Aspects of Two-Level Systems under External Time Dependent Fields

In this paper we discuss a master equation applied to the two level system of an atom and derive an exact solution to it in an abstract manner. We also present a problem and a conjecture based on the three level system. Our results may give a small hint to understand the huge transition from Quantum World to Classical World. To the best of our knowledge this is the finest method up to the present.

We introduce an analytical solution to the one of the most familiar problems from the elementary quantum mechanics textbooks. The following discussion provides simple illustrations to a number of general concepts of quantum chaology, along with some recent developments in the field and a historical perspective on the subject.

We give a technique for calculating the occupation number of quantum fields in time-dependent backgrounds by using the relation between one-dimensional {\em quantum} oscillators and two-dimensional {\em classical} oscillators. We illustrate our method by giving closed analytical results for the time-dependent spectrum of occupation numbers during gravitational collapse in 3+1 dimensions.

We investigate quantum mechanical Hamiltonians with explicit time dependence. We find a class of models in which an analogue of the time independent \S equation exists. Among the models in this class is a new exactly soluble model, the harmonic oscillator with frequency inversely proportional to time.

A general treatment of the quantal time-dependent coupled oscillators in presence of the variable magnetic field is presented. The treatment is based on the use of an alternative canonical transformations, time-dependent unitary transformations and the invariant methods. Exact wave functions for Schr\"{o}dinger equations of this system are constructed.We applied our theory to a particular case and, co,sequently, showed that our results recovers to the perviously known one.

The quantum dynamics of two-level systems under classical oscillator heat bath is mapped to the classical one of a charged particle under harmonic oscillator potential plus a magnetic field in a plane. The behavior of eigenstates and tunneling and localization are studied in detail. The broken symmetry condition and Langevin-like dissipative equation of motion are obtained. Some special dynamic features are considered.

For studying the dynamics of a two-level system coupled to a quantum oscillator we have presented an analytical approach, the transformed rotating-wave approximation, which takes into account the effect of the counter-rotating terms but still keeps the simple mathematical structure of the ordinary rotating-wave approximation. We have calculated the energy levels of ground and lower-lying excited states, as well as the time-dependent quantum dynamics. It is obvious that the ap...

We present a family of exact analytic solutions for non-linear quantum dynamics of a two-level system (TLS) subject to a periodic-in-time external field. In constructing the exactly solvable models, we use a "reverse engineering" approach where the form of external perturbation is chosen to preserve an integrability constraint, which yields a single non-linear differential equation for the ac-field. A solution to this equation is expressed in terms of Jacobi elliptic function...

The article provides a framework to solve linear differential equations based on partial commutativity which is introduced by means of the Fedorov theorem. The framework is applied to specific types of three-level and four-level quantum systems. The efficiency of the method is evaluated and discussed. The Fedorov theorem appears to answer the need for methods which allow to study dynamical maps corresponding with time-dependent generators. By applying this method, one can inv...

The non-Hermitian models, which are symmetric under parity (P) and time-reversal (T) operators, are the cornerstone for the fabrication of new ultra-sensitive optoelectronic devices. However, providing the gain in such systems usually demands precise contorol of nonlinear processes, limiting their application. In this paper, to bypass this obstacle, we introduce a class of time-dependent non-Hermitian Hamiltonians (not necessarily Floquet) that can describe a two-level system...