The study of physical properties condensed phases of matter, including solids and liquids.
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Eigenfunctions in periodic potential
For Hamiltonian $\operatorname H$ and lattice translation operator $\operatorname T$, if
$$\operatorname H\psi=E\psi, \qquad \operatorname T\psi=e^{ik\cdot R}\psi,$$
and
$$\operatorname ...
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116 views
Hamiltonian of a simple graph
I have a spin system:
As shown in the picture, there are two spins S1 and S2, and a pair of interactions between them. One is a ferromagnetic interaction and the other is anti ferromagnetic ...
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152 views
Difference between Monte Carlo and Quantum Monte Carlo methods?
What are the differences between Classical Monte Carlo methods and Quantum Monte Carlo methods in condensed matter physics? If one want to study strongly correlated systems with Quantum Monte Carlo ...
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65 views
The orthogonalized plane waves
An orthogonal plane wave with wave number $k$ is written as
$$ OPW_k=e^{ ik\cdot r}-\sum_\alpha \psi_\alpha(r) \int \psi^*_\alpha (r'') e^{ik\cdot r''} d\tau'',$$
where index $\alpha$ and $k$ ...
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300 views
Why path integral approach may suffer from operator ordering problem?
In Assa Auerbach's book (Ref. 1), he gave an argument saying that in the normal process of path integral, we lose information about ordering of operators by ignoring the discontinuous path.
What did ...
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111 views
Toric Code and Random Bond Ising Model
It was established by Dennis, Kitaev et al. that the 2D Toric Code
can be mapped to a 2D Random Bond Ising Model. The original derivation
was given in the paper "Topological quantum memory" which ...
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452 views
Emergent symmetries
As we know, spontaneous symmetry breaking(SSB) is a very important concept in physics. Loosely speaking, zero temprature SSB says that the Hamiltonian of a quantum system has some symmetry, but the ...
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259 views
Is the “particle number” of “electrons” well defined in Wen's string-net theory of elementary particles?
According to professor Wen's string-net theory(Colloquium: Photons and electrons as emergent phenomena, Levin and Wen, Rev. Mod. Phys. 77, 871(2005), see e.g. http://arxiv.org/abs/cond-mat/0407140), ...
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119 views
Crystal Angular Momentum
In a crystal, we don't have full translational symmetry, but we still have discrete translations. This allows us to define "crystal momentum" that is conserved modulo a reciprocal lattice vector.
In ...
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92 views
In the big crunch theory, when the big crunch singularity forms, can the resulting black hole decay through hawking's radiation?
I've been pondering about this and I couldn't really find the answer for this. The big crunch theory postulates that the universe will eventually stop expanding and reverse back in on its self into a ...
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23 views
What favors island growth of a sputtered material?
What would be the best choice of parameters in general if one would like to get pure island growth (i.e. Volmer-Weber growth) in a sputtering deposition process and what would be a good estimate of ...
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151 views
What happens to atoms inside the black hole?
Black holes have very high gravitational force intending to crush everything. So as we know atoms in a molecule have inter atomic spacing between then and further electron,s also revolve at a certain ...
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178 views
Is the speed of sound almost as high as the speed of light in neutron stars?
Have you ever wondered about the elastic properties of neutron stars?
Such stars, being immensely dense, in which neutrons are bound together by the strong nuclear force on top of the strong gravity ...
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1answer
76 views
Dynamic structure factor
Dynamic structure factor is the spatial and temporal Fourier transform of Van Hoves time dependent pair correlation function. It is written as
$$ S(k,\omega)= \frac{1}{2\pi}\int F(k,t)\exp(i\omega ...
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111 views
Phonon Momentum
I am reading Charles Kittel's solid state physics and wondering what's the mechanism that neutron waves and photons can interact with phonons and the process obey the generalized momentum-energy ...
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69 views
How are X-rays focused? Specifically in XRD. Well do they even focus X-rays in XRD?
I read in a government website that reflecting an x-ray from a parabolic mirror followed by a reflection from a hyperbolic mirror results in focusing the x-ray, but this was for astronomical purposes. ...
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243 views
Is the index of refraction dependent on the wavelength of light?
