The study of physical properties condensed phases of matter, including solids and liquids.

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Ohm's Law: Drude Model

For a very long time now, I've been thinking about the Drude Model derivation of Ohm's Law. I know that a rigorous derivation requires a Quantum Mechanical approach. However, the mere fact that the ...
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1answer
50 views

How does pressure influence temperature in liquids?

Lets say we have a tank with a fixed mass of liquid at atmospheric pressure and room temperature. How do we influence the temperature when we exert pressure (e. g., with a piston) on the liquid? Are ...
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566 views

Analytic continuation of imaginary time Greens function in the time domain

Consider the imaginary time Greens function of a fermion field $\Psi(x,τ)$ at zero temperature $$ G^τ = -\langle \theta(τ)\Psi(x,τ)\Psi^\dagger(0,0) - \theta(-τ)\Psi^\dagger(0,0)\Psi(x,τ) \rangle $$ ...
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2answers
31 views

Correlation in electron gas

In the textbooks that I read (namely Ashcroft/Mermin , Marder, etc.) it seems that a distinction is made between the correlations in electron gas and a Couloumb interaction between the electrons. What ...
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1answer
139 views

Entanglement entropy of 1D chiral Fermion

I was told that the entanglement entropy $S_E$ on the ground state of a (1+1)D conformal field theory (CFT) follows the logarithmic behavior $S_E=\frac{c}{12}\ln L$ where $L$ is the length scale ...
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1answer
22 views

Thomas - Fermi screening

I read in Ashcroft & Mermin's Solid State text that for the Thomas-Fermi approximation to be applicable, the external potential needs to be "slowly varying," What does it mean for a function (in ...
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1answer
81 views

Compute distance between planes in a crystal

I want to compute the distance between two (111) planes in a cubic crystalline structure, in order to do some computations involving Bragg reflection. I have a sketch of which the (111) planes are, ...
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0answers
29 views

Spin wave theory for 1D spin systems

In general, when one performs spin-wave theory, he has to assume some kind of long-range ordered state and perform spin-wave theory (using for instance Holstein-Primakoff bosons) around that state. ...
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94 views

Fermi Energy Variation

What would be a good Internet link that would properly explain Fermi Energy? How does the Fermi Energy of a material vary with external influence, such as doping of the material, and applied ...
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1answer
63 views

Cellular structure in solid phase detonations

For gaseous and liquid detonations, the detonation propagates by the energy released at the triple-points which form a cellular structure. This structure is traced using a soot foil during ...
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37 views

Chirality of Weyl Semimetal

For Weyl semimetal, the effective Hamiltonian reads: $$H=E_0 \mathbb{1} + v_0 \cdot \mathrm{q} \mathbb{1}+\sum_{i=1}^{3} \mathrm{v}_i \cdot \mathrm{q} \sigma_i$$ Why is the chirality given by ...
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44 views

Evaluating low-temperature dependence of the BCS gap function

How does one go about evaluating the behavior of the BCS gap $ \Delta = \Delta(T) $ for $ T \to 0^+ $ under the weak coupling approximation $ \Delta/\hbar\omega_D \ll 1 $? In Fetter & Walecka, ...
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30 views

Sum of Green's functions in Condensed Matter

I am working on the Ginzburg-Landau model for Charge density waves, and I am carrying out the sum of Green's functions to calculate the terms in the GL model. I have the following question: Is the ...
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1answer
25 views

Mapping a continuum XY model to a discrete one

A low energy expansion of a system I am currently investigating is described by this XY-like model: $$ H_1 = \int_0^\beta \mathrm{d} \tau \int_{\left[ 0, L \right]^2} \mathrm{d}^2 x \left( J \left( ...
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1answer
96 views

$Z_2$ topological insulator: odd vs. even number of edge state pairs

I am having trouble in understanding why in $Z_2$ topological insulators odd number of Kramers' pairs on one edge are protected by time reversal symmetry against elastic backscattering while even ...
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266 views

Do all the electrons form Cooper pairs at absolute zero?

