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This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general…
The environment surrounding a quantum system can, in effect, monitor some of the systems observables. As a result, the eigenstates of these observables continuously decohere and can behave like classical states.
We discuss spacetime instability for effective field theories of quantum gravity. The effective action of gravity introduces infinite higher derivative curvature terms $R^{2}, { R }_{ \mu \nu }{ R }^{ \mu \nu }, R_{\mu\nu\kappa\lambda}…
The fact that we rarely directly observe much quantum uncertainty is often attributed to decoherence. However, decoherence does not reduce the quantum uncertainty in the full quantum state. Whether or not it reduces the quantum…
We present here a set of lecture notes on quantum systems with time-dependent boundaries. In particular, we analyze the dynamics of a non-relativistic particle in a bounded domain of physical space, when the boundaries are moving or…
Oscillons are long-lived, spherically symmetric solitons that can arise in real scalar field theories with potentials shallower than quadratic ones. They are considered to form via parametric resonance during the preheating stage after…
A cosmology inspired structure for phase space is introduced, which leads to finitization and lattice-like discretization of position and momentum eigenvalues in a preferred, cosmic frame. Lorentz invariance is broken at very high energies,…
We prove spatial decay estimates on disorder-averaged position-momentum correlations in a gapless class of random oscillator models. First, we prove a decay estimate on dynamic correlations for general eigenstates with a bound that depends…
We study some aspects of the quantum theory of a charged particle moving in a time-independent, uni-directional magnetic field. When the field is uniform, we make a few clarifying remarks on the use of angular momentum eigenstates and…
We treat the effects of quantum field fluctuations on the decay of a meta-stable state of a self-coupled scalar field. We consider two varieties of field fluctuations and their potential effects in a semiclassical description. The first are…
We study a number of different ingredients related to the $\theta$ dependence, metastable excited vacuum states and other related subjects using a simplified version of QCD, the so-called "deformed QCD". This model is a weakly coupled gauge…
This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…
It is shown that quantum uncertainty of motion in systems controlled mainly by gravity generally grows with orbital timescale $H^{-1}$, and dominates classical motion for trajectories separated by distances less than $\approx H^{-3/5}$ in…
We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg's principle and by Einstein's theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation…
This paper summarises a numerical investigation of how the usual manifestations of chaos and regularity for flows in time-independent Hamiltonians can be alterred by a systematic time-dependence of the form arising naturally in an expanding…
There are several results on the stability of nonlinear positive systems in the presence of time delays. However, most of them assume that the delays are constant. This paper considers time-varying, possibly unbounded, delays and…
The dynamic of correlations in a system composed of a two-mode quantum field coupled with the environment is studied. The quantum field corresponds to two entangled coherent states whose amplitude we vary up to the mesoscopic regime. We…
Recently we have introduced a lightweight, perturbative approach to quantum solitons. Thus far, our approach has been largely limited to configurations consisting of a single soliton plus a finite number of mesons, whose classical limit is…
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…
Quantum fields with large degeneracy are often approximated as classical fields. Here, we show how quantum and classical evolution of a highly degenerate quantum field with repulsive contact self-interactions differ from each other.…