scholarly journals Theory of Many-Fermion System on Unitary-Transformation Method

1988 ◽  
Vol 79 (5) ◽  
pp. 1249-1249 ◽  
Author(s):  
K. Suzuki
Keyword(s):  
Unitary Transformation ◽  
Transformation Method ◽  
Fermion System

UNITARY TRANSFORMATION APPROACH FOR THE PHASE OF THE DAMPED DRIVEN HARMONIC OSCILLATOR

2003 ◽  
Vol 17 (26) ◽  
pp. 1365-1376 ◽  
Author(s):  
JEONG-RYEOL CHOI
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Unitary Transformation ◽  
Operator Method ◽  
Classical Equation ◽  
Transformation Method ◽  
Invariant Operator ◽  
Harmonic Oscillators ◽  
Parabolic Cylinder ◽  
Parabolic Cylinder Function

Using the invariant operator method and the unitary transformation method together, we obtained discrete and continuous solutions of the quantum damped driven harmonic oscillator. The wave function of the underdamped harmonic oscillator is expressed in terms of the Hermite polynomial while that of the overdamped harmonic oscillator is expressed in terms of the parabolic cylinder function. The eigenvalues of the underdamped harmonic oscillator are discrete while that of the critically damped and the overdamped harmonic oscillators are continuous. We derived the exact phases of the wave function for the underdamped, critically damped and overdamped driven harmonic oscillator. They are described in terms of the particular solutions of the classical equation of motion.

Intensity-dependent and multi-photon Hamiltonian of two two-level atoms and two-mode field in a Kerr medium solved by virtue of supersymmetric unitary transformation

2021 ◽  
pp. 2150060
Author(s):  
N. H. Abd El-Wahab ◽  
R. A. Zait
Keyword(s):  
Unitary Transformation ◽  
Atomic System ◽  
Quantum Effects ◽  
Transformation Method ◽  
Kerr Medium ◽  
Atomic Systems ◽  
Mode Field ◽  
Q Function ◽  
Supersymmetric Structure ◽  
Intensity Dependent Coupling

We consider a generalized multi-photon interaction of two collectively two-level atoms with two-mode of electromagnetic field in the presence of Kerr medium and intensity-dependent coupling. We show that this atomic system possesses supersymmetric structure. We solved this system by virtue of supersymmetric unitary transformation. The supersymmetric generators of this atomic system are constructed. The diagonalization of the corresponding Hamiltonian is performed by introducing a supersymmetric unitary transformation. Accordingly, the eigenvalues and eigenfunctions of the Hamiltonian of the atomic system are obtained. The time evolution of the atom–field wave functions is derived in an exact form for two cases of the initial states of the atoms and the field modes. Some quantum effects such as the second-order correlation function, cross-correlation, purity and Husimi Q-function are investigated. The effects of the Kerr medium, detuning parameter, intensity-dependent coupling and multi-photon transition on the evolution of these quantum effects are examined. We conclude that the supersymmetric unitary transformation method is very simple and can be applied to a variety of atomic systems which possess a supersymmetric structure.

scholarly journals Time-Dependent Unitary Transformation Method in the Strong-Field-Ionization Regime with the Kramers-Henneberger Picture

2021 ◽  
Vol 22 (16) ◽  
pp. 8514
Author(s):  
Je-Hoi Mun ◽  
Hirofumi Sakai ◽  
Dong-Eon Kim
Keyword(s):  
Unitary Transformation ◽  
Strong Field ◽  
Three Dimensional ◽  
Transformation Method ◽  
Time Dependent ◽  
Moving Frame ◽  
Evolution Operators ◽  
Step Size ◽  
One Dimensional ◽  
Strong Field Ionization

Time evolution operators of a strongly ionizing medium are calculated by a time-dependent unitary transformation (TDUT) method. The TDUT method has been employed in a quantum mechanical system composed of discrete states. This method is especially helpful for solving molecular rotational dynamics in quasi-adiabatic regimes because the strict unitary nature of the propagation operator allows us to set the temporal step size to large; a tight limitation on the temporal step size (δt<<1) can be circumvented by the strict unitary nature. On the other hand, in a strongly ionizing system where the Hamiltonian is not Hermitian, the same approach cannot be directly applied because it is demanding to define a set of field-dressed eigenstates. In this study, the TDUT method was applied to the ionizing regime using the Kramers-Henneberger frame, in which the strong-field-dressed discrete eigenstates are given by the field-free discrete eigenstates in a moving frame. Although the present work verifies the method for a one-dimensional atom as a prototype, the method can be applied to three-dimensional atoms, and molecules exposed to strong laser fields.

Sign in / Sign up

Export Citation Format

Share Document