Questions tagged [exchange-interaction]
An effective, but not actual, force used for effective description of geometric effects between identical particles, such as the apparent repulsion between fermions due to the Pauli principle.
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Are combined fermion wavefunctions still antisymmetric after wavefunction collapse?
If we have two electrons in a state $|\psi\rangle=\frac{1}{\sqrt2}[|\uparrow\downarrow\rangle+|\downarrow\uparrow\rangle]$ and we measure the spin of the first electron to be up, does the wavefunction ...
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Can a photon's angular momentum couple to an electron spin, to cause a spin-flip (thus allowing intersystem crossings)?
Been reading up on intersystem crossing and have gotten rather confused by:
a photon possesses an angular momentum of $h/2\pi$ so it can couple to an
electron spin and in principle induce any ...
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Could the Fermi statistic be a force?
I'm aware that, according to the Pauli principle, identical fermions obey the Fermi-Dirac statistics, so they don't occupy the same state because they just can't, it's simply how they behave. I'm ...
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Fourier Transform of the spin flip green function in s-f model
i have to compute the spin-flip Green function when the band occupation $n$ and temperature $T$ are zero
$$
\langle\langle
\hat{S}_{i}^{\uparrow}
\hat{a}_{i,\uparrow}
;\hat{a}^{\dagger}_{j,\...
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The Hund's J - Why can this be quantified?
I was reading on the the implementation of Hubbard 'U' in Density Functional Theory. The Hubbard 'U' can be thought of as a parameter that accounts for the on-site electron-electron interactions in ...
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Coupling of two spin half particles
If there are two electrons coupled by interaction having hamiltonian H=A*S1*S2 where S1 and S2 are spin angular momentum operators of two electrons, we know we have four possible eigenstates for the ...
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A detail in Bougliobov theory of superfluidity
I'm currently studying superfluidity following Mahan's book and there's a detail I'm not understanding.
The exchange energy of the fluid (boson gas) in the normal state is written as
$\begin{aligned}...
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What's the typical value of exchange field?
I have a thin strips of permalloy and I would like to generate a 90 degrees domain wall parallel on the strip xy plane (the thickness is along z), I know that one way is to use exchange bias coupling, ...
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How to calculate the Fock exchange interaction self-energy of a system in momenttum space
I have a Hamiltonian in the momentum space which has a strong non-local electron-electron interaction.
I know that I have to find its corresponding exchange self-energy and solve the Dyson equation ...
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1answer
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Does the (non-)collision of two fermion wave packets demonstrate that there is no exchange “force”?
In the paper "Quantum statistics: Is there an effective fermion repulsion or boson attraction?" by Mulling and Blaylock (2003), it is claimed that
We can demonstrate there is no real force due to ...
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Exchange has closed form also in DFT?
I have heard from my lecturer that in the context of DFT, the exact exchange energy has a known closed form, even though it is not a functional of the density. I have been trying to figure out what ...
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Anti-mirror subspace geometry within multipartite Hamiltonian space
The exchange-symmetry property demands that a two-system wavefunction satisfy $\psi^{(2)}_{[i]_M [k]_N} =- \psi^{(2)}_{[i]_N [k]_M}$. One then takes the density matrix to be over the entire 2-space as ...
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DFT: When would one use a LDA over a GGA method?
Computationally using Density Functional Theory (DFT), is there any examples where Local Density Approximation (LDA) would be preferred over using Gradient Generalized Approximation (GGA) methods for ...
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Why don't all elements with unpaired electrons become ferromagnetic?
As a necessary condition, ferromagnetism in elements requires the existence of unpaired electrons. However, all elements with unpaired electrons are not ferromagnetic, e.g., metals such as aluminium ...
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Which mechanism causes ferromagnetism in iron?
There are at least three different mechanisms which can give rise to ferromagnetic order in iron.
First is due to the band electrons called band magnetism or itinerant magnetism which is an exchange ...
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1answer
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Why an insufficient overlap cause vanishing exchange interaction?
