Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology

The detailed formulation for loop quantum cosmology (LQC) in the Bianchi I model with a scalar massless field has been constructed. In this paper, its effective dynamics is studied in two improved strategies for implementing the LQC discreteness corrections. Both schemes show that the big bang is replaced by the big bounces, which take place up to three times, once in each diagonal direction, when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. These two strategies give different evolutions: In one scheme, the effective dynamics is independent of the choice of the finite sized cell prescribed to make Hamiltonian finite; in the other, the effective dynamics reacts to the macroscopic scales introduced by the boundary conditions. Both schemes reveal interesting symmetries of scaling, which are reminiscent of the relational interpretation of quantum mechanics and also suggest that the fundamental spatial scale (area gap) may give rise to a temporal scale.Comment: 19 pages, 6 figures, 1 table; one reference added; version to appear in PR

Local stiffener and skin pocket buckling prediction by special PASCO modeling technique: Correlation to test data

Waffle panels are often used on fuselage structures such as that of the Space Shuttle. The waffle panel design is an efficient design for carrying biaxial, in-plane, and shear loads. The WAFFLE program was designed for application on waffle panels. The Panel Analysis and Sizing Code (PASCO) program was designed for analyzing and sizing uniaxially stiffened panels. The application of the PASCO program in conjunction with the WAFFLE program is discussed to account for both the fillet radius and the presence of stiffness in both directions. The results of the tests are used to verify that these adjustments are valid and necessary if accurate analysis of the waffle panel is to be achieved

Cosmological inflation driven by holonomy corrections of loop quantum cosmology

At the level of heuristic effective dynamics, we investigate the cosmological inflation with holonomy corrections of loop quantum cosmology (LQC) in the $k=0$ Friedmann-Robertson-Walker model with a single inflaton field subject to a simple potential. In the symmetric bouncing scenario of LQC, the condition for occurrence of the quantum bounce naturally and uniquely fixes the initial conditions at the bouncing epoch. Around the quantum bounce, the universe undergoes a short super-inflationary phase, which drives the inflaton field to its potential hill and thus sets the proper initial conditions for the standard slow-roll inflation. Between the super-inflation and the standard inflation, there is a non-inflationary phase, which violates the slow-roll condition. The violation of slow roll is expected to give some suppression on the low angular power spectrum of the cosmic microwave background and different orders of holonomy corrections shall yield different suppressions.Comment: 7 pages, 2 figures, 1 table; one reference added

Phenomenological loop quantum geometry of the Schwarzschild black hole

The interior of a Schwarzschild black hole is investigated at the level of phenomenological dynamics with the discreteness corrections of loop quantum geometry implemented in two different improved quantization schemes. In one scheme, the classical black hole singularity is resolved by the quantum bounce, which bridges the black hole interior with a white hole interior. In the other scheme, the classical singularity is resolved and the event horizon is also diffused by the quantum bounce. Jumping over the quantum bounce, the black hole gives birth to a baby black hole with a much smaller mass. This lineage continues as each classical black hole brings forth its own descendant in the consecutive classical cycle, giving the whole extended spacetime fractal structure, until the solution eventually descends into deep Planck regime, signaling a breakdown of the semiclassical description. The issues of scaling symmetry and no-hair theorem are also discussed.Comment: 26 pages, 6 figures, 1 table; version to appear in PR

Loop Quantum Cosmology in Bianchi Type I Models: Analytical Investigation

The comprehensive formulation for loop quantum cosmology in the spatially flat, isotropic model was recently constructed. In this paper, the methods are extended to the anisotropic Bianchi I cosmology. Both the precursor and the improved strategies are applied and the expected results are established: (i) the scalar field again serves as an internal clock and is treated as emergent time; (ii) the total Hamiltonian constraint is derived by imposing the fundamental discreteness and gives the evolution as a difference equation; and (iii) the physical Hilbert space, Dirac observables and semi-classical states are constructed rigorously. It is also shown that the state in the kinematical Hilbert space associated with the classical singularity is decoupled in the difference evolution equation, indicating that the big bounce may take place when any of the area scales undergoes the vanishing behavior. The investigation affirms the robustness of the framework used in the isotropic model by enlarging its domain of validity and provides foundations to conduct the detailed numerical analysis.Comment: 53 pages, 2 figures; more typos corrected; HyperTeX enable

