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Results tagged with solid-state-physics
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user 251599
Solid-state physics studies how macroscopic properties of solids (mechanical, electrical, optical, etc.) result from their microscopic structure. It usually deals with the scale where quantum properties of the particles are substantial.
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Precise definition of "nearest neighbours" in solid-state physics
I am reading Ashcroft and Mermin and, to define coordination number, they use the notion of nearest neighbours which they do not define. I'm sure it's a very trivial definition, but they had been so p …
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How is this expression for the energy of a free electron gas derived with the canonical ense...
Suppose we have some system of free electrons in a (say, 3D) box at a temperature $T$. From Ashcroft and Mermin equation (2.55), we can compute the energy of the system as
$$U=2\sum E(\mathbf{k})f(E(\ …
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The uniqueness of primitive vectors in a Bravais lattice
I am reading Chapter 4 of Ashcroft and Mermin (A&M) in which the basic definitions of a Bravais lattice (BL) -- as considered as a purely mathematical entity -- are being laid down. One of the definit …
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Why can we assume there is no charge in the derivation of dispersion relations (Drude theory)?
In a derivation done by Ashcroft and Mermin (I am now doing the derivation for helicon waves as predicted by the Drude model), the authors use in deriving the condition for propagation of electromagne …
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What "goes wrong" in a Sommerfeld expansion?
Let $f$ be the Fermi function and $H$ be a function which which vanishes as $\epsilon \to -\infty$ and which diverges at $\infty$ no worse than some power of $\epsilon$. In the Sommerfeld expansion of …
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On $k$-space density of states and semiclassical transport
I am reading Chapter 12 of Ashcroft and Mermin and I have a great many questions, but one sticks out in particular.
As background, we note that it can be shown quite generally (by applying Born-von Ka …
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Semiclassical model of electron dynamics
See the footnote given by AM on that very same page. There is no band wherein all orbits are closed; thus, there is no band in which all occupied states and all unoccupied states have closed orbits. T …
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Expressing entropy density in terms of energy density
In some manipulations in the free electron theory, one initially has the energy density $u$ of the system as a function of temperature and it's desirable to have the entropy density $s$ (both volumetr …
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Why is electronic specific heat divided by $V$ rather than $M$?
In Ashcroft and Mermin Chapter 1, just above equation (1.50) and in the context of a classical ideal electron gas, it is said that the electronic specific heat at constant volume $c_v$ is defined by
$ …
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Rigorous definition of the perfect conductor in macroscopic electrodynamics
Zangwill (in Modern Electrodynamics -- most of this discussion relates to Chapters 5.1 and 5.2 if you have access to the book) defines a perfect conductor as a macropscopic model for certain matter in …
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Why do we take $\langle{v^2}\rangle = \langle{v}\rangle^2$?
In Ashcroft and Mermin's Chapter 1, the equipartition theorem is often used to evaluate the mean speed of an electron in an (ideal) electron gas treated with classical statistical mechanics. That is, …
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Are there primitive unit cells which cannot be associated with primitive vectors?
In the theory of Bravais lattices, it is immediate to associate with each set of primitive unit vectors a primitive unit cell (see e.g. here). It is (probably) not hard to show that this map is an inj …
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On describing fcc and bcc planes in a Cartesian system (simple cubic system)
Ashcroft and Mermin remark, at the bottom of page 91 that
As a general rule, face-centered and body-centered cubic Bravais lattice[s] are described in terms of a conventional cubic cell, i.e. as simp …
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Electrostatics of non-equilibrium situations
In footnote 1 of Chapter 13 of Ashcroft and Mermin, they remark that
The only case we shall discuss in which the local equilibrium distribution is not the uniform equilibrium distribution (13.1) (wit …
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Equilibrium carrier distribution appropriate to local temperature
In Chapter 13 of Ashcroft and Mermin there is a general discussion about the nonequilibrium distribution function under the relaxation time/semiclassical transport assumptions. One of the key axioms g …
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