Exact solution of the Heisenberg equation of motion for the surface spin in a semi-infiniteS=1/2XYchain at infinite temperatures

1991 ◽  
Vol 44 (14) ◽  
pp. 7444-7450 ◽  
Author(s):  
Surajit Sen
Keyword(s):  
Exact Solution ◽  
Equation Of Motion ◽  
Heisenberg Equation ◽  
Surface Spin

WEHRL ENTROPY AND ENTANGLEMENT OF A TIME-DEPENDENT TWO-LEVEL TRAPPED ION INTERACTING WITH A LASER FIELD

2008 ◽  
Vol 06 (02) ◽  
pp. 331-339
Author(s):  
MAHMOUD ABDEL-ATY ◽  
SAYED ABDEL-KHALEK ◽  
ABDEL-SHAFY F. OBADA
Keyword(s):  
Exact Solution ◽  
Time Evolution ◽  
Laser Field ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Heisenberg Equation ◽  
Wehrl Entropy ◽  
Entanglement Generation ◽  
Trapped Ion ◽  
Cat States

The time evolution of the atomic Wehrl entropy and long-lived entanglement generation using a single trapped ion interacting with a laser field are analyzed. Starting from the Heisenberg equation of motion, an exact solution of the system is obtained by indicating that there are some interesting features when a time-dependent modulating function is considered. We demonstrate that the long-living quantum entanglement can be obtained using the time-independent interaction when the field is initially in a pair cat states.

A series exact solution for one-dimensional non-linear particle equation of motion

2011 ◽  
Vol 207 (1-3) ◽  
pp. 461-464 ◽  
Author(s):  
M. Jalaal ◽  
H. Bararnia ◽  
G. Domairry
Keyword(s):  
Exact Solution ◽  
Equation Of Motion ◽  
One Dimensional ◽  
Non Linear

Wigner Representation for Investigation of Entangled Photon Evolution in Four-Wave Mixing Process within a Fiber Ring Resonator

2015 ◽  
Vol 804 ◽  
pp. 316-320
Author(s):  
Chatchawal Sripakdee
Keyword(s):  
Ring Resonator ◽  
Equations Of Motion ◽  
Numerical Approach ◽  
Equation Of Motion ◽  
Nonlinear Susceptibility ◽  
Heisenberg Equation ◽  
Fiber Ring ◽  
Wigner Representation ◽  
Fiber Ring Resonator ◽  
Photon States

The aim of this study is to analyze the quantum correlation of entangled photons for four-wavemixing process within Kerr nonlinear susceptibility χ(3) of an optical fiber ring resonator. The main system Hamiltonian composes of two types of coupling photon modes, including pumping and parametric-down conversion. Wigner representation is applied to the Heisenberg equation of motion derived from the system Hamiltonian in order to obtain the corresponding stochastic equations of motion in a c-number. Quantum trajectories obtained from the stochastic equation of motion of photon states are then derived. Finally, the entanglement inseparability criteria for a pair of entangled photonfrom a numerical approach is also satisfied.

scholarly journals QUANTUM KALB–RAMOND FIELD IN D-DIMENSIONAL DE SITTER SPACE–TIMES

2013 ◽  
Vol 28 (05n06) ◽  
pp. 1350011
Author(s):  
G. ALENCAR ◽  
I. GUEDES ◽  
R. R. LANDIM ◽  
R. N. COSTA FILHO
Keyword(s):  
Exact Solution ◽  
Wave Function ◽  
Quantum Theory ◽  
De Sitter Space ◽  
Equation Of Motion ◽  
Time Dependent ◽  
De Sitter ◽  
Sitter Background ◽  
Dynamic Invariant ◽  
Math Phys

In this work, we investigate the quantum theory of the Kalb–Ramond fields propagating in D-dimensional de Sitter space–times using the dynamic invariant method developed by Lewis and Riesenfeld [J. Math. Phys.10, 1458 (1969)] to obtain the solution of the time-dependent Schrödinger equation. The wave function is written in terms of a c-number quantity satisfying the Milne–Pinney equation, whose solution can be expressed in terms of two independent solutions of the respective equation of motion. We obtain the exact solution for the quantum Kalb–Ramond field in the de Sitter background and discuss its relation with the Cremmer–Scherk–Kalb–Ramond model.

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