凝聚态物质和粒子物理|PHYS3036/PHYS3936 Condensed Matter and Particle Physics 代写

PHYS 1901 is one of two introductory courses on astronomy offered by Carleton (the other being PHYS 1902: From Our Stars to the Cosmos). PHYS 1901 focuses on the solar system and planetary phenomena. By the end of this course you will understand the motions of the sky, how telescopes work, the characteristics of the planets, how the solar system formed, and the methods astronomers and scientists use to learn about our neighbourhood in the Universe. I hope that you will gain a deeper appreciation of science and astronomy, and have fun learning!

The order parameters of ELC phases are well known . In the crystalline phases, the order parameters are $\rho_{K}$, the expectation values of the density operators at the set of ordering wave vectors ${\boldsymbol{K}}$ that defines the crystal.
$$\rho_{K}=\int d \boldsymbol{r} \rho(\boldsymbol{r}) e^{t \boldsymbol{K} \cdot \boldsymbol{r}}$$
where $\rho(\boldsymbol{r})$ is the local charge density. Thus, under an uniform translation by $\boldsymbol{R}, \rho_{\boldsymbol{K}}$ transforms as
$$\rho_{K} \rightarrow \rho_{K} e^{i K \cdot R}$$

Smectic phases are unidirectional density waves and their order parameters are also expectation values $\rho_{\mathbf{K}}$ but for only one wave vector $\boldsymbol{K}$. For charged systems, $\rho(\boldsymbol{r})$ is the charge density, and the order parameter $\rho_{K}$ is the charge density wave order parameter. Since $\rho(\boldsymbol{r})$ is real, $\rho_{\boldsymbol{K}}=\rho_{-\boldsymbol{K}}^{*}$, and the density can be expanded as
$$\rho(\boldsymbol{r})=\rho_{0}(\boldsymbol{r})+\rho_{\boldsymbol{K}}(\boldsymbol{r}) e^{i \boldsymbol{K} \cdot \boldsymbol{r}}+\text { c.c. }$$
where $\rho_{0}(\boldsymbol{r})$ are the Fourier components close to zero wave vector, $k=0$, and $\rho_{\boldsymbol{K}}(\boldsymbol{r})$ are the Fourier components with wave vectors close to $k=K$. Hence, a density wave (a smectic) is represented by a conplex order parameter ficld, in this case $\rho_{\boldsymbol{K}}(\boldsymbol{r})$. This is how we will describe a CDW and a charge stripe (which from the point of view of symmetry breaking have the same description). ${ }^{2}$

Smectic order is detected most casily in scattering experiments through the measurement of the static structure factor, usually denoted by $S(k)$,
$$S(k)=\int \frac{d \omega}{2 \pi} S(k, \omega)$$

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