Questions tagged [quantum-tunneling]
Quantum tunneling is a classically-forbidden quantum effect that allows a bound object with energy less than the boundary to penetrate it with a small probability. A notable example is $\alpha$-decay
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Zener diode reverse bias I(V) equation
What is the equation for the reverse bias current in terms of voltage applied? And this even be analytically derived? If so, how to derive it.
I can't seem to find good resources on this topic.
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Reverse bias p-n junction diode and Kinetic energy
In reverse bias p-n junction diode, which energy is lower than the energy of the potential barrier: the average kinetic energy of the would-be-tunnelling electrons or the kinetic energy of the ...
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Tunnelling explained by time-independent Schroedinger equation
I am a retired theoretical physicist. I am currently trying to promote the exact sciences by helping highschool students with their mathematics, physics and chemistry studies. One student, who is in ...
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WKB approximation derivation for $E<V$
I understand that we can write any complex wavefunction on polar form $A\exp(iθ)$ with both $A,θ$ real. Following the logic of Griffiths on WKB (here, page 291):
We write the energy wavefunction in ...
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How to Understand Quantum Phase Slips in Josephson Junction Array in terms of Tunneling?
I am trying to understand quantum phase slips in terms of quantum tunneling between the minima of the Josephson potential (see page 2 right before equation (1)). Consider the following circuit diagram ...
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Momentum conservation in correlation functions
In Mahan "Many particle physics" the following Hamiltonian is considered in studying electron tunnelling through a junction
\begin{equation}
H_t = \sum_{kp} T_{kp} c^\dagger_k c_p + h.c.
\...
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Can wrapped D-branes change the cycle they wrap, by quantum effects?
Suppose the internal manifold in a string compactification of type II, say, contains a D-brane wrapped around a given cycle. Is there an obstruction to the brane changing its wrapping cycle via a sort ...
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Can a kink in a finite one dimensional box tunnel into a trivial solution?
Given a simple kink solution of the Sine Gordon equation, is it possible for such a solution in a finite volume to tunnel into a trivial vacuum solution, given that such tunneling demands a finite ...
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Transmission Coefficient of Finite Square Well
Now I was calculating the Transmission Coefficients of finite square well potential and found something weird
The transmission coefficient is given by
$$T=\left[1+\frac{V_o^2\sin^2(2ka)}{4E(E+V_o)}\...
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How does QFT explain QM phenomena?
I've been studying QFT for a couple of years now, and until today I haven't encountered any of the phenomena that I've studied in my QM course: tunneling, entanglement, probability measurements and ...
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Energy Levels in Double Finite Well potentials [closed]
Why is there a behaviour where $E_1$ and $E_2$ are close to each other? This question is already answered before but I did not understand the explanation about symmetric and asymmetric terms as I do ...
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Why does single electron Coulomb blockade charging use $Q^2/2C$?
Classically stored energy of a capacitor is $\frac{Q^2}{2C}$.
However, the difference in energy when a single electron travels across the gates should be $qV$
But in couloumb blockade calculations, ...
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Tunneling of electrically neutral objects [closed]
The question is motivated by a joke-question posted in this forum, but it is serious: How would we calculate the tunneling probability for a multi-particle/multi-atom object with zero net charge?
The ...
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How fast does a particle need to go to have a significant probability to quantum tunnel through a star?
According to this answer tunneling probability depends, among other things I don't know, on the length of the barrier.
Due to length contraction when going at relativistic speeds, it seems it should ...
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Is there any connection between instantons and surface-interacting polymers?
Excluded volume polymers interacting with a penetrable hypersurface of variable dimension is a very interesting system to study critical behavior via perturbative renormalization. Since a penetrable ...
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Tunneling junction in electromagnetic field [closed]
Why in presence of electromagnetic field hamiltonian,describing 2 systems with tunneling(for example josephson junction )
$$H=H_L+H_R+T(I+I^{\dagger})$$
where $I=c_Lc^{\dagger}_R$ is tunneling ...
