What is Spontaneous: Definition and 157 Discussions

I am reading this chapter 3 from the book called The Quantum Vacuum by P.Milonni.(Attached in the pdf, look at chapter 3.2 Spontaneous emission)There they say that spontaneous emission is due to both quantum fluctuations and radiation reaction. They say the transitions induced by the quantum...

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Hello, Einstein introduced stimulated emission (along with spontaneous emission and absorption) to derive Planck's radiation law using his A and B coefficients in his 1917 paper. My question is, is it possible to separate the Planck radiation spectrum into a fraction that is spontaneous...

In chapter 20 of Peskin&Schroeder about spontaneous symmetry breaking, he considers and example on page 696 of spontaneous symmetry breaking of SU(3) gauge group with generators taken in adjoint representation. Covariant derivative is defined with: $$D_\mu\phi_a = \partial\phi_a +...

If you were to fire a single atom from a fixed point into a chamber of perfect vacuum and measure where it collides with the opposite wall. Could Spontaneous symmetry breaking in the sub atomic particles cause momentum change in the atom, changing the part of the wall the atom interacted with?

Summary:: Help needed on how to calculate on spontaneous fission and effect from alpha decay Heat from alpha decay from Pu-238 is used to generate direct current. At the beginning (1977) it generated 470W, how large is the effect now? And if the efficiency between the electricity and heat...

Hello! I thought that in spontaneous emission (say for an atom with 2 energy levels) we have the electron in the excited state and then it decays to the ground state emitting a photon at the resonance frequency. However I saw the attached figure, which introduces Mollow triplet. I understand the...

Hello, I have a question about the creation of the Bell's entanglement state ##1/\sqrt{2} (|HH> + |VV>)##using type I BBO crystals (https://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion). Two crystals are put orthogonal to each other and each of them emits a photon pair...

I'm wondering what the relationship between blackbody radiation and spontaneous emission is. As far as I know, there are three sources of EM radiation - thermal radiation, oscillating dipole (multipole?), and LASER. And it seems like light emission from an atom can be separated into two...

When trying to describe why the entropy goes up for a irreversible process, such as gas expanding into a vacuum, it seems fairly easy at a high level. the valve between the two chambers opens, the free expansion occurs, the pressure drops proportional to the volume change and the temp remains...

I realize that nothing causes an excited atom to emit a photon, and that it's a random process. But someone was asking me about why energized systems in general tend to lose their energy to the environment and move toward equilibrium. I mentioned that an inflated balloon, given a hole, will tend...

Hello! This questions might not make sense and I am sorry if that is the case (I am asking from a QM class perspective). I am a bit confused about the idea of spontaneously symmetry breaking (SSB), from the point of view of QM. I am talking here about the energy plot looking like a mexican hat...

Hi All In another thread I answered was a question related to this and noticed another as well, so I thought I would give the full answer in its own thread rather than write it out twice. The other question has been deleted but here is the full detail anyway. First see...

If we start with the Lagrangian \begin{equation} \begin{split} \mathcal{L} = & \frac{1}{2}(\partial_\mu \phi)^2 + \frac{1}{2}\mu^2 \phi^2 - \frac{1}{4}\lambda^2 \phi^4\\ \end{split} \end{equation} and give the scalar field a VEV so that we can define the field ##\eta##, where $$\eta = \phi...

Does terrestrial spontaneous fission or natural fission create unstable isotopes similar to nuclear fission in reactors?

Spontaneous symmetry breakingI’m not sure if I understand spontaneous symmetry breaking.In the context of the Mexican hat (and marble) example, wouldn’t the actual path of the marble down the Mexican hat from the top be determined by several small factors that one would normally not consider...

Hello! I am reading about Time Dependent Perturbation Theory from Griffiths book on QM. He derives the fact that for a system with 2 levels with energies ##E_b > E_a##, if you send light to it (or a sinusoidal perturbation) the probability of an electron going from state a to state b is the same...

Hi, Suppose I have a 1D material of length L, and I want to calculate the spontanious emission rate Γ at ressonance frequeny. From my understanding, when light passes in a material at ressonance frequency it gets absorved by an electron in the atom, and after a spontaneous emission time tspont...

