ISOTHERMAL QUANTUM DYNAMICS: NOSÉ–HOOVER DYNAMICS FOR COHERENT STATES

2003 ◽  
Vol 17 (28) ◽  
pp. 5449-5452 ◽  
Author(s):  
D. MENTRUP ◽  
J. SCHNACK
Keyword(s):  
Time Evolution ◽  
Coherent States ◽  
Quantum Dynamics ◽  
Canonical Ensemble ◽  
Equations Of Motion ◽  
Thermal Bath ◽  
Time Averaging ◽  
Quantum Particles ◽  
Dynamics Simulations ◽  
Identical Quantum

The method of Nosé and Hoover1,2 to create canonically distributed positions and momenta in classical molecular dynamics simulations is frequently used. Hamilton's equations of motion are supplemented by time-dependent pseudofriction terms that convert the microcanonical isoenergetic time evolution into a canonical isothermal time evolution, thus permitting the calculation of canonical ensemble averages by time averaging. We show that for one quantum particle in an external harmonic oscillator, the equations of motion in terms of coherent states can easily be modified in an analogous manner to mimic the coupling of the system to a thermal bath and create a quantum canonical ensemble.3 The method is generalised to a system of two identical quantum particles. In the resulting equations of motion, one obtains an additional attractive term for bosons and a repulsive term for fermions in the dynamics of the pseudofriction coefficients, leading to a correctly sampled thermal weight.

scholarly journals Time evolution of decay of two identical quantum particles

2011 ◽  
Vol 84 (3) ◽  
Author(s):  
Gastón García-Calderón ◽  
Luis Guillermo Mendoza-Luna
Keyword(s):  
Time Evolution ◽  
Quantum Particles ◽  
Identical Quantum

scholarly journals QUANTUM DYNAMICS OF THE CUBIT SYSTEM IN EXTERNAL FIELDS

2021 ◽  
Vol 26 (4) ◽  
pp. 68-75
Author(s):  
A. V. Gorokhov ◽  
G. I. Eremenko
Keyword(s):  
Symmetry Group ◽  
Time Evolution ◽  
Coherent States ◽  
Quantum Dynamics ◽  
Dynamic Symmetry ◽  
Classical Dynamics ◽  
External Fields

A system of two dipole-dipole interacting two-level elements (qubits) in external fields is considered. It is shown that using the coherent states (CS) of the dynamic symmetry group of the SU(2)SU(2) system, the time evolution can be reduced to the "classical" dynamics of the complex parameters of the CS. The trajectories of the CS are constructed and the time dependences of the probability of finding qubits at the upper levels are calculated.

scholarly journals Zero-Point Energy Leakage in Quantum Thermal Bath Molecular Dynamics Simulations

2016 ◽  
Vol 12 (12) ◽  
pp. 5688-5697 ◽  
Author(s):  
Fabien Brieuc ◽  
Yael Bronstein ◽  
Hichem Dammak ◽  
Philippe Depondt ◽  
Fabio Finocchi ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Zero Point ◽  
Thermal Bath ◽  
Zero Point Energy ◽  
Point Energy ◽  
Energy Leakage ◽  
Dynamics Simulations

scholarly journals Electron Trajectories in Molecular Orbitals

2020 ◽  
Author(s):  
Isaiah Sumner ◽  
Hannah Anthony
Keyword(s):  
Lagrange Multiplier ◽  
Equations Of Motion ◽  
Bohmian Mechanics ◽  
Molecular Orbitals ◽  
Quantum Hydrodynamics ◽  
Relativistic Limit ◽  
Quantum Particles ◽  
Quantum Force ◽  
Trajectory Methods ◽  
Structure Calculations

The time-dependent Schrödinger equation can be rewritten so that its interpretation is no longer probabilistic. Two well-known and related reformulations are Bohmian mechanics and quantum hydrodynamics. In these formulations, quantum particles follow real, deterministic trajectories influenced by a quantum force. Generally, trajectory methods are not applied to electronic structure calculations, since they predict that the electrons in a ground state, real, molecular wavefunction are motionless. However, a spin-dependent momentum can be recovered from the non-relativistic limit of the Dirac equation. Therefore, we developed new, spin-dependent equations of motion for the quantum hydrodynamics of electrons in molecular orbitals. The equations are based on a Lagrange multiplier, which constrains each electron to an isosurface of its molecular orbital, as required by the spin-dependent momentum. Both the momentum and the Lagrange multiplier provide a unique perspective on the properties of electrons in molecules.

scholarly journals Investigating Tunneling Controlled Chemical Reactions Through Ab-Initio Ring Polymer Molecular Dynamics

2021 ◽  
Author(s):  
Xinyang Li ◽  
Pengfei Huo
Keyword(s):  
Molecular Dynamics ◽  
Ab Initio ◽  
Chemical Reaction ◽  
Quantum Tunneling ◽  
Quantum Dynamics ◽  
Density Functional ◽  
Molecular System ◽  
Ring Polymer ◽  
Ring Polymer Molecular Dynamics ◽  
Dynamics Simulations

<div>We use the ab-initio ring polymer molecular dynamics (RPMD) approach to investigate tunneling controlled reactions in methylhydroxycarbene. Nuclear tunneling effects enable molecules to overcome the barriers which can not be overcome classically. Under low-temperature conditions, intrinsic quantum tunneling effects canfacilitate the chemical reaction in a pathway that is neither favored thermodynamically nor kinetically. This</div><div>behavior is referred to as the tunneling controlled chemical reaction and regarded as the third paradigm of chemical</div><div>reaction controls. In this work, we use the ab-initio RPMD approach to incorporate the tunneling effects in our quantum dynamics simulations. The reaction kinetics of two competitive reaction pathways at various temperatures are investigated with the Kohn-Sham density functional theory (KS-DFT) on-the-fly molecular dynamics simulations and the ring polymer quantization of the nuclei. The reaction rate constants obtained here agree extremely well with the experimentally measured rates. We demonstrate the feasibility of using ab-initio RPMD rate calculations in a realistic molecular system, and provide an interesting and important example for future investigations on reaction mechanisms dominated by quantum tunneling effects.</div>

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