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Questions tagged [discrete]

Discrete means as opposed to continuous. For instance, people may ask questions about discrete electric charges, discrete spacetime, discrete energies, etc. If discretization is vital/essential to the question, then tag it with this tag.

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Dirac's quantisation condition and non-quantised charge

After some time searching for a convincing demonstration of the Dirac quantisation condition, I've finally come across not one but three of them in David Tong's book: Gauge Theory. Nonetheless, it all ...
Lagrangiano's user avatar
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2 votes
1 answer
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Is energy contained in/transferred by light really discrete or is it continuous? [duplicate]

I don't really understand the wave-particle duality of light.I don't really understand the idea of photon, The idea of photon that is generally taught is that it is a fundamental unit of light with ...
Seeker's user avatar
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3 votes
2 answers
190 views

Epidemic spreading model

I'm studying a model in the field of complex systems regarding the epidemic spreading. The model is the susceptible-infected model, i.e., there is a population of N subjects and each of them can ...
Salmon's user avatar
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2 votes
1 answer
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Abelian vs non-abelian discrete symmetries in neutrino physics

I was reading about the parametrization of the PMNS matrix and stumbled upon an article of Serguey Petcov$^1$ about discrete flavour symmetries. It endeavors to see if there is a pattern induced by a ...
AZ0409's user avatar
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1 vote
0 answers
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Elasticity theory: homogeneous deformations of a perfect lattice

I want to understand how the macroscopic (linear) elasticity theory emerges from the microscopic properties of matter. My question is about the model of the "perfect lattice", which is used ...
Plemath's user avatar
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1 answer
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Discrete to continuous quantum operator

Let's say that we have a discrete lattice with $N$ sites. Let's label the site by the index $i$. Let's say that we have the operators $a_i$ and $a_i^\dagger$ which correspond to the creation and ...
Stallmp's user avatar
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1 answer
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Clarification on Transforming from Discrete to Continuous Systems in Quantum Mechanics [closed]

In Quantum Mechanics: A Paradigms Approach by David H. McIntyre, a transformation from discrete systems to continuous ones is provided, outlined as follows: $\vert\psi\rangle \rightarrow \psi(x)$ $\...
GedankenExperimentalist's user avatar
1 vote
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85 views

Quantization of charge implying charge exist in the form of point particles

The statement for quantization of charge says that total charge of a body is constant. Now the word " body " seems vague. We may consider any part of space which we want and call it a body. ...
Users's user avatar
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Implications of quantized space (a la LQG) on defining "realistic" number systems [duplicate]

Disclaimer: not a professional physicist or mathematician, so (deserved) tomato-throwing is welcome. I've been pondering the "naturalness" of real numbers for some time now, in the sense of ...
RuslanD's user avatar
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0 votes
2 answers
60 views

How small can we measure space? [closed]

I got this question after looking into transcendental numbers and I noticed how there are some distinctions that should be made from numbers and reality especially in measurement of length for example ...
How why e's user avatar
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5 votes
1 answer
255 views

Renormalization in quantum field theory by discretizing space (but not time)

I'm a mathematician slowly trying to learn quantum field theory and I have a small question about renormalization, which I still have a shaky understanding of. One common way to explain what's ...
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0 answers
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Does the Existence of Planck Units Suggest Discontinuity in Time and Space? [duplicate]

I’ve posed the following inquiry on Philosophy Stack Exchange: Can the idea of continuity make sense in the real world? A summary of it is presented here: Continuity in mathematics means no jumps or ...
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How to properly discretize and solve the Liouville equation?

Consider some dynamical system $\dot{\textbf{X}}(\textbf{x},t)=F(\textbf{X})$ where $\textbf{X}$ is discretized along a 1-dimensional spatial coordinate $\textbf{x}=(x_1,\dots,x_N)^T$. Let $\rho(\...
thespaceman's user avatar
1 vote
0 answers
54 views

Is it possible that black holes spin in discreet spin quanta?

Roy Kerr recently wrote a paper critical of the Penrose singularity theorem. One interpretation of his paper is that the singularity problem might be an artifact of the Schwarzchild metric and that a ...
Daniel Shulman's user avatar
1 vote
0 answers
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What is the reason for discreteness in energy level when an electron (electron-hole pair) is confined? [duplicate]

I studied about quantum confinement for a presentation on Quantum Well, wire and dots and came across a term 'Quantum Confinement', it said quantum confinement leads to discrete in energy level. And ...
Udit Chauhan's user avatar
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1 answer
200 views

How to understand this Dirac delta function?

I am reading this paper about quantization of the electromagnetic field, and there is a point where the author imposes the fundamental commutation relation between the vector potential and its ...
Claudio Saspinski's user avatar
3 votes
2 answers
616 views

Why radial quantization gives different spectrum?

For example we work with 1+1D massless free boson, in canonical quantization we allow creation operators at any momentum so the Hamiltonian has continuous spectrum. But if we conformally map to a ...
Peter Wu's user avatar
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How Are Discrete Energy Levels Identified in Metals and Liquids?

