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Exchange interaction is an addition to other interactions between identical particles caused by permutation symmetry. This addition is a result of specific form of multi-particle wave function. It gives no contribution to Hamiltonian unlike "usual" interactions but appears as an additional term in equations for single-particle wave functions (e.g. Hartree-...


3

In earlier DFT studies of ferroelectric materials, GGAs such as PBE were avoided as they tended to exaggerate the ferroelectric distortion. Instead, LDA calculations were performed and an artificial (offset) pressure was applied to compensate for LDA otherwise overestimating lattice constants Philippe Ghosez, Javier Junquera: cond-mat/0605299 "First-...


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The contribution of the $4sp$ bands to the total moment in iron, nickel and cobalt is quite negligible compared to that of the $3d$ electrons. It is also oscillating as a function of the electron wave vector. Several experiments show that there are effects: hyperfine effects (Mössbauer), NMR (Knight shift) and spin-dependent STM show that $s$ orbitals are ...


2

Interactions have to conserve angular momentum and spin is angular momentum, so trivially "Yes". In your hypothetical with two uncharged (I assuming you mean the electric charge here) particles there will be no electromagnetic repulsion because there will be no electromagnetic interaction. But Hartree-Fock is used for interacting systems...


1

Hole is not a particle. Microscopically, hole is a quasiparticle perturbation of many-electron system. And what is called electron in semiconductors is also a perturbation in the same many-electron system. Exchange interaction within this many-electron system results in a complicated interaction between quasiparticles which live there. Which is called ...


1

Materials with localised moments may exhibit ferro-, ferri- or antiferromagnetism. Depending on crystal symmetry magnetic frustration may also occur. Materials with delocalised electrons can display itinerant magnetism under suitable conditions.


1

A lot of work has been done since the 1984 review by Moriya and Takahashi, both theory and experiments. On the theoretical side, calculations have been refined a lot. The effect of the on-site $dd$ correlation energy $U$ was taken into account first by LSDA+U, then by LSD+DMFT (a dynamic mean field theory), for example this paper from 2001 about high ...


1

For ferromagnetic materials like iron the cause of alignment of the individual atomic magnetic moments is the direct exchange interaction, that is number 3. This is the mainstream explanation as given in the Feynman lectures ( https://en.m.wikipedia.org/wiki/Ferromagnetism). Fe is definitely not an itinerant magnet. The electrons responsible for the ...


1

Your are correct in saying that screening is a major reason for long-range Coulomb interaction effects to appear as short-range interactions, for example, in metals. The intuitive picture is that an individual electron is surrounded by a 'screening cloud' formed by the surrounding electron gas. This collective object is called a quasi-electron. These ...


1

If you reversed the directions of the two spins, the spin part of the wavefunction is a singlet and it is anti-symmetric. The total wavefunction (spatial * spin) needs to be overall antisymmetric for fermions, which means in your case the spatial part of the wavefunction is symmetric - there is the highest probability of finding the particles at the same ...


1

The exchange interaction includes not only a term reflecting the repulsive Pauli interaction, but also a correction for the electron self-energy of the Hartree equations. That is because the electron density that is used to calculate the Hartree potential includes the density of the orbital of the electron under consideration as well as all the other ...


1

If you're asking about the principal contribution to the repulsive part of the interaction between two hydrogen atoms as they get close together, it's easy: it's almost exclusively driven by the electrostatic repulsion between the two protons. When the protons are closer together than one angstrom, there is very little electron charge between the two protons,...


1

The column vector notation can be used to express the result of exchange of spatial or spin arguments of the psi function, if we adopt this convention: if the symbol is on the left side of the tensor product, it belongs to particle 1, if it is on the right side, it belongs to particle 2. This means that when the symbol $\psi_n$ is moved from the left ...


1

I would normally approach this by flipping your initial formulas: take the conjugate of $$ \langle \mathbf r_1,\sigma_1,\mathbf r_2,\sigma_2| P_{12}^\mathrm{space} |\psi\rangle = \langle \mathbf r_2,\sigma_1,\mathbf r_1,\sigma_2|\psi\rangle $$ to get $$ \langle \psi|P_{12}^\mathrm{space}|\mathbf r_1,\sigma_1,\mathbf r_2,\sigma_2\rangle = \langle \psi|\mathbf ...


1

The argument for the temperature to go up would be that the conversion of mass to energy produces some sensitive heat which increased the average temperature of the system. Correct. You're converting energy in one form to energy in another form. A simpler example would be burning wood inside the system. But is that violating the first law - as at ...


1

All half integer particles are antisymmetric by the virtue of the spin-statistics theorem, which states that half integer particles must follow Fermi-Dirac statistics. As for your doubt concerning the spatial part of the wave function is symmetric, the net wave function comprising of the spin part and the spatial wave part must be antisymmetric, and this ...


1

Let's take a usual non-relativistic many body bosonic (there is not much difference in taking bosons of fermions, at least for the purpose here) Hamiltonian for $N$ particles of mass $1/2$ on $L^2_{s}(\mathbb{R}^{Nd})$ (where $s$ stands for symmetric functions, wrt exchange of particles): $$H=H_0+H_{int}=\sum_{j=1}^N -\Delta_{x_j}+\frac{1}{N}\sum_{j<i}V(...


1

Neutrino can interact only by exchange of electroweak boson. So in each reaction with neutrino $W^\pm$ or $Z$ bosons must be involved. Also, Standard Model neutrino is assumed to be massless, so there is defined handedness: neutrino is left-handed and antineutrino is right-handed. Consequence of it is that left-handed neutrino will interact only with ...


1

The short answer is that Feynman diagrams definitely do not represent the trajectories of particles in spacetime; they are simply a way of writing down formulae that would otherwise be pretty hard to remember. The long answer is below. Quantum Field Theory, which is the mathematical formalism behind particle physics, dictates that when we scatter two ...


1

"The nonrelativistic theory has no necessary relation between spin and statistics, as you can understand from the example of a nonrelativistic 2d spinless fermion (imagine 2d confined electrons with a huge magnetic field in the z-direction which forces the spin to always be along the z-axis). The electrons behave as spinless particles with respect to the 2d ...


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