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0answers
27 views

What is the fluctuations of the energy of a simple harmonic oscillator? [on hold]

$$\begin{align} \varepsilon&=\frac{\vec{p}^{\,2}}{2m}+\frac{K}{m}\vec{q}^{\,2}\\ \rho(q,p)&=\biggl(\frac{\omega}{2\pi k_BT}\biggr)^3e^{-\frac{\varepsilon}{k_bT}} \end{align}$$ where ...
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2answers
80 views

Phase space derivation of quantum harmonic oscillator partition function

I would like to derive the partition function for the quantum Harmonic oscillator from scratch: $$\tag{1} Z = \int dp \, dx\, e^{-\beta H}.$$ The free particle appears in many textbooks. $H = ...
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1answer
116 views

General way to model baths? Harmonic Oscillators valid?

I am trying to model an open system interaction without making strong assumptions on coupling strength or temperature. In general i understand that open systems are modeled by a Lindbladian, but as ...
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votes
1answer
322 views

Accessible microstates of harmonic oscillator in microcanonical enemble

While reading up on statistical physics, I am going through the calculation of the partition function of the harmonic oscillator in the microcanonical ensemble. The result for the partition function ...
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3answers
1k views

Partition function for quantum harmonic oscillator

Hi guys I'm currently trying to solve a mock exam for an exam in a few days and am a bit confused by the solutions they gave us for this exercise: Exercise: A solid is composed of N atoms which ...
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1answer
255 views

Spectrum of quantum fluctuations in a harmonic oscillator

If we have a harmonic oscillator and look at it on small scale the energy is quantized and we can calculate the different eigenstates. In general the energy eigenvalues are given by $$E_n = ...
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votes
1answer
286 views

Simulating quantum network of harmonic oscillators

Let's say that I have a system of $n$ particles $p_1,\ldots,p_n\in\mathbb{R}^3$ (where $n$ here is on the order of 10,000). Furthermore, suppose we have a graph $G=(V,E)$ describing some network, ...