Questions tagged [quantum-spin]
Fundamental characteristic property of particles which together with orbital angular momentum acts as the generator of rotations and which doesn't have a classical equivalent but is sometimes compared to and contrasted with classical intrinsic angular momentum.
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Prove that in Bell's inequality $\langle{\Psi}|\left(\bf{\sigma}\cdot\bf{a}\right)\left(\bf{\sigma}\cdot\bf{b}\right)|{\Psi}\rangle=-\bf a \cdot\bf b$
I am trying to understand how the correlation function in John Bell's paper on EPR is derived for a spin singlet state $|{\Psi}\rangle$. This is defined to be
$$
\langle{\Psi}|\left(\bf{\sigma}\cdot\...
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Spin (helicity) and polarizations of photons: are they secretly related?
Edit Circularly polarized photons have $$\textbf{S}\cdot\hat{\textbf{p}}=\pm \hbar\tag{1}$$ and it also satisfies $$\boldsymbol{\epsilon}\cdot\hat{\textbf{p}}=0\tag{2}$$ where $\textbf{S}$ is the spin,...
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Linear spin wave theory applied to 2D Heisenberg antiferromagnet
I have recently studied the Holstein-Primakoff transformation, and saw how it can be used to diagonalize the Heisenberg Hamiltonian and find the magnon dispersion relation. For the antiferromagnetic ...
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Does the $\bf{1+3}$ representation of $SU(2)$ also represent $SU(2)\times SU(2)$?
I'm a bit confused about this following issue concerning representations of $SU(2)$.
Denote by 1 the 1-dimensional representation of the group $SU(2)$ (=the spin 0). Similarly, denote by 2 and 3 the ...
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Understanding Quantum Spin as a Vector And Spin Operators
I just started learning quantum physics and there is a particular notion confusing me.
While reading McIntyre book, he suggests I find the matrix representation of the $S_n$ operator, which is the ...
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Mach's Principle and spin angular momentum
According to Mach's Principle, angular momentum (as in the Newton bucket experiment) is relative to the overall mass distribution of the universe, or perhaps some other characteristic of the universe'...
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Why all materials are not quantum materials, eventhough all materials work under principles of quantum mechanics?
Quantum materials are now an emerging field of study. I didn't actually understand the need for classifying materials as quantum materials and normal materials. Wave functions of electrons and their ...
AccidentalFourierTransform
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Can black holes interact with the weak force? (I.e., is this a reasonable expectation?)
This question is mostly about a strange seeming similarity that I've noticed between the nature of the weak force and the nature of black holes, which seems to imply that even some astrophysical black ...
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Why doesn't the spin-orbit coupling term in the Hamiltonian have to be Hermitian?
I am currently looking at a paper (C. Ortix, "Quantum mechanics of a spin-orbit coupled electron constrained to a space curve", Phys. Rev. B 91 (2015) 245412, arXiv:1504.00840) where spin-...
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Composite systems
Studying QM attracted my attention to the concept of a composite system. I erroneously thought, following classical reasoning, that a composite system can be i.e. a system formed by two qubits and ...
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Do particles remain entangled even after repeated measurements in different directions?
If we measure the spin of an electron along the $x$-direction and it turns out to be up then we know that upon measurement along the $y$-direction and in turn along the $x$-direction, the probability ...
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Comparison between two flavor neutrino oscillation and a system of up-spin and down-spin states of an electron?
In the system of up-spin and down-spin states of an electron, we can write a general state of electron at time $t$ as
$$\left|\psi(t)\right>=a\left|\uparrow\right>+b\left|\downarrow\right>,$$...
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Why nuclear spin is ignored in Stern-Gerlach experiment?
I can't sure what isotopes of silver(107 or 109) was used.
But Silver has non-zero nuclear spin since the number of proton and neutron are not even.
Since we use Silver atom not electron in SG ...
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Why do we think the graviton is not the photon?
Why couldn't the photon be the graviton? How sure are we that the photon could not fill the role of gravitons?
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How do you use gauge symmetry to describe measurement of spin up electron?
I have been reading about gauge symmetry and how it arised from special relativity and the interaction can be understood using economical model as an analogy, I know the grids represent space and ...
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Why must the electron's electric dipole moment (EDM) always be aligned with the spin?
The electron has magnetic dipole moment which points in the spin direction, which is relatively easy to understand because it mostly follows from the definition. However, why is it that the (possibly ...
