Multidimensional path integral calculations with quasiadiabatic propagators: Quantum dynamics of vibrational relaxation in linear hydrocarbon chains

1992 ◽  
Vol 97 (12) ◽  
pp. 9001-9015 ◽  
Author(s):  
Maria Topaler ◽  
Nancy Makri
Keyword(s):  
Path Integral ◽  
Vibrational Relaxation ◽  
Quantum Dynamics ◽  
Hydrocarbon Chains

Small matrix modular path integral: iterative quantum dynamics in space and time

2021 ◽  
Author(s):  
Nancy Makri
Keyword(s):  
Path Integral ◽  
Quantum Dynamics ◽  
Matrix Decomposition ◽  
Propagation Time ◽  
Molecular Aggregates ◽  
Space And Time ◽  
Small Matrix

This work presents a small matrix decomposition of the modular path integral for spin arrays or molecular aggregates, which leads to an iterative treatment with respect to the units that comprise the system and the propagation time.

scholarly journals Path-integral approximations to quantum dynamics

2021 ◽  
Vol 94 (7) ◽  
Author(s):  
Stuart C. Althorpe
Keyword(s):  
Molecular Dynamics ◽  
Correlation Function ◽  
Path Integral ◽  
Quantum Dynamics ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Imaginary Time ◽  
Integral Methods ◽  
Ring Polymer ◽  
Recent Extension

Abstract Imaginary-time path-integral or ‘ring-polymer’ methods have been used to simulate quantum (Boltzmann) statistical properties since the 1980s. This article reviews the more recent extension of such methods to simulate quantum dynamics, summarising the chain of approximations that links practical path-integral methods, such as centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD), to the exact quantum Kubo time-correlation function. We focus on single-surface Born–Oppenheimer dynamics, using the infrared spectrum of water as an illustrative example, but also survey other recent applications and practical techniques, as well as the limitations of current methods and their scope for future development. Graphic abstract

Path integral for quantum dynamics with position-dependent mass within the displacement operator approach

2020 ◽  
Vol 35 (30) ◽  
pp. 2050246
Author(s):  
H. Benzair ◽  
M. Merad ◽  
T. Boudjedaa
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Quantum Dynamics ◽  
Translation Operator ◽  
Integral Approach ◽  
Operator Approach ◽  
Square Well ◽  
Dependent Mass ◽  
Position Dependent Mass ◽  
Coulomb Potentials

In the context of quantum mechanics reformulated in a modified Hilbert space, we can formulate the Feynman’s path integral approach for the quantum systems with position-dependent mass particle using the formulation of position-dependent infinitesimal translation operator. Which is similar a deformed quantum mechanics based on modified commutation relations. An illustration of calculation is given in the case of the harmonic oscillator, the infinite square well and the inverse square plus Coulomb potentials.

Quantum dynamics of vibrational relaxation in condensed media

1975 ◽  
Vol 62 (4) ◽  
pp. 1572-1578 ◽  
Author(s):  
Dennis J. Diestler ◽  
Robert S. Wilson
Keyword(s):  
Vibrational Relaxation ◽  
Quantum Dynamics ◽  
Condensed Media
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