Foldy-Wouthuysen transformation for a Dirac-Pauli dyon and the Thomas-Bargmann-Michel-Telegdi equation

The classical dynamics for a charged point particle with intrinsic spin is governed by a relativistic Hamiltonian for the orbital motion and by the Thomas-Bargmann-Michel-Telegdi equation for the precession of the spin. It is natural to ask whether the classical Hamiltonian (with both the orbital and spin parts) is consistent with that in the relativistic quantum theory for a spin-1/2 charged particle, which is described by the Dirac equation. In the low-energy limit, up to terms of the 7th order in $1/E_g$ ($E_g=2mc^2$ and $m$ is the particle mass), we investigate the Foldy-Wouthuysen (FW) transformation of the Dirac Hamiltonian in the presence of homogeneous and static electromagnetic fields and show that it is indeed in agreement with the classical Hamiltonian with the gyromagnetic ratio being equal to 2. Through electromagnetic duality, this result can be generalized for a spin-1/2 dyon, which has both electric and magnetic charges and thus possesses both intrinsic electric and magnetic dipole moments. Furthermore, the relativistic quantum theory for a spin-1/2 dyon with arbitrary values of the gyromagnetic and gyroelectric ratios can be described by the Dirac-Pauli equation, which is the Dirac equation with augmentation for the anomalous electric and anomalous magnetic dipole moments. The FW transformation of the Dirac-Pauli Hamiltonian is shown, up to the 7th order again, to be also in accord with the classical Hamiltonian.Comment: 18 page

CEO Compensation And Firm Value

This paper examines the effect of CEO equity-based compensation (EBC) on firm value. In particular, we study the interaction between EBC and the percentage of independent directors as well as the interaction between EBC and managerial entrenchment. Our findings suggest a positive relation between firms’ value and EBC. Further, we show that the percentage of independent directors has a positive impact on the marginal effect of EBC on firm value

Quantum Mechanical Search and Harmonic Perturbation

Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some important technology advances, such as masers, lasers, nuclear magnetic resonance, etc., originated from it. Here we add quantum computation to this list with a theoretical demonstration. Based on harmonic perturbation, a quantum mechanical algorithm is devised to search the ground state of a given Hamiltonian. The intrinsic complexity of the algorithm is continuous and parametric in both time T and energy E. More precisely, the probability of locating a search target of a Hamiltonian in N-dimensional vector space is shown to be 1/(1+ c N E^{-2} T^{-2}) for some constant c. This result is optimal. As harmonic perturbation provides a different computation mechanism, the algorithm may suggest new directions in realizing quantum computers.Comment: 6 pages, 4 figures, revtex

Unimodular Loop Quantum Cosmology

Unimodular gravity is based on a modification of the usual Einstein-Hilbert action that allows one to recover general relativity with a dynamical cosmological constant. It also has the interesting property of providing, as the momentum conjugate to the cosmological constant, an emergent clock variable. In this paper we investigate the cosmological reduction of unimodular gravity, and its quantization within the framework of flat homogeneous and isotropic loop quantum cosmology. It is shown that the unimodular clock can be used to construct the physical state space, and that the fundamental features of the previous models featuring scalar field clocks are reproduced. In particular, the classical singularity is replaced by a quantum bounce, which takes place in the same condition as obtained previously. We also find that requirement of semi-classicality demands the expectation value of the cosmological constant to be small (in Planck units). The relation to spin foam models is also studied, and we show that the use of the unimodular time variable leads to a unique vertex expansion.Comment: 26 pages. Revised version taking into account referee's comment