On the Casimir energy for a massive quantum scalar field and the Cosmological constant

We present a rigorous, regularization independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass $\mu\ne0$ which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field at fixed cosmic time, in which the expectation value of the renormalized energy-momentum tensor is independent of the space coordinate and is of the perfect fluid form $g_{\mu,\nu}\rho_{vac}$ with $\rho_{vac}>0$, thus providing a quantum field theoretic foundation of the Cosmological constant. Using some values of $\mu$ suggested in the literature for the hypothetical axion particle, there results a model for dark energy which is consistent with past and future evolution and is also in good agreement with experimental data.Comment: 15 pages, 2 figures, conceptually improved version, to appear in Ann. Phy

Aspects of Two-Level Systems under External Time Dependent Fields

The dynamics of two-level systems in time-dependent backgrounds is under consideration. We present some new exact solutions in special backgrounds decaying in time. On the other hand, following ideas of Feynman, Vernon and Hellwarth, we discuss in detail the possibility to reduce the quantum dynamics to a classical Hamiltonian system. This, in particular, opens the possibility to directly apply powerful methods of classical mechanics (e.g. KAM methods) to study the quantum system. Following such an approach, we draw conclusions of relevance for ``quantum chaos'' when the external background is periodic or quasi-periodic in time.Comment: To appear in J. Phys. A. Mathematical and Genera

Existence of the Bogoliubov S(g) operator for the (:ϕ4:)2(:\phi^4:)_2 quantum field theory

We prove the existence of the Bogoliubov S(g) operator for the $(:\phi^4:)_2$ quantum field theory for coupling functions $g$ of compact support in space and time. The construction is nonperturbative and relies on a theorem of Kisy\'nski. It implies almost automatically the properties of unitarity and causality for disjoint supports in the time variable.Comment: LaTeX, 24 pages, minor modifications, typos correcte

Converging Perturbative Solutions of the Schroedinger Equation for a Two-Level System with a Hamiltonian Depending Periodically on Time

We study the Schroedinger equation of a class of two-level systems under the action of a periodic time-dependent external field in the situation where the energy difference 2epsilon between the free energy levels is sufficiently small with respect to the strength of the external interaction. Under suitable conditions we show that this equation has a solution in terms of converging power series expansions in epsilon. In contrast to other expansion methods, like in the Dyson expansion, the method we present is not plagued by the presence of ``secular terms''. Due to this feature we were able to prove absolute and uniform convergence of the Fourier series involved in the computation of the wave functions and to prove absolute convergence of the epsilon-expansions leading to the ``secular frequency'' and to the coefficients of the Fourier expansion of the wave function

Quantum NOT operation and integrability in two-level systems

Abstract We demonstrate the surprising integrability of the classical Hamiltonian associated to a spin 1/2 system under periodic external fields. The one-qubit rotations generated by the dynamical evolution is, on the one hand, close to that of the rotating wave approximation (RWA), on the other hand to two different ''average'' systems, according to whether a certain parameter is small or large. Of particular independent interest is the fact that both the RWA and the averaging theorem are seen to hold well beyond their expected region of validity. Finally, we determine conditions for the realization of the quantum NOT operation by means of classical stroboscopic maps