The exact fermionic four-level system is studied in the presence of time-dependent magnetic field. The system is considered under two initial conditions: general initial vector state, and, at thermal equilibrium. The exact time evolution of one-particle operators is derived.
The case of a quantum two-level system coupled to a time variable magnetic field is investigated. The Schrodinger equation pertaining to the system is reduced to a second order linear equation in time and its solutions are sought by an integrating factor technique. A differential equation for the integrating factor and, therefrom, a criterion for fields leading to exact solutions are derived. The formalism is capable of giving a wide variety of closed form radio frequency (RF) wave forms for which Schrodinger's equation is exactly solvable.
We investigate the evolution of the atomic quantum entropy and the atom-field entanglement in a system of a Ξ-configuration three-level atom interacting with a single-mode field with additional forms of nonlinearities of both the field and the intensity-dependent atom-field coupling. With the derivation of the unitary operator within the frame of the dressed state and the exact results for the state of the system, we perform a careful investigation of the temporal evolution of the entropy. A factorization of the initial density operator is assumed, considering the field to be initially in a squeezed coherent or binomial state. The effects of the mean photon number, detuning, Kerr-like medium and the intensity-dependent coupling functional on the entropy are analyzed.
Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional subdynamics. Each of the subdynamics is shown to be brought into an exactly solvable form by appropriately engineering the magnetic fields and thus we obtain an exact time evolution of the compound system. Several physically relevant and interesting quantities are evaluated exactly to disclose intriguing phenomena in such a system.
We investigate the evolution of the atomic quantum entropy and the atom–field entanglement in a system of a Λ-configuration three-level atom interacting with a single-mode field with additional forms of nonlinearities of both the field and the intensity-dependent atom–field coupling. With the derivation of the unitary operator within the frame of the dressed state and the exact results for the state of the system, we perform a careful investigation of the temporal evolution of the entropy. A factorization of the initial density operator is assumed, considering the field to be initially in a squeezed coherent or binomial state. The effects of the mean photon number, detuning, Kerr-like medium, and the intensity-dependent coupling functional on the entropy are analyzed.
An exact solution of the Liouville equation for the XY model with time-dependent external magnetic fields is obtained. Standard transformations allow a decomposition of the space of states into a direct product of four-dimensional subspaces. The Liouville equation is reduced to a set of coupled differential equations in each subspace. These equations have been explicitly solved for several cases.