[HN Gopher] What are Majorana zero modes?
___________________________________________________________________
What are Majorana zero modes?
Author : ColinWright
Score : 66 points
Date : 2025-02-19 19:54 UTC (4 days ago)
(HTM) web link (mathstodon.xyz)
(TXT) w3m dump (mathstodon.xyz)
| prof-dr-ir wrote:
| > there's a chance neutrinos are Majorana particles.
|
| Pet peeve: don't say "are Majorana particles", say "have a
| Majorana mass term".
|
| All spin 1/2 fermions in four spacetime dimensions can be
| constructed from the chiral (or Weyl) representation. A Dirac
| fermion is two independent chiral fermions. A Majorana fermion is
| just a chiral fermion written in a funny way. And people saying
| that chiral fermions cannot have mass are lying. (/rant)
|
| By the way, a nicer explanation for the neutrino masses is the
| so-called seesaw mechanism:
|
| https://en.wikipedia.org/wiki/Seesaw_mechanism
|
| In this wiki article the Majorana mass is denoted B'. However, as
| the article explains, it must vanish by gauge invariance in the
| standard model.
| sigmoid10 wrote:
| > And people saying that chiral fermions cannot have mass are
| lying
|
| People usually say that in the context of the vanilla Standard
| Model. So far, experiments say we don't see right handed
| neutrinos and we also don't see lepton number violation. So we
| can't have masses there. This stuff only works if you start
| with the assumption that the Standard Model is an effective
| field theory and introduce higher dimension operators. Or if
| you go full BSM. The most simple expansion of the standard
| model that allows for Neutrino oscillations precisely needs
| them to be (pure) Majorana particles. Though that doesn't
| explain their weird masses as you say and the more complex
| expansion that results in seesaw (which adds a Dirac mass)
| seems a bit more natural. So your argument is mostly a case of
| missing context.
| noone_important wrote:
| I kind of disagree on your statement about lepton violation.
| The standard model predicts lepton violating processes
| (sphalerons). The true symmetry of the standard model is B-L.
| Of course you are right, that these topological effects will
| not lead to majorana mass terms.
| sigmoid10 wrote:
| Well, while sphalerons theoretically break B+L in the non-
| perturbative regime, they are exponentially suppressed at
| the energy level of our colliders. At the same time,
| irrelevant operators that also violate it are suppressed by
| the GUT scale. So even if you take the minimal Standard
| Model at face value, you're out of luck finding any sign of
| the violation either way. But if Neutrinos get Majorana
| masses, that would be an _additional_ explicit violation at
| the perturbative level. That would be something we can
| directly observe, as in neutrinoless double beta decay.
| noone_important wrote:
| I agree, that neutrinoless double beta decay would be
| incredibly interesting, but it is very speculative (and
| depending on the neutrino mass hierarchy not really
| falsifiable).
|
| My original point was just that lepton number is not a
| good symmetry as it is broken by rhe chiral anomaly,
| which is not speculative at all. Of course, the sphaleron
| effects are negligible in collider settings, but for
| cosmology they are crucial and might be indirectly
| observable.
| cmcconomy wrote:
| Welcome to the era of Majoranal Computing
| hackandthink wrote:
| https://scottaaronson.blog/?p=8669
|
| "Q2. What is a topological qubit?
|
| A. It's a special kind of qubit built using nonabelian anyons,
| which are excitations that can exist in a two-dimensional medium,
| behaving neither as fermions nor as bosons. The idea grew out of
| seminal work by Alexei Kitaev, Michael Freedman, and others
| starting in the late 1990s. Topological qubits have proved harder
| to create and control than ordinary qubits."
|
| https://en.wikipedia.org/wiki/Anyon
| random3 wrote:
| The more relevant bit, beyond the paper
|
| > I foresee exciting times ahead, provided we still have a
| functioning civilization in which to enjoy them.
| dr_dshiv wrote:
| Aren't the 0 and 1 states of a qubit basically the zero mode
| (ground state) and first mode of the quantum system? So, there
| can be superposition of the modes, but when measured (with an EM
| pulse), it either re-emits the pulse (producing a 1) or absorbs
| it (producing a 0). Is that correct?
|
| I recently learned there are qubits that have more than 2
| modes... like a qutrit, with 3:
| https://en.wikipedia.org/wiki/Qutrit
___________________________________________________________________
(page generated 2025-02-23 23:01 UTC)