On a Dynamical Treatment of a Quantum

Edward B. Manoukian, S. Sukkhasena

A functional differential treatment, via the quantum dynamical prin-ciple, is given for the coupling of quantum systems to the environment. As one is involved in taking the trace over the dynamical variables of the environment, the analysis necessarily deals with transition probabilities rather than with amplitudes. It is shown that the functional differential treatment is quite suitable for such a study as it involves in carrying out functional differentiations, with respect to classical sources, on func-tionals describing decoupled physical systems from the environment.

Włodzimierz M. Tulczyjew

Yue‐Xun Huang, Ming Li, Zi-Jie Chen +4 more

Abstract Mean‐field treatment (MFT) is frequently applied to approximately predict the dynamics of quantum optics systems. It simplifies the system Hamiltonian by neglecting the quantum statistics of certain modes that are driven strongly by lasers or couple weakly with other modes. However, the neglected quantum correlations between different modes result in unanticipated quantum effects and might lead to significantly distinct system dynamics. Here, a general and systematic theoretical framework based on perturbation theory in company with MFT is provided to capture these quantum effects. The form of nonlinear dissipation and parasitic Hamiltonian as well as their relationship to the nonlinear coupling rate are predicted. Furthermore, the indicator is also proposed as a measure of the accuracy of mean‐field treatment. As an example, this theory is applied to quantum frequency conversion, in which mean‐field treatment is commonly applied, to test its limitation under strong pump and large coupling strength. The analytical results show excellent agreement with the numerical simulations. This work clearly reveals the residual quantum effects neglected by MFT and provides a more precise theoretical framework for nonlinear optics and quantum optics.

Benno Fuchssteiner

Ronald J. Adler, David Santiago

Chen, C. Y.

The textbook treatment in that the wave function of a dynamical system is expanded in an eigenfunction series is investigated. With help of an elementary example and some mathematical theorems, it is revealed that in terms of solving the time-dependent Schrödinger equation the treatment involves in divergence trouble . The root reason behind the trouble is finally analyzed.