At $T=0K$, do all the electrons form Cooper pairs, or just the electrons near the Fermi Surface do?
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1answer
46 views

Ground state Phase Diagram of Bose-Hubbard Model

The Hamiltonian of Bose-Hubbard model reads as $$H=-J\sum\limits_{<i,j>}b_i^{\dagger}b_j+h.c.+\frac{U}{2}\sum\limits_{i}n_i(n_i-1)-\mu\sum\limits_in_i~~~~~~~~~(1)$$ For this we plot phase ...
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38 views

What kind of free energy do we use for a superconductor in a magnetic field?

My reasoning is as follows (using Gaussian units): Start from the second law: $$dU=TdS+dW,$$ where $dW$ is the work done by the magnetic field. To derive $dW$, we consider a solenoid with current ...
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0answers
15 views

Excitations of a quantum spin-liquid

I have a simple (yet perhaps profound ?) question related to the physics of quantum spin liquids (QSL). These states of matter are "defined" as state that do not break any symmetry of the Hamiltonian ...
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1answer
106 views

Superconductivity in graphene with spin orbital coupling, is it proper to let the order parameter on two sub-lattice equal?

I am reading this article: Edge superconducting correlation in the attractive-U Kane-Mele-Hubbard model. Considering just the first part of the article, where a negative-U Hubbard model with the ...
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1answer
130 views

How to derive electron number equation of Bogoliubov Hamiltonian using thermodynamic relations.

My question arise from this article: Edge superconducting correlation in the attractive-U Kane-Mele-Hubbard model. I will describe my question in detail so that you might not need to look into that ...
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3answers
200 views

Distinguishable, Indistinguishable Paramagnetic Ideal Gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...
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1answer
28 views

Why does proximity to a superconductor open a gap in the surface states of topological insulators

I have read in many places that the gapless surface states of 3D topological insulators are robust to perturbations which do not break time-reversal symmetry. I have recently also seen many papers ...
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1answer
269 views

Donors/Acceptors in Metal Oxides

Can anyone explain to me why most articles describe chromium as an acceptor in titanium dioxide? In TiO2, titanium has the charge state Ti$^{4+}$ and oxygen has the charge state O$^{2-}$. When Cr ...
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2answers
200 views

Mean field theory = large-N approximation?

Wikipedia entry of 1/N expansion (or 't Hooft large-N expansion) mentions that It (large-N) is also extensively used in condensed matter physics where it can be used to provide a rigorous basis ...
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1answer
50 views

Quasi-particle and quasi-hole excitations of Laughlin states and generalization of Laughlin states

The Laughlin wave function at filling fraction $\nu=\frac{1}{m}$ is \begin{equation} \Psi_m=\prod_{i<j}(z_i-z_j)^m e^{-\sum|z_i|^2/4l_B^2} \end{equation} It is claimed in section 7.2.3 of Wen's ...
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1answer
36 views

SPTs and systems with Topological Order

I am an undergrad interested in Condensed Matter Theory. Particularly topological phases and systems exhibiting topological order. A potential research advisor doing a lot of work in Symmetry ...
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26 views

Is that possible to derive Landau-Fermi liquid theory from microscopic equation?

The question arised from reading Wen's book "Quantum Field Theory of Many-body Systems (Oxford 2004)" p204 To appreciate the brilliance of Landau-Fermi liquid theory, let us look at the ...
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4answers
425 views

How does the speed of electrons change around a circuit?

I have been thinking about ways of teaching electronics and I'm wondering if the following is true... For starters, when we talk about voltage as energy per unit charge, is this energy manifest ...
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1answer
81 views

Phonon-phonon-interaction as higher order terms in the potential

Is there a simple way to understand why phonon-phonon-interaction is described by higher order terms in the potential? I mean: Having a quadratic potential is essential for the definition of the ...
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0answers
62 views

What does “optical conductivity” mean?

Does it just mean "AC electric conductivity"? If so, why have a special name for it, and why mention optical specifically? The wikipedia page on it is very sparse. This (warning, PDF) document just ...
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25 views

Ising formulation of the graph isomorphism problem

Context I have been going through Ising formulations of many NP problems by Andrew Lucas. In section 9 on page 22, the author gave an Ising formulation of the graph isomorphism problem. Here I ...
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1answer
47 views

How does band gap vary with the cell volume?