The NIST atomic spectra database has atomic energy levels well documented. I understand that discrete energy levels in gases can be identified using emission and absorption spectroscopy, due to the ...
cconsta1's user avatar
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-1 votes
2 answers
131 views

Is quantization chosen as a model due to us primarily observing light generated by atoms?

The two main ideas that led to quantization are Planck's solution to black body radiation and Einstein's solution to the photoelectric effect. In both cases, we are dealing with absorption and ...
Blacklight MG's user avatar
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0 answers
66 views

How can Planck-length elements exists in spacetime? [duplicate]

My question is simple, how can the theory of finite-sized elements (Planck-sized elements) in spacetime be correct, when you find the number $\pi$ in the Schwartzchild representation of the black hole,...
Superunknown's user avatar
3 votes
1 answer
109 views

Relationship between position kets in different topologies

Consider a particle moving on a ring $\mathcal{S}^1 \sim \mathbb{R} / \mathbb{Z}$ of circumference $L$. Due to periodic boundary conditions, $$ \langle x\mid p_n\rangle=\frac{1}{\sqrt{L}}e^{ip_{n}x/\...
ikj's user avatar
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0 answers
54 views

$\mathbb Z_N$ (discrete) gauge theory

I am currently trying to go through some literature on symmetry protected topological phases and gauge theories defined on lattices. I am looking for a mathematically precise reference that discusses $...
0 votes
1 answer
37 views

Is it possible to label particles of a continuum body?

In basic continuum mechanics (e.g. fluid dynamics), we label particles of the continuum, i.e., each particle can be identified by a label, e.g., $p$. Then other quantities are defined accordingly, e.g....
Naghi's user avatar
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1 vote
0 answers
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A confusion about a question on photoelectric effect [closed]

Q. Photoelectric effect supports quantum nature of light because There is minimum frequency of light below which no photoelectrons are emitted. Electric charge of photoelectrons is quantized. ...
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1 vote
1 answer
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Does the Lagrangian being invariant under substitution of variables imply a conserved quantity?

Consider the following Lagrangian: $$ \mathcal{L} = \frac{Ma^2\dot\theta^2}{6} +\frac{1}{2}ma^2\left(4\dot\theta^2 + \dot\phi^2 + 4\dot\theta\dot\phi\cos(\theta - \phi) \right) - \frac{a^2k}{2}\left( ...
sconsolato's user avatar
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0 answers
52 views

On discretization in QFT and second quantization

Some time ago i saw in a QFT lecture series by the IFT UNESP that in QFT we need to discretize space by dividing it into tiny boxes of an arbitrary Volume $ \Delta V $ and then define canonical ...
Tomás's user avatar
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0 answers
56 views

Discrete Schrödinger equation and Fourier transformation

I am currently working on an exercise involving the discretized version of Schrödinger's equation in an infinite potential well. The problem involves a well with a width of 1 and assumes $$\frac{\hbar}...
Gonzalo Chiva San Román's user avatar
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0 answers
47 views

Is the electric force quantum?

I'm asking if the electric force is quantum, and I'm not referring to photons, which I understand is quantized. Unless of course, the answer is that the electric force is only felt upon absorption of ...
HardlyCurious's user avatar
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0 answers
39 views

Planck time - what would I see? [duplicate]

Impossibly hypothetical, but to communicate the question: when the universe "ticks" a plank second, what does a particle do? I'd imagine the natural conception that it moves from position a ...
Rabbi Kaii's user avatar
6 votes
1 answer
125 views

Why is mass so variable in elementary particles compared to charge, spin, etc [duplicate]

Why is it that the standard model gives very even charge and spin for elementary particles that can easily be compared to each other as integers and simple 1/2, 1/3, fractions whereas some particles ...
The Burger King's user avatar
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0 answers
24 views

Is there some sort of periodicity in the gauge which is responsible for particle number discretization?

I have been thinking about how periodicity in a physical parameter is related to the discretization of its canonical conjugate, much like the periodicity in time results in the discretization of the ...
K. Pull's user avatar
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1 vote
2 answers
81 views

Is temperature truly continuous and if not by what amount is it discrete? [closed]

I have heard people say that temperature is basically continuous (the temperature can’t jump from 10 degrees to 30 it gradually increases) is this true at a quantum level and if not what is the ...
Mustafa's user avatar
  • 19
0 votes
1 answer
39 views

What happens to a photon leaving a grav well if it doesn't have the energy to get out of the well and the object it's leaving isn't a black hole?

