A Nonlinear Master Equation for Open Quantum Systems

A nonlinear master equation is derived, reflecting properly the entropy of open quantum systems. In contrast to linear alternatives, its equilibrium solution is exactly the canonical Gibbs density matrix. The corresponding nonlinear equation for the Wigner function accounts rigorously for the thermo-quantum entropy. It reduces at large friction to the quantum Smoluchowski equation in the coordinate subspace. The previously derived Maxwell–Heisenberg relation for the nonequilibrium momentum dispersion of quantum Brownian particles is confirmed as well as the related quantum generalization of the classical Einstein law of Brownian motion.

ANNIHILATION AND CREATION OPERATORS FOR THE CALDIROLA–KANAI HAMILTONIAN WITH COMPLEX FRICTION COEFFICIENT

In the present note, we consider the annihilation and creation operators with complex friction coefficient and we find the coherent, squeezed states, the uncertainty Heisenberg relation and the behavior of the PT and, CPT symmetries. Also we demonstrated that the (CK) Hamiltonian is a special case of the complex time-dependent mass.

GENERALIZED HEISENBERG RELATION AND QUANTUM HARMONIC OSCILLATORS

We study the consequences of the generalized Heisenberg uncertainty relation which admits a minimal uncertainty in length such as the case in a theory of quantum gravity. In particular, the theory of quantum harmonic oscillators arising from such a generalized uncertainty relation is examined. We demonstrate that all the standard properties of the quantum harmonic oscillators prevail when we employ a generalized momentum. We also show that quantum electrodynamics and coherent photon states can be described in the familiar standard manner despite the generalized uncertainty principle.

THE LIGHT SPEED AND THE INTERPLAY OF THE QUANTUM VACUUM, THE GRAVITATION OF ALL THE UNIVERSE AND THE FOURTH HEISENBERG RELATION

A recently proposed model which accounts for the observed time dependence of the fine structure constant is summarized. The model is based on the combined effect of the fourth Heisenberg relation and the gravitation of all the expanding universe on the quantum vacuum. As is shown here, it predicts that the light must have now an acceleration close to H0c≃6.9×10-10 m/s2. This suggests an explanation of the anomalous acceleration aP≃8.5×10-10 m/s2 found in the Pioneer 10 spacecraft, because an acceleration of light has the same radio observational signature as an acceleration of the ship.

CONNECTION BETWEEN Q-ALGEBRAS AND NONCANONICAL HEISENBERG ALGEBRAS

We stress the connection between [Formula: see text]-algebras and noncanonical Heisenberg algebras. We prove that the known Heisenberg–Weyl algebras for the deformed harmonic oscillators are partial cases of the Lie-admissible [Formula: see text]-algebras. We also point out the existence of a scale factor which plays an important role for the eigenvalue spectrum and for the generalized uncertainty Heisenberg relation. This factor has the form (Δx)(Δp) ≥ ℏ′/2 with ℏ′ = ℏκ and κ > 0.