How does band gap vary with the cell volume? is there a relation? If the volume is compressed, the interaction between atoms would be more, therefore the perturbation is higher hence the splitting ...
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1answer
166 views

Does the low-energy gauge structure depend on the choice of $SU(2)$ gauge freedom?

The starting point and notations used here are presented in Two puzzles on the Projective Symmetry Group(PSG)?. As we know, Invariant Gauge Group(IGG) is a normal subgroup of Projective Symmetry ...
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46 views

Question about bosonization method

I have a question about bosonization method used in 1D system. Generally the bosonized field is assume to the following form \begin{equation} \psi = e^{i\phi}, \quad \phi = \phi^\dagger ...
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1answer
56 views

Why can't a dislocation terminate in the bulk?

We are told that they can only terminate on surfaces, grain boundaries or other dislocations but we are not told why they can't terminate inside the crystal.
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2answers
268 views

Quantum to classical mapping: quantum criticality and path integral Monte Carlo

I'm trying to understand the connections between quantum models in d dimensions and classical models in (d+1) dimensions within two, possibly related, contexts: (i) in path integral monte carlo, the ...
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1answer
70 views

can gapped systems have gravitational anomalies?

The question is in the title. If it is possible, what are some examples of gapped systems--either quantum field theories or condensed matter systems--which exhibit some kind of anomaly when coupled ...
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1answer
30 views

Plasma Treatment of LaAlO3: Surface Roughening

I'm trying to understand something I've observed in exposing LaAlO3 substrates to an oxygen plasma (yielding atomic oxygen). In literature, these substrates are frequently "cleaned" in a oxygen rich ...
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1answer
126 views

Do indirect optical transitions “cool” the material a little?

So I'm reading in Ashcroft and Mermin about indirect optical transitions: So, a photon comes in, and it only excites the electron across the indirect band gap if a phonon with the appropriate wave ...
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1answer
31 views

Atomic physics - lattice energy

Question: Why is ionic lattice energy inversely proportional to the radius of the atom? Most heterogeneous covalent molecules are polar to some extent. The degree of polarity, or the dipole moment, ...
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3answers
653 views

What observables are indicative of BCS Cooper pair condensation?

What observables are indicative of BCS Cooper pair condensation? "Thought" experiments and "numerical" experiments are allowed. This question is motivated by the question Has BCS Cooper pair ...
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1answer
94 views

A formula in Sung-Sik Lee's paper

I want to ask if anyone has gone through the derivation of the second equality in the following formula which comes from http://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165102.
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2answers
67 views

Question about Landau's phase transition theory

I have a question about Landau's theory of quantum phase transition. In his model, the free energy is assumed to be \begin{equation} F = f_0 + \alpha (T-T_c) \Delta^2 + \beta \Delta^4 ...
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1answer
89 views

Is diffraction through an aperture similar to diffraction by a plane of atoms?

I'm asking because I have a problem asking me what the diffraction pattern would be if instead of spherical atoms I'd have triangular atoms. I can't find anything about this in my X-ray diffraction ...
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1answer
26 views

Neutron Diffraction Device

I was just wondering if we have a beam of neutrons, lets say of various energies meeting or colliding with a powder of monoatomic crystallites, what would happen to the neutron beam and the energies ...
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47 views

Why is the Hubbard model written down so late?

It is just the tight binding model plus on-site interaction. What prevented people from arriving at the Hubbard model?
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116 views

Does electron-electron scattering contribute to resistivity?

Electron-phonon and electron-defect scattering clearly contributes to resistance, but pure electron-electron scattering conserves the total momentum (and energy) of all the electrons. Then, how is it ...
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1answer
36 views

Capillary action meniscus height in a tube fitted inside another tube?

I was thinking about how would capillary action change in a tube (classic example) and in a tube fitted inside another tube (considering water as the liquid involved). Height of liquid column: ...
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2answers
275 views

Momentum change in colisions (Drude Model)

A particle suffers elastic colisions with scattering centers with a probability of colision per unit time $\lambda$. After a colision the particle is in a direction caracterized by a solid angle ...