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Interpretation of Ising model simulations
I've been working on numerically solving the Ising model in a study of phase transitions, but I'm having difficulty finding material to help me discuss the results. I'm studying spontaneous ...
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Suppose I give you $2^N$ functions that are eigenvectors of a fermionic $H$. How do I determine which function describes which spin configuration?
Consider the hamiltonian
$$
H = - \frac{1}{2} \nabla^2 + V.
$$
The potential $V : (\mathbb{R^3})^N \to \mathbb{R}$ is symmetric, so for each eigenvalue, there is an antisymmetric eigenvector. There is ...
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Hamiltonian of a particle in magnetic field squared
I'm trying to follow Tong lectures about Gauge Theories, but I think I'm doing some really stupid mistake.
At one point he takes the Hamiltonian for a spin $1/2$ particle in a potential as the usual
\...
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Are electron spin axis and magnetic moment axis fully aligned?
It is known that the electrons behave in magn. moment detectors experiments at 45 degrees non classically but quantum mechanically where the amount of spin up and spin down electrons in percentage is ...
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Supersymmetry beyond $D=11$ spacetime dimensions
Taking into account the higher spin theories, from which string theory is an effective field theory, I just wondering if there is something to do to extend supersymmetry to any dimension without any ...
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Forbidden transitions from triplet to singlet states in the deuteron?
The dipolar moment for the deuteron is
$$\vec{\mu}_{d}=\frac{\mu_{N}}{2 h}\left\{\left(g_{s}^{(p)}+g_{s}^{(n)}\right) \vec{S}+\left(g_{s}^{(p)}-g_{s}^{(n)}\right)\left(\vec{s}_{p}-\vec{s}_{n}\right)+\...
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Why is there this relationship between quaternions and Pauli matrices?
I've just started studying quantum mechanics, and I've come across this correlation between Pauli matrices ($\sigma_i$) and quaternions which I can't grasp: namely, that $i\sigma_1$, $i\sigma_2$ and $...
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The polarization summation for photons
I was interested to know how we can prove the summation polarization for photons which is $\sum\epsilon_\mu\epsilon^*_\nu\xrightarrow{}-g_{\mu\nu}$ for the process $e^-\gamma\xrightarrow{}e^-\gamma$???...
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Does the Stern-Gerlach experiment really suggest superposition?
The Stern-Gerlach experiment is often cited as evidence of quantum superposition and there are some very simple explanations like this one https://www.youtube.com/watch?v=hkmoZ8e5Qn0 in which spin on ...
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Time evolution of state in rotating $B$-field spin system
I'm given a state $|\psi(t)\rangle$ that solves the time dependent Schroedinger equation with the Hamilton operator $\hat{H}(t)$. $\hat{H}(t)$ describes a Spin-$\frac{1}{2}$ in a rotating magnetic ...
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What is the moment of inertia of a free electron?
Well, elementary particles have no moment of inertia $I$. But what is the nearest possible answer to the question for a free, spinning electron?
In general, one has a relation with spin $J$ given by
$$...
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Why is there a factor of $\hbar$ in the physicists' $\mathfrak{su}(2)$ Lie algebra?
The standard (mathematicians') basis for the $\mathfrak{su}(2)$ Lie algebra is:
$$X_j = -i\frac{\sigma_j}2$$
where $\sigma_j$ are the Pauli matrices. In physics, observables correspond to real numbers,...
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How can you prove that the squares of the expected values of the three components of spin sum to 1?
I am working through Leonard Susskind's The Theoretical Minimum: Quantum Mechanics. In this book a statement called the "spin-polarization principle" is introduced, which essentially states ...
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Why does a spinning nucleon generate a magnetic field?
I am trying to understand how NMR works, but I am not sure why a spinning nucleon produces a magnetic field. Is this a consequence of the quark structure inside?
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Why don't the electrons in a paramagnetic material precess around an external field?
When a paramagnetic material is placed in a strong external magnetic field, then you'll find that the magnetic momenta of the electrons in the material will align to the field, causing a net magnetic ...
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Are all gapless acoustic magnon modes essentially Goldstone modes?
We know gapless Goldstone mode appears when the system exhibits spontaneously symmetry broken. Does this means whenever we observe gapless acoustic modes it is Goldstone mode i.e. spontaneous symmetry ...
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What's the difference and relations between $SU(N)$ Schwinger boson and $CP(N\!-\!1)$ non-linear sigma model?
