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In this work, a novel ring polymer representation for multi-level quantum system is proposed for thermal average calculations. The proposed presentation keeps the discreteness of the electronic states: besides position and momentum, each…

Chemical Physics · Physics 2017-05-24 Jianfeng Lu , Zhennan Zhou

The quantum thermal average plays a central role in describing the thermodynamic properties of a quantum system. Path integral molecular dynamics (PIMD) is a prevailing approach for computing quantum thermal averages by approximating the…

Numerical Analysis · Mathematics 2024-06-25 Xuda Ye , Zhennan Zhou

Path integral molecular dynamics (PIMD) has been successfully applied to perform simulations of large bosonic systems in a recent work (Hirshberg et al., PNAS, 116, 21445 (2019)). In this work we extend PIMD techniques to study Green's…

Quantum Physics · Physics 2022-04-22 Xiong Yunuo , Xiong Hongwei

The quantum harmonic oscillator is the fundamental building block to compute thermal properties of virtually any dielectric crystal at low temperatures in terms of phonons, extended further to cases with anharmonic couplings, or even…

Statistical Mechanics · Physics 2021-10-05 Vladislav Efremkin , Jean-Louis Barrat , Stefano Mossa , Markus Holzmann

We introduce a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition…

Chemical Physics · Physics 2019-07-11 Neil Raymond , Dmitri Iouchtchenko , Pierre-Nicholas Roy , Marcel Nooijen

We show that a recently introduced stochastic thermostat [J. Chem. Phys. 126 (2007) 014101] can be considered as a global version of the Langevin thermostat. We compare the global scheme and the local one (Langevin) from a formal point of…

Computational Physics · Physics 2008-06-06 Giovanni Bussi , Michele Parrinello

A methodology to sample the isothermal-isobaric ensemble using Langevin dynamics is proposed, which combines novel features of geometric integrators for the equations of motion. By employing the Trotter expansion, the methodology generates…

Statistical Mechanics · Physics 2018-08-29 Samuel Cajahuaringa , Alex Antonelli

With the path integral approach, the thermal average in a multi-electronic-state quantum systems can be approximated by the ring polymer representation on an extended configuration space, where the additional degrees of freedom are…

Numerical Analysis · Mathematics 2020-11-24 Xiaoyu Lei , Zhennan Zhou

In this manuscript, we present a novel approach for sampling from a continuous multivariate probability distribution, which may either be explicitly known (up to a normalization factor) or represented via empirical samples. Our method…

Machine Learning · Statistics 2025-03-14 Hamidreza Behjoo , Michael Chertkov

We discuss the use of a Langevin equation with a colored (correlated) noise to perform constant-temperature molecular dynamics simulations. Since the equations of motion are linear in nature, it is easy to predict the response of a…

Statistical Mechanics · Physics 2010-01-04 Michele Ceriotti , Giovanni Bussi , Michele Parrinello

Path integral molecular dynamics (PIMD), which maps a quantum particle onto a fictitious classical system of ring polymers and propagates the "beads" of this extended classical system using molecular dynamics, is widely used to capture…

We present a new method of conducting molecular dynamics simulation in isothermal-isobaric ensemble based on Langevin equations of motion. The stochastic coupling to all particle and cell degrees of freedoms is introduced in a correct way,…

Statistical Mechanics · Physics 2016-04-28 Xingyu Gao , Jun Fang , Han Wang

Reliable dynamical properties from molecular dynamics simulations require careful control of thermostatting artifacts. We systematically assess how NVE, deterministic thermostats, velocity-rescale dynamics, and stochastic Langevin-type…

Chemical Physics · Physics 2025-12-01 Frederick Heinz , Sascha Jähnigen , Joana-Lysiane Schäfer , Bettina G. Keller

We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales.…

Numerical Analysis · Mathematics 2021-06-08 Xiaocheng Shang

Path integral quantum Monte Carlo (PIMC) is a method for estimating thermal equilibrium properties of stoquastic quantum spin systems by sampling from a classical Gibbs distribution using Markov chain Monte Carlo. The PIMC method has been…

Quantum Physics · Physics 2021-02-22 Elizabeth Crosson , Aram W. Harrow

Multiple time scale molecular dynamics enhances computational efficiency by updating slow motions less frequently than fast motions. However, in practice the largest outer time step possible is limited not by the physical forces but by…

Statistical Mechanics · Physics 2011-01-13 Joseph A. Morrone , Thomas E. Markland , Michele Ceriotti , B. J. Berne

A systematic comparison was carried out to assess the influence of representative thermostat methods in constant-temperature molecular dynamics simulations. The thermostat schemes considered include the Nos\'e--Hoover thermostat and its…

Computational Physics · Physics 2026-04-24 Kumpei Shiraishi , Emi Minamitani , Kang Kim

A recently proposed method for computer simulations in the isothermal-isobaric (NPT) ensemble, based on Langevin-type equations of motion for the particle coordinates and the ``piston'' degree of freedom, is re-derived by straightforward…

Soft Condensed Matter · Physics 2016-08-31 A. Kolb , B. Duenweg

In this work we compare and characterize the behavior of Langevin and Dissipative Particle Dynamics (DPD) thermostats in a broad range of non-equilibrium simulations of polymeric systems. Polymer brushes in relative sliding motion,…

Soft Condensed Matter · Physics 2007-08-31 C. Pastorino , T. Kreer , M. Mueller , K. Binder

Path-integral molecular dynamics (PIMD) simulations are crucial for accurately capturing nuclear quantum effects in materials. However, their computational intensity and reliance on multiple software packages often limit their applicability…