Related papers: Eigenvalues of the volume operator in loop quantum…
We describe a method for the calculation of accurate energy eigenvalues and expectation values of observables of separable quantum-mechanical models. We discuss the application of the approach to one-dimensional anharmonic oscillators with…
We compute some components of the graviton propagator in loop quantum gravity, using the spinfoam formalism, up to some second order terms in the expansion parameter.
We study the role of composite operators in the Asymptotic Safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources we are able to keep track of operators which do not belong to…
Several eigenvalue equations that could describe quantum black holes have been proposed in the canonical quantum gravity approach. In this paper, we choose one of the simplest of these quantum equations to show how the usual Feynman's path…
The eigenfunctions and eigenvalues of orbital angular momentum operator on noncommutative lattice for a circle poset by theta-quantization are constructed, and it is demonstrated that they are equivalent to those of the conventional quantum…
Quantum estimation of the operators of a system is investigated by analyzing its Liouville space of operators. In this way it is possible to easily derive some general characterization for the sets of observables (i.e. the possible quorums)…
In a quantum theory of gravity the gravitational Wilson loop, defined as a suitable quantum average of a parallel transport operator around a large near-planar loop, provides important information about the large-scale curvature properties…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
The volume of the quantum mechanical state space over $n$-dimensional real, complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean measure is computed, and explicit formulas are presented for the expected value of…
We introduce a new operator representing the three-dimensional scalar curvature in loop quantum gravity. The operator is constructed by writing the Ricci scalar classically as a function of the Ashtekar variables and regularizing the…
Polymer quantization is a non-standard representation of the quantum mechanics that inspired by loop quantum gravity. To study the associated statistical mechanics, one needs to find microstates' energies which are eigenvalues of the…
This work is devoted to the asymptotic behavior of eigenvalues of an elliptic operator with rapidly oscillating random coefficients on a bounded domain with Dirichlet boundary conditions. A sharp convergence rate is obtained for isolated…
We present an efficient method for estimating the eigenvalues of a Hamiltonian $H$ from the expectation values of the evolution operator for various times. For a given quantum state $\rho$, our method outputs a list of eigenvalue estimates…
Quantum polyhedra constructed from angular momentum operators are the building blocks of space in its quantum description as advocated by Loop Quantum Gravity. Here we extend previous results on the semiclassical properties of quantum…
We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level…
We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization the model and…
An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after…
In this paper we consider eigenvalues asymptotics of the energy operator in the one of the most interesting models of quantum physics, describing an interaction between two-level system and harmonic oscillator. The energy operator of this…
We construct the operator that projects on the physical states in loop quantum gravity. To this aim, we consider a diffeomorphism invariant functional integral over scalar functions. The construction defines a covariant, Feynman-like,…
We analytically calculate the average value of i-th largest Schmidt coefficient for random pure quantum states. Schmidt coefficients, i.e., eigenvalues of the reduced density matrix, are expressed in the limit of large Hilbert space size…