Related papers: Numerical Techniques in Loop Quantum Cosmology
We show that the standard Hamiltonian of isotropic loop quantum cosmology is selected by physical criteria plus one choice: that it have a `minimal' number of terms. We also show the freedom, and boundedness of energy density, even when…
Harmonic slicing has in recent years become a standard way of prescribing the lapse function in numerical simulations of general relativity. However, as was first noticed by Alcubierre (1997), numerical solutions generated using this…
In this article we review the foundations and the present status of loop quantum gravity. It is short and relatively non-technical, the emphasis is on the ideas, and the flavor of the techniques. In particular, we describe the kinematical…
In contrast to previous work in the field, we construct the Loop Quantum Cosmology (LQC) of the flat isotropic model with a massless scalar field in the absence of higher order curvature corrections to the gravitational part of the…
Cosmology is in an era of rapid discovery especially in areas related to dark energy, dark matter and inflation. Quantum cosmology treats the cosmology quantum mechanically and is important when quantum effects need to be accounted for,…
In this article, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: Firstly, we…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique…
Holonomy corrections to scalar perturbations are investigated in the loop quantum cosmology framework. Due to the effective approach, modifications of the algebra of constraints generically lead to anomalies. In order to remove those…
Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both on the gravitational and matter sectors…
The scheme of using the Chern-Simons action to regularize the gravitational Hamiltonian constraint is extended to including the Lorentzian term in the $k=0$ cosmological model. The Euclidean term and the Lorenzian term are thus regularized…
Robust control design for quantum systems has been recognized as a key task in the development of practical quantum technology. In this paper, we present a systematic numerical methodology of sampling-based learning control (SLC) for…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…
Advances in our understanding of the origin, evolution and structure of the universe have long been driven by cosmological perturbation theory, model building and effective field theory. In this review, we introduce numerical relativity as…
We previously established that in principle, it is possible to quantum compute using passive linear optics with photo-detectors (quant-ph/0006088). Here we describe techniques based on error detection and correction that greatly improve the…
We consider a k=0 Friedman-Robertson-Walker (FRW) model within loop quantum cosmology (LQC) and explore the issue of its semiclassical limit. The model is exactly solvable and allows us to construct analytical (Gaussian) coherent-state…
We study stability conditions of the full Hamiltonian constraint equation describing the quantum dynamics of the diagonal Bianchi I model in the context of LQC. Our analysis has shown robust evidence of an instability in the explicit…
In Loop Quantum Cosmology, the quantization of the Hamiltonian constraint involves a regularization procedure which is affected by certain ambiguities. Moreover, different regularizations lead to distinct mathematical formulations and,…
Effective equations often provide powerful tools to develop a systematic understanding of detailed properties of a quantum system. This is especially helpful in quantum cosmology where several conceptual and technical difficulties…
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo…