Quantum mechanical reaction probabilities via a discrete variable representation‐absorbing boundary condition Green’s function

1992 ◽  
Vol 97 (4) ◽  
pp. 2499-2514 ◽  
Author(s):  
Tamar Seideman ◽  
William H. Miller
Keyword(s):  
Boundary Condition ◽  
Green’S Function ◽  
Green's Function ◽  
Absorbing Boundary Condition ◽  
Quantum Mechanical ◽  
Discrete Variable ◽  
Discrete Variable Representation ◽  
Absorbing Boundary ◽  
Variable Representation

TIME-DEPENDENT QUANTUM MECHANICAL TREATMENT OF He–CO INELASTIC SCATTERING

2004 ◽  
Vol 03 (03) ◽  
pp. 291-303 ◽  
Author(s):  
SINAN AKPINAR ◽  
NIYAZI BULUT ◽  
FAHRETTIN GOGTAS
Keyword(s):  
Wave Packet ◽  
Mechanical Treatment ◽  
Total Angular Momentum ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Discrete Variable ◽  
Discrete Variable Representation ◽  
Quantum Mechanical Treatment ◽  
Quantum Wave ◽  
Variable Representation

The state-to-state and state-to-all reaction probabilities for He + CO (v,j)→ He + CO (v',j') reaction at zero total angular momentum have been calculated by using a time-dependent quantum wave packet method. The time-dependent method used is based on Fourier Grid and Discrete Variable Representation (DVR) techniques. The time-dependent propagation of the wave packet is accomplished by an expansion in terms of modified complex chebyshev polynomials. The results show that the He + CO reaction is not reactive in the studied energy range.

scholarly journals Pole-skipping and hydrodynamic analysis in Lifshitz, AdS2 and Rindler geometries

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Haiming Yuan ◽  
Xian-Hui Ge
Keyword(s):  
Boundary Condition ◽  
Green’S Function ◽  
Green's Function ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Boundary Theory ◽  
Hydrodynamic Analysis ◽  
Dimensionless Variables ◽  
Pass Through ◽  
Special Points

Abstract The “pole-skipping” phenomenon reflects that the retarded Green’s function is not unique at a pole-skipping point in momentum space (ω, k). We explore the universality of pole-skipping in different geometries. In holography, near horizon analysis of the bulk equation of motion is a more straightforward way to derive a pole-skipping point. We use this method in Lifshitz, AdS2 and Rindler geometries. We also study the complex hydrodynamic analyses and find that the dispersion relations in terms of dimensionless variables $$ \frac{\omega }{2\pi T} $$ ω 2 πT and $$ \frac{\left|k\right|}{2\pi T} $$ k 2 πT pass through pole-skipping points $$ \left(\frac{\omega_n}{2\pi T},\frac{\left|{k}_n\right|}{2\pi T}\right) $$ ω n 2 πT k n 2 πT at small ω and k in the Lifshitz background. We verify that the position of the pole-skipping points does not depend on the standard quantization or alternative quantization of the boundary theory in AdS2× ℝd−1 geometry. In the Rindler geometry, we cannot find the corresponding Green’s function to calculate pole-skipping points because it is difficult to impose the boundary condition. However, we can still obtain “special points” near the horizon where bulk equations of motion have two incoming solutions. These “special points” correspond to the nonuniqueness of the Green’s function in physical meaning from the perspective of holography.

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