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What's the largest possible particle/atom that can experience quantum tunneling?
Quantum tunneling occurs when the energy state of a particle gets sufficiently high. Does this mean that particles traveling at relativistic speeds are more likely to experience this phenomena?
Is ...
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How to derive the Gamow complex energy?
Consider the following potential
It was shown how to derive the complex energy (near the ground energy) of a resonance in the left well from the Euclidean path integral by Callan and Coleman, see ...
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Quantum Tunneling, Superposition, and The Uncertainty Principle
After looking through various papers and articles on explanations of quantum tunneling I've been left wondering about one thing. I've read explanations of tunneling as an affect of a particles wave ...
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Will the electrons flowing in a metal wire come out of it and even through non conducting insulation outside it due to quantum tunneling?
Lets imagine that electrons are passing through a conducting wire. According to quantum mechanics , each electron is in form of wave function . Does that wave function have a value above 0 even ...
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Value of E1 or E2 in tunnelling diode current
I am trying to understand the meaning of the value E1,E2 in a tunnelling current expression derived in the following paper.
http://aip.scitation.org/doi/pdf/10.1063/1.1735965
A more succinct overview ...
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What is the probability of a person quantum tunneling? [duplicate]
I understand that it has been shown that small particles can quantum tunnel to just about anywhere in space (with decreasing probability the further out they go) since they all act as waves when they ...
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Landauer's formula with non-reciprocal tunneling probability
The Landauer's formula for ballistic transport in a mesoscopic conductor is often derived by assuming the transmission probability of the channel follows reciprocity symmetry, i.e.
$I \propto \int M(...
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Is transition between field configurations a tunneling process?
I'm considering D=1+1 kink solution here.
Given a D=2 theory with $\mathbb{Z}_2$ symmetry, there are 4 different mappings (or 2 distinct sectors---trivial and kink) from spacetime manifold (or just a ...
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Confusion about quantum tunneling through potential energy vs quantum tunneling through energy spectrum
It seems like that the drawing above describes the "energy spectrum" of a (final) hamiltonian. However, whenever we talk about quantum tunneling, we describe it as traversing through some kind of ...
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Energy of a particle
When a particle such as an electron borrow energy to overcome a physical barrier, ( according to Heisenberg principle ) that energy has to be returned after a short while. Since total or a part of the ...
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Tunneling for hydrogen fusion
So I'm trying to find a rough estimate of the temperature required for Hydrogen to turn into Helium through quantum tunneling. In the lecture we were presented with the following:
$$\frac{p^{2}}{2\mu}=...
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Can particles have imaginary momentum / energy less than their rest mass?
In the Feynman lectures on Physics, he talks about quantum tunneling and, basically, there's a non-zero amplitude to be found in the barrier, where the particle's energy is below the rest mass, i.e. ...
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Quantum tunnelling eigenfunctions
I'm currently studying particles at a potential step of finite width, and am confused with the nature of the eigenfunctions in the 3 regions.
\begin{align}
\psi_I =& Ae^{ikx} + Be^{-ikx} \\
\psi_{...
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Obtaining Transmission Coefficient of Beam Upon a Linear Potential
I would like to determine the transmission coefficient $\mathcal{T}$ for a particle beam $$\Psi(x,t) = A_o e^{ikx}e^\frac{-iE_ot}{\hbar}$$ with energy $$E = \frac{\hbar^2k^2}{2m}$$
incident upon a ...
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What are the advantages of using a hetero-junction in Tunneling Field Effect Transistors (TFETs)?
What are the advantages of using a hetero-junction in Tunneling Field Effect Transistors (TFETs)? How is the heterojunction able to improve the Ion/Ioff ratio of a TFET?
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What are the differences between the hopping model and the coherence corrected hopping model?
I am trying to understand the difference between the hopping model and the coherence corrected hopping model of electron transport at the molecular level.
I understand that hopping is a process ...
