一个简单谐振子系统模型的模拟与计算

周文渊, 张伯宇, 罗世平, 杨正波, 魏彦锋

doi:10.16854 /j.cnki.1000-0712.190595

大学物理 >

2020 , Vol. 39 >Issue 11: 72 - 75

DOI: https://doi.org/10.16854 /j.cnki.1000-0712.190595　

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一个简单谐振子系统模型的模拟与计算

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湖北文理学院物理与电子工程学院，湖北襄阳441053

周文渊( 1998—) ，男，湖北十堰人，湖北文理学院物理与电子工程学院2017 级物理学专业本科生.

收稿日期: 2020-12-31

修回日期: 2020-06-11

网络出版日期: 2020-11-18

基金资助

湖北省高等学校教学研究项目( 2017423)

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Simulation and calculation of a simple harmonic oscillator system

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School of Physics and Electronic Engineering，Hubei University of Arts and Science，Xiangyang，Hubei 441053，China

Received date: 2020-12-31

Revised date: 2020-06-11

Online published: 2020-11-18

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摘要

本文通过对一个简单谐振子系统模型的计算机模拟，演示了热力学系统从有序的非平衡态向无序的平衡态演变过程，得到粒子数在平衡状态下分布规律，即玻尔兹曼分布.对分布曲线进行拟合，可以求出总能量已知的谐振子系统在平衡状态时的温度，拟合结果与理论计算是吻合的.进一步研究能量与温度的关系，证明了这个简单谐振子系统模型在高温极限下，能量均分定理是成立的.

关键词： 玻尔兹曼分布; 计算机模拟; 谐振子; 能量均分定理

本文引用格式

周文渊, 张伯宇, 罗世平, 杨正波, 魏彦锋 . 一个简单谐振子系统模型的模拟与计算[J]. 大学物理, 2020 , 39(11) : 72 -75 . DOI: 10.16854 /j.cnki.1000-0712.190595　

Abstract

Through the computer simulation of a harmonic oscillator model，the evolution process of thermodynamic

system from ordered nonequilibrium state to disordered equilibrium state is demonstrated. It is also proved

that when the system is in equilibrium，the distribution of particles number satisfies the Boltzmann distribution. By

fitting the distribution curve，the temperature of this isolated system with known total energy at equilibrium state can

be obtained，and the fitting result is consistent with the following theoretical calculation. The relationship between

internal energy and temperature is further studied and it is proved that the equipartition theorem is valid in the high

temperature limit of the harmonic oscillator model.

Key words： Boltzmann distribution; computer simulation; harmonic oscillator; equipartition theorem

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