### 物理代写|热力学代写thermodynamics代考|MECH 3720

statistics-lab™ 为您的留学生涯保驾护航 在代写热力学thermodynamics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写热力学thermodynamics代写方面经验极为丰富，各种代写热力学thermodynamics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|热力学代写thermodynamics代考|Equilibration of Large Quantum Systems

The tendency of large systems to evolve to an equilibrium, namely, a stationary state that does not depend on their initial state, is called thermalization. The stationary state of a closed system is described by the microcanonical ensemble corresponding to a narrow energy distribution.

Large-system thermalization is commonplace. Yet it appears to contradict the unitarity of quantum mechanics, which requires symmetry with respect to time inversion. This contradiction has not yet been fully reconciled with the fundamental reversibility of quantum mechanics, despite a continuing endeavor that may be traced back to von Neumann’s work in 1929. The central paradigm is the eigenstate thermalization hypothesis (ETH) put forward by Srednicki. It relies on the conjecture that a typical (randomly picked) eigenstate of a realistic many-body Hamiltonian yields the same mean value for any reasonable observable as predicted by a microcanonical ensemble with the same total energy. The ETH predicts that almost any superposition of such eigenstates relaxes at long times to a state that is practically indistinguishable from a thermal equilibrium state. Studies of thermalization in closed quantum manybody systems are aimed at bridging unitarity with irreversibility, ergodicity, and the onset of thermodynamic behavior in complex or open systems. Yet the quantum thermalization mechanism and the route to the bridging of quantum and classical descriptions of the world by this mechanism remain enigmatic and are still being debated. However, under generic conditions, one can show that the observables of a large system are governed at long times by a canonical density operator, as detailed in this chapter.

## 物理代写|热力学代写thermodynamics代考|From Quantum Dynamics to Thermodynamics

In an isolated system with a large but countable number of degrees of freedom (DOF), $1 \ll f \ll \infty$, governed by an autonomous Hamiltonian $H$, the spectrum is discrete (quantized). Its (typically infinitely many) eigenstates $|n\rangle(n=0,1, \ldots)$ possess eigenvalues $E_{n}$, ordered as
$$E_{0} \leq E_{1} \leq E_{2} \leq \ldots$$
with a bounded ground state energy, $E_{0}>-\infty$. The Hamiltonian can then be written as
$$H:=\sum_{n} E_{n}|n\rangle\langle n| .$$
In the presence of energy degeneracy, we may use the projectors onto subspaces of degenerate energies $E_{m}=E_{n}$,
$$P_{E_{n}}:=\sum_{E_{m}=E_{n}}|m\rangle\langle m|,$$
to rewrite the Hamiltonian (1.2) as
$$H=\sum_{E_{n}} E_{n} P_{E_{n}},$$
where $\sum_{E_{n}}$ is a summation over all mutually different $E_{n}$ values.

## 物理代写|热力学代写thermodynamics代考|From Quantum Dynamics to Thermodynamics

$$E_{0} \leq E_{1} \leq E_{2} \leq \ldots$$

$$H:=\sum_{n} E_{n}|n\rangle\langle n| .$$

$$P_{E_{n}}:=\sum_{E_{m}=E_{n}}|m\rangle\langle m|,$$

$$H=\sum_{E_{n}} E_{n} P_{E_{n}},$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。