There are two ways when dealing with spin system(Heisenberg model): non-linear $\sigma$ model and Schwinger boson.
Non-linear $\sigma$ model
When taking large $S$ limit, the quantum fluctuation of ...
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$\rm SU(2)$ symmetry and rotation invariance
I've read in this paper (doi:10.1038/nature07871) that in the context of quantum mechanics, $\rm SU(2)$ symmetry leads to the conservation of spin polarization, or in other words invariance with ...
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In what sense are spin coherent states “classical”?
Spin coherent states are often introduced as "the most classical states of a finite-dimensional system", or as the analogous of coherent states of light for finite-dimensional systems. See e....
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Alternative classical explanation of the Stern-Gerlach Experiment?
Many questions have been asked on this site about the Stern-Gerlach experiment, but as far as I can tell this one hasn't. Does the following classical explanation of the SG experiment work?
Model ...
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Spin vector representation in an arbitrary direction $\hat{n}$
Take a spin $1/2$ particle with its spin pointing along $\hat{n}$ defined by
$$\hat{n}=(\sin{\phi}\cos{\theta},\sin{\phi}\sin{\theta},\cos{\phi})$$
We are measuring the spin along $\hat{n}$ and the ...
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Time reversal operator for general spin
Gross' QFT textbook states that spin-0, spin-1/2 and spin-1 fields transform as follows under a time reversal operation,
$$
\begin{align}
\mathcal T \phi(t,\mathbf x) \mathcal T^{-1} &= \eta_\phi^...
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In the field of spintronics, what does it mean to change the order of an (anti) ferromagnet using torque?
I have been reading statements like "Ferromagnetic (anti-ferromagnetic) order can be detected or changed electrically using spin-transfer (spin-orbit) torque".
What is the exact meaning of ...
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Where are current flowing in a permanent magnet?
We know that moving charges produce magnetic fields if then all elements have electron with some non zero angular momentum so all substances must be magnetic to some extend.But this does not happen. ...
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Expected Gaussian distribution on screen in Stern-Gerlach Experiment
In the Stern-Gerlach experiment, they used a beam of silver atoms travelling in z direction (which has valence electron in the 5s shell), so the electrons carry zero angular momentum. Now since they ...
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In the electron density, what exactly do you mean by $\sigma$ mathematically?
Suppose there is a many-body eigenvalue problem
$$
H(r_1,\cdots,r_n) = - \frac{1}{2} \nabla^2|_{r_1\cdots,r_n} + V(r_1,\cdots,r_n).
$$
This potential is symmetric and the hamiltonian does not depend ...
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Why Spin angular momentum effect (quantization) is observed only under varying magnetic field?
Is there some reason behind the appearance of spin effects only under the application of variable magnetic field.
I know that we need variable magnetic field to act force on charge particle with some ...
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Why, if photons have their spin in the same direction of the electrons, the formers will less likely be able to flip the spins of the latters
It's about the Goldhaber experiment, where the exercise I'm trying to solve is:
Photons are filtered according to their helicity thanks to the magnetic field. For a given
magnetic field, the electrons ...
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How does the coherence of a spin state relate to the physical concept of “coherence”?
In my textbook the coherence of a spin state $|\psi\rangle $ is measured by the quantity $|\langle \uparrow|\psi| \downarrow \rangle|$. The thing is that I am not sure how this quantity is related to ...
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What is the evidence (experimental observation) that elementary particles have spin angular momentum?
From what I have read here, the concept of spin is attributed to a calculation based on a mathematical model using quantum mechanics. For example,
How can a particle with no size have angular momentum?...
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An electron has no known internal structure, does that imply it has an unknown one?
I'm currently reading Alonso and Finn's Electromagnetism book.
It explains that the spin contributes to the magnetic moment and is somewhat comparable to a rotation of the particle around its own ...
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What's the solution of EPR paradox? [duplicate]
I know that Einstein said that if quantum entanglement is true, then the information of one particle state would be sent to the other particle faster than light which contradicts absolutely the ...
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What is a VLEED-type detector?
I know there are two kinds of detectors which resolve spin polarization in spin-resolved ARPES experiments. one is a Mott-type detector and the other is a VLEED-type detector. the former uses the ...
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How do the different ways to map spins on bosons differ?
There are multiple ways I have found to map spin operators $S^+=S_x+iS_y,\quad S^-=S_x-iS_y,\quad S_z$ onto bosons.
most trivial: a spin-1/2 system is equivalent to bosons with hard-core interactions ...
