Related papers: Unitary Time Evolution and Vacuum for a Quantum St…
We present a simple class of mechanical models where a canonical degree of freedom interacts with another one with a negative kinetic term, i.e. with a ghost. We prove analytically that the classical motion of the system is completely…
Negative kinetic energies correspond to ghost degrees of freedom, which are potentially of relevance for cosmology, quantum gravity, and high energy physics. We present a novel wide class of stable mechanical systems where a positive energy…
The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the…
We discuss exactly solvable systems involving integrals of motion with higher powers of momenta. If one of these integrals is chosen for the Hamiltonian, we obtain a higher-derivative system involving ghosts, i.e. a system whose Hamiltonian…
We consider the simplest nontrivial supersymmetric quantum mechanical system involving higher derivatives. We unravel the existence of additional bosonic and fermionic integrals of motion forming a nontrivial algebra. This allows one to…
It is noted that the Schrodinger equation with any self-adjoint Hamiltonian is unitary equivalent to a set of non-interacting classical harmonic oscillators and in this sense any quantum dynamics is completely integrable. Higher order…
We find the conditions under which the spectrum of the unitary time evolution operator for a periodically rank-N kicked system remains pure point. This stability result allows one to analyse the onset of, or lack of chaos in this class of…
We consider the classical linear stability of a static universe filled with a non-interacting mixture of isotropic radiation and a ghost scalar field. Unlike the conventional Einstein static model, this cosmology is stable against…
Dynamical evolution of the quantum ground state (vacuum) is analyzed for time variant harmonic oscillators characterized by asymptotically constant frequency. The oscillatory density matrix in the asymptotic future is uniquely determined by…
The evolution problem for a quantum particle confined in a 1D box and interacting with one fixed point through a time dependent point interaction is considered. Under suitable assumptions of regularity for the time profile of the…
In this article, we formulate the study of the unitary time evolution of systems consisting of an infinite number of uncoupled time-dependent harmonic oscillators in mathematically rigorous terms. We base this analysis on the theory of a…
We consider the flavor evolution of a dense neutrino gas by taking into account both vacuum oscillations and self interactions of neutrinos. We examine the system from a many-body perspective as well as from the point of view of an…
We present a new understanding of the unstable ghost-like resonance which appears in theories such as quadratic gravity and Lee-Wick type theories. Quantum corrections make this resonance unstable, such that it does not appear in the…
Recently a Hamiltonian formulation for the evolution of the universe dominated by multiple oscillatory scalar fields was developed by the present author and was applied to the investigation of the evolution of cosmological perturbations on…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
We investigate the details of the canonical quantization of effective quantum field theories in anti-de Sitter spacetime, emphasizing the stability of the quantum vacuum. We take the scalar and Maxwell fields as examples. For the…
We quantise integrable point-particle systems with opposite-sign kinetic terms and nontrivial interactions. Using methods from separability theory, we show that previously determined classical stability conditions also imply discrete…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
We consider the quantum dynamics of a single particle in the plane under the influence of a constant perpendicular magnetic and a crossed electric potential field. For a class of smooth and small potentials we construct a non-trivial…
We study the unitary time evolution of a simple quantum Hamiltonian describing two harmonic oscillators coupled via a three-level system. The latter acts as an engine transferring energy from one oscillator to the other and is driven in a…