I was wondering if there is a good example of a chemical reaction cascade that reverses itself, or does a "loop" in nature outside of life? First thing that came to mind was water evaporating and coming back down from clouds, but that is not really a chemical reaction. Or would it be considered...

How easy (or not) is it for spontaneous chemical reactions to occur in a living cell, but particularly reactions that are not a result of and between coded molecules? For example, when we eat food, in the process while the essential molecules are being taken to be integrated into "coded...

I have a question regarding the development of cancer. Cancer can be a genetical mutation inside a cell that can have an external/environmental cause, such as UV light, oncogenes in food sources, or with the help of oncoviruses and carcinogenic bacteria. Other than that, cancer is also said to...

Feynman tells us, "The probability that an atom will emit a photon into a particular final state is increased by the factor (n+1) if there are already n photons in that state." 4–4 Emission and absorption of photons, http://www.feynmanlectures.caltech.edu/III_04.html The 1 in (N+1) comes from...

When I look at certain experiments involving entangled photons generated by spdc, for example quantum eraser experiments, it seems to me that each observed pair of entangled photons is propagated in a horizontal plane. However, aren't the entangled photons generated randomly in all planes...

I know I can't speak for everyone here, but I would presume that most people in the sciences have either naturally or through schooling become analytical thinkers. Especially for the ones that are naturally analytical, have you found difficulty in being spontaneous, romantic, artistic, or any...

i know there is a certain probability for an electron to fall to a lower energy level,without an exciting event,like a collision. Is the reverse also true I.e that a electron could jump to a higher level,without absorbing any extraneous energy..if so are the lifetimes in the new state the same...

Homework Statement Determine the mass of the scalars and show that one remains zero in accordance with goldstones theorem.Homework Equations $$L=\dfrac {1}{2} (\partial_\mu \phi_a)(\partial^\mu \phi_a)-\dfrac{1}{2} \mu^2 (\phi_a \phi_a) - \dfrac{1}{4} \lambda (\phi_a \phi_a)^2+ i\bar{\psi}...

This is a question that I have tried to pose several times without any success but, anyway, I would like to try again for the very last time. Asume for a moment that EW-SSB (electroweak spontaneous symmetry breaking) actually happened in our early universe. Imagine that our Standard Model of...

Hi, it is well known that spontaneous emission of an atom can be enhanced, if the atom sits at a node of the vacuum standing wave field in a cavity. My question is, why is it the node? At a node of a standing wave, there is zero intensity, so there should be no interaction between the atom and...

Hello, I have a short question: In relation to the Sun - is Black-body radiation ultimately the result of a combination of spontaneous (majority) and stimulated (minority) emission of photons? In relation to the IR emissions from everyday objects due to their temperature - is Black-body...

I have heard of frustrated spontaneous emission that somehow says that an atom that normally emit light will cease to do so when its surroundings is incapable of absorbing light. How is this possible, and is this experimentally proven?

Recently I've come across Alexander Vilenkin paper . I can't seem to find the 1988 version so if you can help me with that I would appreciate it. I have 2 basic questions: 1)Am I right in saying that the "nothing" in this paper is not the "philosophical nothing" as in no thing at all ? From...

Many introductory (high school chemistry) texts speak of reactions that are “always” or “never” spontaneous (in the former case they reference reactions where ∆H is - and ∆S is +, for example). I struggle with this concept when considering reactions in closed systems. Premise: All reactions...

I'm reading Gerald Folland's "Quantum Field Theory: A Tourist Guide for Mathematicians" and I'm up to Section 6.2 which is called "A toy model for electrons in an atom". He has a nonrelativistic particle of mass M and a scalar field with quanta of mass m and the state space for the particle is...

Hi. In thermodynamic equilibrium, the ratio between spontaneous and stimulated emission is $$\frac{A_{21}\cdot N_2}{B_{21}\cdot N_2\cdot u(f)}=e^{\frac{hf}{k_B T}}-1$$ where ##A_{21}## and ##B_{21}## are Einstein coefficients. This means, that there's always much more spontaneous than...