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Explanation of crystal formation in a Fitzroy's storm glass with the change in weather conditions
I was recently reading about Admiral Robert FitzRoy's storm glass and how it was used to predict the weather conditions based on the formation of camphor crystals in a sealed glass tube containing ...
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Chiral tunneling in Weyl Equation
I am trying to understand perfect tunneling of particles obeying Weyl equation through a potential barrier at normal incidence. I know that this has something to do with chirality, but I am not ...
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Can a particle tunnel from inside a black hole?
Event horizon isn’t special from GTR standpoint, and at least in AdS/CFT correspondence gravity can be “removed” from consideration entirely. So can a particle whose wave function is completely inside ...
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Can you communicate future information through the event horizon?
According to Hawking on "Particle Creation by Black Holes", there exists a relationship between the entropy outside of an event horizon, flux within the event horizon, and the area of that same event ...
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Why the current through a resonant tunnel diode drops when the bound state goes below the conduction band?
The IV curve of a resonant tunneling diode is N-shaped. The rise in current flow happens because the bound state (the energy state in the well) enters the thermal area of the conductor ($\mu_1 + ...
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Is energy lost in an elastic tunneling process?
Suppose we had two metal plates separated by an Angstrom. Now, apply a voltage $V$ between the two metal plates. There will be a tunneling current $I$ between the metal plates.
Since $P=IV$, does ...
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Quantum tunneling in a time dependent potential
I wonder if I could use the technique for finding the tunneling rate given by $$ \Gamma=2 \Im[ F]$$ where $F$ is the free energy in case of time dependent potentials?
Relevant to the previous ...
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In quantum physics, apparently every "particle/wave" is capable of tunneling. Why then is there a shadow at all?
A layman's question: In quantum physics, apparently every "particle/wave" is capable of tunneling/passing through material. Why then is there a shadow at all?
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What happens step-by-step (and why) when a particle tries to escape an infinite potential well?
I am aware that the following question might be quite elementary. My background is mainly in mathematics and my physics education is limited to high-school level material (discounting analogues made ...
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On gravitational quantum tunnelling
All celestial bodies have a gravitational well, and particle in the vicinity of this well would feel a gravitational force. My questions are:
a)How can I find the thickness of such a gravitational ...
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Could Dark Matter be a manifestation of tachyons tunnelling between black holes? [closed]
Among the many Dark Matter candidates, I wondered if there are any along the lines of the title.
The inner horizon of a black hole, with its mass inflation, and/or the high spacetime curvature, seems ...
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Quantum tunnelling of an electron in ground state
I asked my question on Quora and i got various conflicting answers. So, I decided that here I could get a definite answer. Unless the question is not too vague.
According to quantum mechanics, is ...
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Question about tunneling and energy
So I am in my course of physical chemistry and in my book there is this image. And quite frankly i am struggling to understand it. I believe i understand the liquid drop model. This is supposed to ...
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Why do quantum tunneling consume energy, if not then why it must pay back borrowed energy quickly? [duplicate]
I understand that quantum tunneling is a pure example of the uncertainty principle but clearly transistor had to be powered to work properly, anyhow I like to know if it is true that particle must ...
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Dirac Delta potential [closed]
As we know a particle in attractive Dirac delta potential has discontinuity in the derivative of its wavefunction.
I have two questions in this regard:
Can a second-order differential equation (the ...
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Strong force and quantum tunnelling
I am well aware of how quantum tunnelling works and how it is responsible (among other things) for the alpha decay.
Inside a nucleon, there are two quarks with the same charge, so they will repel ...
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Quantum tunneling and a football permeating a wall
I was wondering if I can say to a layman that "upon throwing the ball on a wall an enormously large number of times, there is a small probability that the ball will go through the wall", while ...
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Invisible walls paradox in quantum mechanics
Background
Quantum mechanics considers only electromagnetic interactions. This fact might be a jut obscured in the introductory texts, but all the potentials in discussions of scattering, tunneling, ...
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