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.

scholarly journals LCE Violation for the Relational to Quantum Transition

2021 ◽  
Author(s):  
Chitradeep Gupta
Keyword(s):  
Quantum Theory ◽  
Path Integral ◽  
Uncertainty Principle ◽  
Quantum Transition ◽  
Arrow Of Time ◽  
Local Conservation ◽  
Conservation Of Energy ◽  
Space And Time

Abstract Quantization historically was never as much a problem as it was a solution to a problem and the problem was the failure of the classical material evolution statement. Under the axiomatic assumption that quantum theory is founded in Heisenberg’s principle and Feynman’s evolution we show that the QM path integral exists at the negation of the evolution of local conservation of energy(LCE) which in its presence fails with arbitrarily many interference terms. Along with LCE violation we uncover another GR-QM contradiction between the local arrow of time and the uncertainty principle. Every contradiction ∼ (p)∩(q) is also a transition in p changing to q. The problem is GR is also caught up in an implication trail and cannot go through multiple parallel changes for LCE violation in presence of the QM path integral. To improve the recovery we go to an alternate projection of GR that has a set of independent frame invariant statements with a Lorentz invariant distinction of space and time.

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