In Griffith and Sakurai QM book, spontaneous emission is treated as a closed system subject to time-dependent perturbation. Yet in quantum optics sponantanoues emission is treated as in the form master equation of density matrix. Even in two levels system where there is only one spontaneous...

In spontaneous symmetry breaking, you expand the Lagrangian around one of the potential minima and write down the Feynman rules using this new Lagrangian. Will it make any difference to your Feynman rules if you expand the Lagrangian around different minima of the potential?

I was wondering whether it is possible for amino acids that end up in a cell (ready to be made into proteins) to spontaneously start to bond in the cytoplasm (or wherever the routing channel is I guess) and create randomly floating short strands of polymers? Furthermore, can it ever happen that...

I suppose that my questions are pretty basic, but I've been trying to find out the answers and not succeeded. 1.- Do cosmologists really think that the vacuum state suddenly changed in the early Universe? If so, would it be like a phase transition? If so, first or second orther? 2.- Does the...

The quark sector of the QCD lagrangian can be written as (restricting to two flavours) $$\mathcal L = \sum_{i=u,d} \bar q_i ( i \gamma_{\mu} D^{\mu} + m) q_i .$$ Write ##q = (u d)^T## and $$M = \begin{pmatrix} m_u & 0 \\ 0 & m_d \end{pmatrix}$$ Given that the masses of the u and d quarks are...

Let's consider a two state quantum system in which an electron is either in the ground state or in the excited state with the energy difference E. We know that if we put this system in a monochromatic electromagnetic field (with frequency E/h) the electron can become excited by means of...

Heisenberg model of ferromagnet is defined by \hat{H}=-J \sum_{\langle i,j \rangle} \vec{S}_i \cdot \vec{S}_j where ##J>0## and summation is between nearest neighbours. Hamiltonian is perfectly rotational symmetric. However, the ground state “spontaneously” chooses a particular orientation...

Homework Statement A simple classical example that demonstrates spontaneous symmetry breaking is described by the Lagrangian for a scalar with a negative mass term: ##\mathcal{L}=-\frac{1}{2}\phi\Box\phi + \frac{1}{2}m^{2}\phi^{2}-\frac{\lambda}{4!}\phi^{4}##. (a) How many constants ##c##...

It seems I remember hearing (either on tv or mag) that there was a theory that the original singularity which resulted in the big bang could have been created from essentially nothing by ripples or something in the space energy...or something like that. Can anyone point me toward any articles...

Consider a theory with two multiplets of real scalar fields ##\phi_i## and ##\epsilon_i##, where ##i### runs from 1 to N. The Lagrangian is given by: $$\mathcal L = \frac{1}{2} (\partial_{\mu} \phi_i) (\partial^{\mu} \phi_i) + \frac{1}{2} (\partial_{\mu} \epsilon_i) (\partial^{\mu} \epsilon_i)...

Dear All I am studying spontaneous breaking of supersymmetry but i am confused about something. Why should the goldstone be a spin 1/2, why it is not a boson? I have read that this is due to supersymmetry is a fermionic symmetry but i am not convinced with this answer! Thank you

Is it possible for a nucleus to undergo antisymmetric spontaneous fission? And if so, what is the process responsible? Thanks

Are there isotopes that decay only through spontaneous fission, or in other words can normally stable nuclei decay through spontaneous fission?

Hypothetically, a particle p of mass M is sitting at velocity v. Assuming M = 0, and the vi of p is 0 m/s, 0 seconds passes and vf 100 m/s is reached. Since time t is 0, acceleration cannot exist, as no t has passed between the vi and vf states. And, knowing that a = (vf - vi)/ Δt, a = (100 -...

As we know topological phases cannot be explained using spontaneous symmetry breaking and order parameter. But can they coexist? Suppose there is a system which is undergoing quantum phase transition to a anti-ferromagnetic phase from a disordered phase. So in the anti-ferromagnetic phase...

I would like to ask about the case of: ##SU(2)\otimes U(1) \rightarrow U(1)\otimes U(1),## spontaneous symmetry breaking. It is given that the Wilson Loop: ##W \equiv exp[ig \oint dy H T^1]= diag(−1,−1,1).## Where ##y## is the ##S^1/Z^2## fifth/extra dimension, ##H = \frac{1}{g R}## and...