Why should the exchange interaction vanish if the atoms do not have sufficient overlap in their overfunctions? For exchange interaction not to vanish, the only requirement seems to be that the ...
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1answer
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Symmetry in Fock-space 2-body interaction
The simplest two body interaction term for fermions is
$$H = \sum_{ijkl} U_{ijkl} a_i^\dagger a_j^\dagger a_k a_l$$
and I'm trying to determine the symmetries on $U$. Unfortunately I keep getting ...
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1answer
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To get short-range interaction from long-range interaction
Interactions in Condensed matter systems are almost exclusively the electromagnetic interactions which are long-range. But it often gives rise to short-range interactions in systems e.g., exchange ...
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Exchange Interaction Time Evolution
This is a hypothetical based on a result in Griffiths (which is my level of QM understanding). In it, he derives an "exchange force" - two particles states A and B, a two-particle state composed of ...
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Exchange stiffness for HCP
I am studying the exchange interaction, which can be described with the Heisenberg Hamiltonian:
$\hat{H} = -\sum_{i,j}J_{ij}\hat{\mathbf{S_i}}\cdot \hat{\mathbf{S_j}}$
In the framework of constant ...
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Triplet states and the Hund's rule in identifying the ground state configuration (open shell)
I referred to some of the questions about Hund's rule on StackExchange, such as this for example, but still wasn't able to have my question resolved.
(the wikiepdia page has $E_{ex} = C - \frac{1}{2}...
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Heisenberg exchange term in phenomenological nuclear potentials
In phenomenological nucleon-nucleon potentials there are three exchange forces terms:
$V_M=V_M(r) P_{x}$ : Majorana exchange (exchange of position coordinates, $P_{x}$ is the operator of exchange of ...
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1answer
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magnetic and electric interactions in atomic level
From what I understand Van der Waals (VDW) forces are the primary source of inter-molecular interaction. There are three different possible origins for van der Waals forces: permanent dipole-permanent ...
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particle exchange versus spin
Before us are two half-integer-spin particles. Their spin directions are parallel, aligned with the line connecting their locations. They are indistinguishable but for the fact we have affixed the ...
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Attractive exchange energy and correlation energy of different spin in DFT
In DFT, why do most texts ignore/don't mention the attractive exchange "force" between two antiparallel spins electrons?
The repulsive "exchange" force of two same spins electrons are always ...
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Why does exchange lower energy with increasing electron density in Hartree-Fock
The Hartree-Fock equations include a term for the exchange interaction, which is usually explained as a repulsive force due to the Pauli exclusion principle. (It says so right in the description for ...
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Precise definition of exchange
I was wondering about how could one define the exchange interaction in the most general way.
I am aware of the definition of exchange for the Coulomb interaction, which looks basically like $\int \...
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1answer
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Understanding interatomic potential between hydrogen
Interatomic potential is usually described as consisting of two parts: one attractive and one repulsive, where the repulsive one prevails at short distances.
The repulsive part is typically ...
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2answers
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Defining the exchange operator $P_{12}$ without reference to dummy variables
Let $\Psi \in \mathcal{L}^{2}(\mathbb{R}^{6}; \mathbb{C}^{2}\otimes\mathbb{C}^{2})$ so that $\Psi$ represents the state of two interacting fermions.
Traditionally, we define the exchange operator $P_{...
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Is there an exchange of electrons between two Cooper pairs in the BCS state?
The BCS state is
$$\left|\psi\right>=\prod_k \left(u_k +v_k c_{k\uparrow}^\dagger c_{-k\downarrow}^\dagger\right)\left|0\right>$$
which pairs all the electrons into Cooper pairs. The ...
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1answer
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Conduction electrons in ferromagnetic materials
As I understand it, in a ferromagnetic material unpaired electrons on the atomic sites interact (exchange interaction) with nearest neighbours, aligning the moments and producing the magnetisation ...
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Can the average temperature increase in a closed adiabatic (isolated) system?