Light exists with energy E = hf. That is supposed to be quantized and discrete but maybe "f" in the equation is continuous when not emitted specifically from an electron (moving through the ...
Mike's user avatar
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1 vote
1 answer
128 views

Finite Differencing with Incompressible Navier-Stokes Equations (Only Advection)

I'm trying to improve the advection method in a 2D-windfield. The Navier-Stokes Equations (NSE) are currently used for the influence of pressure, viscosity,... I am just focusing on the convective ...
CFD98's user avatar
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0 votes
3 answers
117 views

Landau QM Angular Momentum Eigenvalues Derivation

In Landau & Lifshitz's QM book, p86, a derivation of the eigenvalues of the angular momentum operator is given by taking its expression in polar form in one component (say $z$): $$-i\frac{\partial{...
summersfreezing's user avatar
2 votes
0 answers
105 views

Discrete symmetries of General relativity?

What are the discrete symmetries of General Relativity? Is it invariant under CP, C, P,T or all?
KaraboMadisa's user avatar
0 votes
0 answers
52 views

Discretize a point on the surrounding grid and maintain Gaussian distribution

I now have a point located at x, and the value at that point is q(x). I want to discretize the point to the surrounding grid points and maintain a Gaussian distribution. A one-dimensional grid is fine....
Zhao Dazhuang's user avatar
2 votes
2 answers
76 views

Quantisation of mass [duplicate]

My textbook says: Quantisation of electric charge is a basic (unexplained) law of nature; interestingly, there is no analogous law on quantisation of mass. Does this mean we can have arbitrarily ...
Shoes's user avatar
  • 100
2 votes
1 answer
107 views

What is the error in a naive computation of a path integral? [closed]

If I were to try to brute force compute the following integral: $$F(t_{i-1}, x_{i-1})= e^{-r(t_{i}-t_{i-1})}\int_{-\infty}^{\infty} dx_{i} \cdot G(x_{i}, t_{i}|x_{i-1}, t_{i-1})F(t_i, x_{i}),$$ where $...
NX37B's user avatar
  • 239
0 votes
1 answer
60 views

Approximating curved spacetime with a grid of cartesian metric tensors?

Let's assume a universe with only some ($n$) single point masses $m_i$ in it. The point masses have initial positions in space-time, $x_{i0}$. The spacetime between them is curved due to general ...
MartyMcFly's user avatar
6 votes
1 answer
473 views

What happens to left-over energy in atomic excitations?

The question relates to quantization of energy. As we know, to make an electron jump to a higher energy level, a discrete amount of energy must be given to it. If the energy provided is less than the ...
washikiballa's user avatar
1 vote
4 answers
323 views

How can energy be discrete when momentum and position are not?

In quantum mechanics, it's said that the total energy of a system can only take certain discrete values. That is, the set of all possible energies of a system can be indexed by the natural numbers and ...
Joseph_Kopp's user avatar
-1 votes
1 answer
289 views

Is it correct to say that a particle in the box can only acquire discrete velocities?

My thermodynamics lecture script says the following: Translational Energy Levels In addition to electronic energy, atoms have translational energy. To find allowed translational energies we solve Ψ ...
iwab's user avatar
  • 211
1 vote
0 answers
41 views

Continuity with respect to initial conditions

Buridan's Ass is a paradox that I am gradually, very grudgingly, beginning to accept as not-as-silly-as-it-seems. See the wiki article and this paper by Leslie Lamport. Quote: "Buridan’s ...
Erhannis's user avatar
  • 327
0 votes
1 answer
73 views

An elementary question about an integration formula (nomenclature probably archaic)

so I am working on this research paper: https://docdro.id/sZsZiYL Basically, the authors use a so-called Yee grid in order to discretize Maxwell's equations for computational purposes. In the paper, ...
Shadat  Singh's user avatar
8 votes
4 answers
1k views

All periodic phenomena should have quantized energy levels?

I was watching a Lecture by Douglas Hofstadter on "Albert Einstein on Light; Light on Albert Einstein". And there was a slide which said that Einstein had idea that All periodic phenomena ...
coobit's user avatar
  • 957
2 votes
1 answer
104 views

How to understand why physics formulas are continuous while in microscope everything is discrete?

When I see physics formulas everything is perfect continuous everywhere, like momentum conserving Navier-Stokes equation, even like Schrödinger equation. But in atom scale everything is not continuous,...
Smith's user avatar
  • 21
1 vote
1 answer
101 views

If spacetime is discrete, would we observe continuous models to show non-rounding and non-truncation errors?

Typically, the ground truth is taken to be the continuous model. Numerical simulations are taken to be the approximation. These simulations deviate from the continuous model due to both a constant ...
Livid's user avatar
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0 votes
0 answers
54 views

Noether's Theorem application [duplicate]

So I know that Noether's theorem has a symmetry that corresponds to a conservation law. I was wondering what quantity is conserved in charge conjugation symmetry.
averageenjoyer1234's user avatar
0 votes
0 answers
48 views

Asking about a clarification of a rather strange notation of a Yee Grid used for discretizing Maxwell's Equations

The thesis I am following requires me to discuss a rather strange formulation of a Yee grid used to discretize Maxwell's equations in order to solve them numerically mentioned in a research paper. The ...
Shadat  Singh's user avatar

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