scholarly journals Path integral Monte Carlo for dissipative many-body systems

2003 ◽  
Vol 237 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Luca Capriotti ◽  
Alessandro Cuccoli ◽  
Andrea Fubini ◽  
Valerio Tognetti ◽  
Ruggero Vaia
Keyword(s):  
Monte Carlo ◽  
Path Integral ◽  
Many Body ◽  
Path Integral Monte Carlo ◽  
Many Body Systems

QUASICLASSICAL FOURIER PATH INTEGRAL QUANTUM CORRECTION TERMS TO THE KINETIC ENERGY OF INTERACTING QUANTUM MANY-BODY SYSTEMS

2009 ◽  
Vol 23 (20n21) ◽  
pp. 3979-3991
Author(s):  
K. A. GERNOTH
Keyword(s):  
Monte Carlo ◽  
Kinetic Energy ◽  
Path Integral ◽  
Quantum Correction ◽  
Many Body ◽  
Quantum Distribution ◽  
Many Body Systems ◽  
The Many ◽  
Correction Terms ◽  
Integral Quantum

A quasiclassical expression for the kinetic energy of interacting quantum many-body systems is derived from the full quantum expression for the kinetic energy as derived by means of the Fourier path integral representation of the canonical many-body density matrix of such systems. This quasiclassical form of the kinetic energy may be cast in the shape of thermodynamic expectation values w.r.t. to the classical Boltzmann distribution of the many-body system, which involves only the many-body interaction in contrast to the full Fourier path integral quantum distribution, which carries contributions also from the many-body kinetic energy operator. The quasiclassical quantum correction terms to the classical Boltzmann equipartition value are valid when the product of temperature and particle mass is large and then lead to significant technical simplifications and increase of speed of Monte Carlo computations of the quantum kinetic energy. The formal findings are tested numerically in quantum Fourier path integral versus classical Monte Carlo simulations.

Constructing accurate interaction potentials to describe the microsolvation of protonated methane by helium atoms

2017 ◽  
Vol 19 (12) ◽  
pp. 8307-8321 ◽  
Author(s):  
Dennis Kuchenbecker ◽  
Felix Uhl ◽  
Harald Forbert ◽  
Georg Jansen ◽  
Dominik Marx
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Ab Initio ◽  
Path Integral ◽  
Interaction Potential ◽  
Stationary Point ◽  
Path Integral Monte Carlo ◽  
Interaction Potentials ◽  
Helium Atoms

An ab initio-derived interaction potential is derived and used in path integral Monte Carlo simulations to investigate stationary-point structures of CH5+ microsolvated by up to four helium atoms.

TI/PIMC METHOD WITH THE TAKAHASHI–IMADA APPROXIMATION FOR THE EQUILIBRIUM CONSTANT OF THE O + HCl ⇌ OH + Cl REACTION

2013 ◽  
Vol 12 (04) ◽  
pp. 1350026 ◽  
Author(s):  
MARCIN BUCHOWIECKI
Keyword(s):  
Monte Carlo ◽  
Temperature Dependence ◽  
Equilibrium Constant ◽  
Path Integral ◽  
Thermodynamic Integration ◽  
Partition Functions ◽  
Integration Path ◽  
Path Integral Monte Carlo

The thermodynamic integration/path integral Monte Carlo (TI/PIMC) method of calculating the temperature dependence of the equilibrium constant quantum mechanically is applied to O + HCl ⇌ OH + Cl reaction. The method is based upon PIMC simulations for energies of the reactants and the products and subsequently on thermodynamic integration for the ratios of partition functions. PIMC calculations are performed with the primitive approximation (PA) and the Takahashi–Imada approximation (TIA).

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