I just read in some class notes for a crystallography class that there are no refractive lenses for X-rays because the index of refraction of most materials is close to 1. Is the index of refraction ...
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75 views
What are some ways of inducing spin polarization?
I saw a talk today and they mentioned how nitrogen-vacancy diamond centers can be used to optically induce spin polarization and now I wonder what other ways there are to induce a spin polarization.
...
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1answer
72 views
Phonon wavevector $q\le 2k_{F}$ for Electron-Phonon Scattering
I am reading "Supercollision cooling in undoped graphene." There the authors write: ``Above $T_{BG}$ (the Bloch-Gruneisen temperature), only a fraction of acoustic phonons with wave vector $q\le ...
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180 views
Calculation of number density from material density
Material density is given by $ \rho =m/V$, where $m$ is mass and $V$ is volume.
Again number density given by $n=N/V$, where $N$ is the total number of particle. How can I calculate number density $n$ ...
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1answer
123 views
Semi-conductor band-gap and deformation potential
Submitting a semi-conductor to stress leads to a deformation in the energy-bands, roughly described by:$$H_{ij} = {\cal{D}}_{ij}^{\alpha\beta}\;\epsilon_{\alpha\beta}$$
$\epsilon$ being the strain ...
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1answer
117 views
Rewriting Creation and Annihilation Operators
I am playing with the Landau Level problem and Algebraic solutions to it. I am given
$$a=\frac{l_{b}}{\sqrt{2}\hbar}(\pi_{x}-i\pi_{y}) ...
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33 views
Residual symmetries of the superposition of two fcc lattices
Fcc lattices are Bravais lattices and so are invariant under a set of discrete translations plus inversions over the 3 axis ($x\rightarrow -x$,$y\rightarrow -y$,$z\rightarrow -z$). When one superposes ...
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118 views
How to judge whether a symmetry will be spontaneously broken while only given a Hamiltonian preserving this symmety
As asked in the title, is Hamiltonian containing enough information to judge the existence of spontaneously symmetry breaking?
Any examples?
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156 views
Typical operators in tight binding
Let the tight-binding Hamiltonian be $\sum\limits_{ij} {{t_{ij}}\left| i \right\rangle \left\langle j \right|}$. Where ${\left| i \right\rangle }$ is the atomic orbit at lattice site $i$.
My question ...
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Partition function of a gas of $N$ identical classical particles
Partition function of a gas of $N$ identical classical particles is given by
$$ Z~=~\frac {1}{N! h^{3N}} \int \exp[-\beta H(p_1.......p_n, x_1....x_n)]d^3p_1...d^3p_n,d^3x_1...d^3x_n $$
in this ...
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20 views
Rice Allnatt distribution function
Can anyone give me an article of which explains Rice Allnatt distribution function or can you explain the function here?
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298 views
Validity of Bogoliubov transformation
In condensed matter physics, one often encounter a Hamiltonian of the form
$$\mathcal{H}=\sum_{\bf{k}}
\begin{pmatrix}a_{\bf{k}}^\dagger & a_{-\bf{k}}\end{pmatrix}
\begin{pmatrix}A_{\bf{k}} ...
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182 views
Zero Resistance in Quantum Hall Effect and Superconductivity
What is the difference between the zero resistance of $R_{xx}$ in integer quantum Hall effect and the zero resistance in superconductivity?
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79 views
Why is the BCS trial function valid across the BEC-BCS crossover?
In one of the two main theoretical approaches used in describing ultracold Fermi gases and the BEC-BCS crossover, the so-called BCS-Leggett approach, the starting point is the BCS trial wavefunction:
...
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33 views
Why the peak of spectrum gets vague when the dimension is lower?
In a many-body system, we can know the spectrum function at a particular temperature from Green function. It means density of states. A peak of spectrum represents one mode. My question is that in the ...
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198 views
Chiral edge state as topological properity of bulk state
As far as I know, quantum hall effect and quantum spin hall effect has chiral edge state. Chiral edge state is usually closely related with delocalization, since back scattering is forbidden. However, ...
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487 views
The difference between the Wannier function and atomic orbit in a tight binding model
In a tight binding model, we usually start from the atomic orbits and linearly combine them to get the wave function of the crystal energy band.
My questions are:
Since this kind of tight binding ...
