the universe. A dominant view which had propagated for a quarter of a century asserts yes, based on the belief that the large squeezing of a quantum state after a duration of inflation renders the system effectively classical. This paper debunks this view by identifying the technical fault-lines in its derivations and revealing the pitfalls in its arguments which drew earlier authors to this wrong conclusion. We use a few simple quantum mechanical models to expound where the fallacy originated: The highly squeezed ellipse quadrature in phase space cannot be simplified to a line, and the Wigner function cannot be replaced by a delta function. These measures amount to taking only the leading order in the relevant parameters in seeking the semiclassical limit and ignoring the subdominant contributions where quantum features reside. Doing so violates the bounds of the Wigner function, and its wave functions possess negative eigenvalues. Moreover, the Robertson-Schrödinger uncertainty relation for a pure state is violated. For inflationary cosmological perturbations, in addition to these features, entanglement exists between the created pairs. This uniquely quantum feature cannot be easily argued away. Indeed, it could be our best hope to retroduce the quantum nature of cosmological perturbations and the trace of an inflation field. All this points to the invariant fact that a closed quantum system, even when highly squeezed, evolves unitarily without loss of coherence; quantum cosmological perturbations do not decohere by themselves.

DETERMINATION OF FIBER ORIENTATION IN HIGH ANGULAR RESOLUTION DIFFUSION IMAGING USING SPHERICAL HARMONICS AND PARTICLE SWARM OPTIMIZATION

The fiber directions in High Angular Resolution Diffusion Imaging (HARDI) with low fractional anisotropy or low Signal to Noise Ratio (SNR) cannot be estimated accurately. In this paper, the fiber directions are estimated using Particle Swarm Optimization and Spherical Deconvolution (PSO-SD). Fiber orientation is modeled as a Dirac delta function in [Formula: see text]. The Spherical Harmonic Coefficients (SHC) of the Dirac delta function in the [Formula: see text] direction are obtained using the rotational harmonic matrix and the SHC of the Dirac delta function in the [Formula: see text]-axis. The PSO-SD method is used to determine ([Formula: see text]). We generated noise-free synthetic data for isotropic regions (FA varied from 0.1 to 0.8) and synthetic data with two crossing fibers for anisotropic regions with SNRs of 20, 15, 10 and 5 (FA [Formula: see text] 0.78). In the noise-free signal (FA [Formula: see text] 0.3), the Success Ratio (SR) and Mean Difference Angle (MDA) of the PSO-SD method were 1∘ and 9.48∘, respectively. In the noisy signal (FA [Formula: see text] 0.78, SNR [Formula: see text] 10, crossing angle [Formula: see text] 40), the SR and MDA of PSO-SD (with [Formula: see text]) were 0.46∘ and 12.3∘, respectively. The PSO-SD method can estimate fiber directions in HARDI with low fractional anisotropy and low SNR. Moreover, it has a higher SR and lower MDA in comparison with those of the super-CSD method.

Variational approach to the Schrödinger equation with a delta-function potential

We obtain accurate eigenvalues of the one-dimensional Schr\"{o}dinger equation with a Hamiltonian of the form $H_{g}=H+g\delta (x)$, where $\delta (x)$ is the Dirac delta function. We show that the well known Rayleigh-Ritz variational method is a suitable approach provided that the basis set takes into account the effect of the Dirac delta on the wavefunction. Present analysis may be suitable for an introductory course on quantum mechanics to illustrate the application of the Rayleigh-Ritz variational method to a problem where the boundary conditions play a relevant role and have to be introduced carefully into the trial function. Besides, the examples are suitable for motivating the students to resort to any computer-algebra software in order to calculate the required integrals and solve the secular equations.

Generalization of the Gross–Pitaevskii equation for multi-particle cases

A new method is proposed to obtain Gross–Pitaevskii equation by the chain of Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) quantum kinetic equations. In that sense, we investigate the dynamics of a quantum system including infinite number of identical particles which interact via a (special) pair potential on the form of Dirac delta-function.

Influence of radiation transport on discharge characteristics of an atmospheric pressure plasma jet in Argon

In the current work the method of radiation trapping treatment infinite coaxial cylinders using spherical coordinates is introduced. The operator of resonant transition process is obtained explicitly in the matrix form and its response to delta-function is analyzed in both hollow and solid cylinders. The influence of radiation trapping effect is shown on the example of model of miniaturized non-thermal atmospheric pressure plasma jet. The results of the calculations with the developed matrix method are compared to those based on the effective probability approximation. It is shown that the use of matrix method leads to significant spatial redistribution of the excited plasma species due to the non-local effects of radiation transport mechanism.

Convergence of eigenfunction expansions for flexural gravity waves in infinite water depth

In the present paper, point-wise convergence of the eigenfunction expansion to the velocity potential associated with the flexural gravity waves problem in water wave theory is established for infinite water depth case. To take into account the hydroelastic boundary condition at the free surface, a flexible membrane is assumed to float in water waves. In this context, firstly the eigenfunction expansion for the velocity potentials is obtained. Thereafter, an appropriate Green’s function is constructed for the associated boundary value problem. Using suitable properties of the Green’s functions, the vertical components of the eigenfunction expansion is written in terms of the Dirac delta function. Finally, using the property of the Dirac delta function, the convergence of the eigenfunction expansion to the velocity potential is shown.

Bending of a Viscoelastic Timoshenko Cracked Beam Based on Equivalent Viscoelastic Spring Models

Considering the transverse crack as a massless viscoelastic rotational spring, the equivalent stiffness of the viscoelastic cracked beam is derived by Laplace transform and the generalized Dirac delta function. Using the standard linear solid constitutive equation and the inverse Laplace transform, the analytical expressions of the deflection and rotation angle of the viscoelastic Timoshenko beam with an arbitrary number of open cracks are obtained in the time domain. By numerical examples, the bending results of the analytical expressions are verified with those of the FEM program. Additionally, the effects of the time, slenderness ratio, and crack depth on the bending deformations of the different cracked beam models are revealed.