Springer Science and Business Media LLC

The quantization of the scalar field is reconsidered in some of its basic elements in the context of the Robertson-Walker space-time. The integration of the generalized Klein-Gordon equation is performed by preliminary separation of the equation with the usual separation method. The orthonormal mode solutions are determined by the explicit integration of the resulting angular and radial equations and by standard properties of the time equation. The time evolution given by the standard cosmological model is briefly discussed.

We show that, under certain conditions, the micromaser can act as an effective source of highly correlated atoms. It is possible to create an extended robust entanglement between two successive, initially unentangled atoms passing through a cavity filled with a nonlinear medium taking into consideration a slight level shift. Information is transfered from the cavity to the atoms in order to build up entanglement. The scheme has an advantage over conventional creation of entanglement if the two atoms (qubits) are so far apart that a direct interaction is difficult to achieve. The interaction of the atoms with the micromaser occurs under the influence of a two-quantum transition process. Interesting phenomena are observed, and an extended robust entangled state is obtained for different values of the system parameters. Illustrative variational calculations are performed to demonstrate the effect within an analytically tractable two-qubit model.

The generalized correlated coherence is not stored locally, but does exist within the correlations between subsystems. We show that, in tripartite quantum systems, the generalized correlated coherence obeys the polygamy relation when the used coherence measure is strong subadditive. We further provide a sufficient condition, on which the generalized correlated coherence monogamy inequalities hold. These distribution results could just apply to the generalized correlated coherence, but not all quantum coherence.

In this paper, we study the stochastic local operation and classical communication (SLOCC) and local unitary (LU) equivalence for multi-qudit states by mode-n matricization of the coefficient tensors. We establish a new scheme of using the CANDECOMP/PARAFAC (CP) decomposition of tensors to find necessary and sufficient conditions between the mode-n unfolding and SLOCC&LU equivalence for pure multi-qudit states. For multipartite mixed states, we present a necessary and sufficient condition for LU equivalence and necessary condition for SLOCC equivalence.

The convergence of the Hamiltonians of classicalprojections to the Hamiltonian of the classical limit isinvestigated. The convergence of dynamics is shown forHamiltonians generated by a certain class of functions, in particular by functions fromthe Schwartz space.

A precise meaning is given to the idea of a kink theory approximating a vectoror vector-bundle-valued theory. It is shown that vector theories taking values in a vector bundle with groupSO(n- s,s;ℝ), acting naturally, do not approximate any kink theory. It is further shown that, where a kink theory is approximated by a vector bundle theory, the field equations in the vector theory can give rise to field equations in the kink theory. The theory of Skyrme and the sine-Gordon theory are of this form. An example is given of a nonlinear modification of electromagnetism having solitonlike solutions.

A structure of generator of a quantum dynamical semigroup for the dynamics of a test particle interacting through collisions with the environment is considered, which has been obtained from a microphysical model. The related master-equation is shown to go over to a Fokker–Planck equation for the description of Brownian motion at quantum level in the long wavelength limit. The structure of this Fokker–Planck equation is expressed in this paper in terms of superoperators, giving explicit expressions for the coefficient of diffusion in momentum in correspondence with two cases of interest for the interaction potential. This Fokker–Planck equation gives an example of a physically motivated generator of quantum dynamical semigroup, which serves as a starting point for the theory of measurement continuous in time, allowing for the introduction of trajectories in quantum mechanics. This theory has in fact already been applied to the problem of Brownian motion referring to similar phenomenological structures obtained only on the basis of mathematical requirements.

By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a generalized time-dependent Jaynes-Cummings model. It is found that the geometric phases in a cycle case have nothing to do with the frequency of the electromagnetic wave, the energy difference between two levels of the atom, and the coupling strength between the atom and the light field.

We elaborate an interpretation of quantum physics founded on the hypothesis that quantum particles are conceptual entities playing the role of communication vehicles between material entities composed of ordinary matter which function as memory structures for these quantum particles. We show in which way this new interpretation gives rise to a natural explanation for the quantum effects of interference and entanglement by analyzing how interference and entanglement emerge for the case of human concepts. We put forward a scheme to derive a metric based on similarity as a predecessor for the structure of ‘space, time, momentum, energy’ and ‘quantum particles interacting with ordinary matter’ underlying standard quantum physics, within the new interpretation, and making use of aspects of traditional quantum axiomatics. More specifically, we analyze how the effect of non-locality arises as a consequence of the confrontation of such an emerging metric type of structure and the remaining presence of the basic conceptual structure on the fundamental level, with the potential of being revealed in specific situations.