Related papers: Singularity in classical and quantum Kepler Proble…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
Globally-constrained classical fields provide a unexplored framework for modeling quantum phenomena, including apparent particle-like behavior. By allowing controllable constraints on unknown past fields, these models are retrocausal but…
We review here the recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations. The concept is introduced in successive steps through the studies of mapping of…
A modification of the spiked harmonic oscillator is studied in the case for which the perturbation potential contains both an inverse power and a linear term. It is then possible to evaluate trial functions by solving an integral equation…
Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. Using both the Hilbert space (Koopman) and the phase-space (Moyal) formalisms we investigate how robust this classicality is. We find…
We present a detailed numerical study of a chaotic classical system and its quantum counterpart. The system is a special case of a kicked rotor and for certain parameter values possesses cantori dividing chaotic regions of the classical…
A precise physical description and understanding of the classical dual content of quantum theory is necessary in many disciplines today: from concepts and interpretation to quantum technologies and computation. In this paper we investigate…
We continue our investigation of an improved quantization scheme for spherically symmetric loop quantum gravity. We find that in the region where the black hole singularity appears in the classical theory, the quantum theory contains…
A definition of quantum singularity for the case of static spacetimes has recently been extended to conformally static spacetimes. Here the theory behind quantum singularities in conformally static spacetimes is reviewed, and then applied…
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution…
Classical linear wave superposition produces the appearance of interference. This observation can be interpreted in two equivalent ways: one can assume that interference is an illusion because input components remain unperturbed, or that…
The quantum-mechanical collapse (alias fall onto the center of particles attracted by potential -1/r^2), or "quantum anomaly", is a well-known issue in the quantum theory. We demonstrate that the mean-field repulsive nonlinearity prevents…
The earlier suggested criterion of quantum chaoticity, borrowed from the nuclear compound resonance theory, is used in the analysis of the quantum diamagnetic Kepler problem (the spinless charged particle motion in the Coulomb and…
We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop--tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the…
We demonstrated that classical mechanics have, besides the well known quantum deformation, another deformation -- so called hyperbolic quantum mechanics. The classical Poisson bracket can be obtained as the limit $h\to 0$ not only of the…
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…
We present a novel form of relativistic quantum mechanics and demonstrate how to solve it using a recently derived unitary perturbation theory, within partial wave analysis. The theory is tested on a relativistic problem, with two spinless,…
The purpose of this work is to investigate the consequences of quantum gravity for the singularity problem. We study the higher-derivative terms that invariably appear in any quantum field theoretical model of gravity, handling them both…
Energy-parity has been introduced by Kaplan and Sundrum as a protective symmetry that suppresses matter contributions to the cosmological constant [KS05]. It is shown here that this symmetry, schematically Energy --> - Energy, arises in the…
Quantum decoherence refers to the phenomenon when the interaction of a quantum system with its environment results in the degradation of quantum coherence. Decoherence is considered to be the most popular mechanism responsible for the…