Assume a closed and adiabatic (isolated) system (no energy or mass transfer at the boundaries) then is it possible for the average temperature to change (increase or decrease)?
Corollary:
1. If yes ...
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Why does the weak interaction not conserve the flavour quantum number? [duplicate]
The weak interaction, in contrast to the strong and electromagnetic, is the mediator of the decay of the strange quark, purely because the weak interaction is 'allowed' to break conservation of ...
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Could someone explain how antisymmetric position states and symmetric spin states work in an atom?
I'm reading Griffiths QM 2nd ed and he talks about how all fermions are antisymmetric in nature. Later he talks about how exchange forces with identical particles. He states that because fermions are ...
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Is Blatt-Weisskopf's treatment of nuclear forces still relevant today?
As in the title, is the treatment of nuclear forces by Blatt and Weisskopf, as in Chapter III of "Theoretical Nuclear Physics", still relevant today, especially with regard to the role of exchange ...
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463 views
many body wavefunction and exchange correlation
Everywhere I ready about HF or DFT the term exchange correlation functional comes up. I have a couple of fundamental questions about these:
1) Books say that the correlation energy is the difference ...
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Mathematical form of the de facto repulsive “force” associated with the Pauli Exclusion Principle [duplicate]
One of the principles of General Relativity is that test objects follow a geodesic unless otherwise acted upon by a force. From this perspective, it is clear that physicists, consciously or ...
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Can both types of W boson be responsible for a neutron-neutrino interaction?
My textbooks lists the exchange particle for a neutron-neutrino interaction as being the W- boson. Is this the only option, or can it also be a W+ boson? Nothing jumps out at me that would suggest it ...
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1answer
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Outside of string theory, can exchange particles be understood as being one-dimensional?
I'm pretty new to quantum, without any formal education therein, so forgive my general layman ignorance when I ask how it is that point-like exchange particles can be modeled in Feynman diagrams as ...
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spin conservation in exchange polarization process
Exchange polarization is the process by which spin is transferred between an electron beam and a system of polarized atoms (with a single valence spin). The process occurs as a result of the Pauli ...
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Exchange operator in terms of rotation operator
I have studied about exchange operators and rotation operators and I know that an exchange between 2 particles in a combined state is the same as rotating each particle 180 degrees (according to http:/...
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1answer
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Is there a point interaction model of the electron?
Is there a point interaction model of the electron? Is there a point interaction model of the electron? I imagine something like $\propto(\bar \psi\psi)^2$ (edited). Is such a thing in use?
Since I ...
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1answer
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Does spin alone have any effect on the physical interactions of particles?
In Hartree-Fock theory the time-independent electronic energy of a single (restricted) determinant electronic wavefunction consists of one electron terms, $h_{ii}$, Coulomb interaction energies, $J_{...
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Simple description of exchange interaction?
What is a simple bare-bones description of exchange interaction between two electrons?
For instance, it seems to me that the only necessary ingredients are the Coulomb interaction and the requirement ...
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1answer
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electron hole exchange
If exchange is an interaction between indistinguishable particles, how can there be an exchange interaction between electrons and holes? I see mention of e-h exchange often in the literature.
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Are all electrons identical?
Why should two sub-atomic (or elementary particle) - say electrons need to have identical static properties - identical mass, identical charge? Why can't they differ between each other by a very ...
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Example of a wavefunction that cannot be represented by a single Slater determinant
I know that in general, interacting fermions cannot necessarily be described by a single Slater determinant. Can anyone provide a simple example of a state that has no such representation?
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How would Kohn-Sham orbitals differ from 'true' elecron wavefunctions?
How would the non-interacting electron orbitals from a perfect DFT solution for a given potential shape differ from the 'true' electron wavefunctions? Or can you only really talk about the total ...
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existing bounds on maximum density achieved by a Bose condensate
As we know, fermions are subject to exchange interactions that limit the densities they can achieve. However bosons (simple or composite) are not constrained by this, which implies physical phenomena ...