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1answer
141 views
What are the statuses of Silicene and Graphene for real world circuit production?
A lot of hype is out there about both of them (especially the latter) and I was wondering if there is more concrete information about them other than the news IBM posted on a circuit 2 years ago and ...
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305 views
Why should the Fermi level of a n-doped semiconductor be below the one of a p-doped?
In a pn-junction, the difference in Fermi level between the p doped and the n doped regions causes the apparition of a built-in electric field at equilibrium. This electric field goes from the n to ...
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227 views
Quantum dimension in topological entanglement entropy
In 2D the entanglement entropy of a simply connected region goes like
\begin{align}
S_L \to \alpha L - \gamma + \cdots,
\end{align}
where $\gamma$ is the topological entanglement entropy.
$\gamma$ is ...
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396 views
Why quantum hall effect has chiral edge state?
The most popular explaination may be the following: in magnetic field, electrons move in cycolotron orbits, such cycolotron orbits ensure electrons to move in one direction at the edge. That is why ...
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357 views
Exact diagonalization of graphene's tight binding Hamiltonian
While directly diagonalize graphene's tight binding Hamiltonian, which is numerical. We have to use a finite-sized graphene.
So how to deal with boundary conditions? The usual solutions are zigzag or ...
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228 views
P-T Phase diagram. Density of material at critical point
One of the questions I had while reading through some material was:
Why is the density of a given volume of gas uniquely defined at the critical point, but not at the triple point?
Is it because at ...
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1answer
99 views
Question about Classical Transport Theory
With a distribution function of the form $f=f_{0} + \vec{v} \cdot \vec{g}$, one can obtain the current density. My question is about $\vec{g}$; we assume a general solution to $\vec{g}$ of the form ...
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1answer
61 views
Where to learn Temperature Dependent Conductivity induced by Electron-Phonon Interaction? [closed]
I want to learn how to calculate the temperature dependent conductivity induced by electron-phonon interaction.
I know in low temperature, the resistance in metal $\rho$ is proportional to $T^5$, $T$ ...
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1answer
611 views
Effective Mass and Fermi Velocity of Electrons in Graphene:
In graphene, we have (in the low energy limit) the linear energy-momentum dispersion relation: $E=\hbar v_{\rm{F}}|k|$. This expression arises from a tight-binding model, in fact $E =\frac{3\hbar ...
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129 views
Notation in Spin Liquid
When construct spin liquid by projective symmetry group, we can classified spin liquids by the invariant group (IGG) of their mean field ansatze. For example, we can have Z2, U(1) and SU(2) spin ...
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1answer
145 views
Band Structure and Carrier Recombination/Generation
So i've been a bit confused, looking at PN junction, semiconductors and the like (trying to nail down how exactly semiconductors work, transistors and such). I've read the wiki on band structure ...
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1answer
269 views
Wave functions for three identical fermions
I would like to express the wave functions for three identical particles, each with orbital angular momentum $L=1$ and spin angular momentum $S=1/2$, in terms of single-particle wave functions. In ...
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1answer
147 views
Double-counting correction in a LDA + DMFT calculation
To theoretically study correlated materials, one usually has to consult to the LDA + DMFT calculations, in which the two-particle interaction is usually double-counted. A general recipe for the ...
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29 views
What is a Palais-Smale sequence?
I was studying a paper on existence of discrete breathers by F. Gazzola and he uses the properties of Palais-Smale sequences to do many things that i dont understand,
my questions are
...
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1answer
145 views
Energy spectrum of a tight-binding model
Consider the one-dimensional tight-binding Hamiltonian
$$\mathcal{H}=t\sum_m\left(a^\dagger_m a_{m+1}+a^\dagger_{m+1} a_{m}\right).$$
With the lattice constant set to 1, the energy spectrum is given ...
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294 views
Can a first order phase transition have an order parameter?
Order parameter is used to describe second order phase transition. It seems that in some papers it is used in the first order phase transitions. Can first order phase transition have an order ...
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92 views
why is orbital moment quenched while atoms forming solid
atom has well defined spin(up and down) and orbital(s,p,d,etc) momentum, but when forming crystals, why the spin degree continues to be good quantum number while orbital momentum is quenched?
