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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8answers
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Can a particle be physically observed inside a quantum barrier?

I understand that if a particle approaches a finite potential barrier of height $V_0$ with energy $E < V_0$, there is still a finite probability of finding the particle on the other side of the ...
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In aluminum, how does electricity travel through the surface oxide layer?

Suppose I connect a conductive wire (cross section 1 mm$^2$) to an aluminum object. Since aluminum is highly conductive, electricity will flow smoothly inside the object with little resistance. ...
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Is there a classical analog to quantum mechanical tunneling?

In comments to a Phys.SE question, it has been written: 'Tunneling' is perfectly real, even in classical physics. [...] For sufficiently large temperatures this can put the system above a hump in ...
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Physical intuition for the Wilczek-Parikh tunneling picture of Hawking radiation

There's a naive pop-sci explanation of Hawking radiation, where a particle-antiparticle pair is produced just inside the event horizon. The particle with positive energy tunnels out and escapes, while ...
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Hawking Radiation as Tunneling

Firstly, I'm aware that Hawking radiation can be derived in the "normal" way using the Bogoliubov transformation. However, I was intrigued by the heuristic explanation in terms of tunneling. The ...
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How to understand “analytical continuation” in the context of instantons?

Since this is a subtle and interesting question to me. I will give a rather detailed description. I hope you can keep reading it and find it interesting too. For simplicity, in the following I will ...
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Probability conservation in WKB tunneling

Suppose we have quantum mechanical plane waves of energy $E$ incident upon a one-dimensional potential barrier $V(x)$ with sloping sides. One can compare the WKB solutions in the three relevant ...
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Why is tunneling not a classical idea?

There is no tunneling in the case of infinite potential barrier, but there is when we have a finite well. In the classical analog, in the first case we have a particle bouncing between to infinitely ...
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Is quantum tunneling related to imaginary time?

I was studying for my exam and looking at the chapter which talks about Potential-energy graphs. Let's take this as an example: My book states that: "If the object is in $B$ and has a total energy ...
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Does tritium hydride exhibit measurable spontaneous fusion via proton tunneling?

In a fascinating 30 June 2013 article in Nature Chemistry, researchers from the University of Leeds found that when molecules of hydroxyl (OH, a fairly stable radical) and methanol (CH$_3$OH) are cold ...
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Hawking Radiation from the WKB Approximation

Reading this paper which is itself an exposition of Parikh and Wilczek's paper, I get to a point where I fail to be able to follow the calculation. Now this is undoubtably because my calculational ...
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What is the kinetic energy of a quantum particle in forbidden region?

I have read that if a particle is trapped in a finite potential well, it has a finite chance to tunnel out from it. Therefore, one can find a particle in a region where its potential energy is greater ...
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Tunneling of alpha particles

Consider this explanation of the alpha decay: It says The Coulomb barrier faced by an alpha particle with this energy is about 26 MeV, so by classical physics it cannot escape at all. Quantum ...
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How can quantum tunnelling lead to spontaneous decay?

I have never understood what measuring process (if any) is supposed to be continuously polling the quantum state of an unstable bound system subjected to decay via quantum tunnelling. The reason I ...
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Tunneling v. Hopping

Can someone explain the difference between hopping and tunneling? The context I'm considering is conduction in semiconductors, specifically between impurity states within the bandgap. It's always ...
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Understanding multiple instanton contributions to vacuum tunneling in a double potential well

I'm trying to understand the method of calculating the transition probability of one vacuum state to another in a double well potential, using instantons. The reference I am following is Sidney ...
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Is there a time delay during tunnelling?

A particle hitting a square potential barrier can tunnel through it to get to the other side and carry on. Is there a time delay in this process?
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Quantum tunneling into a black hole

The currently accepted answer to Throwing a micro black hole into the sun: does it collapse into a black hole or does it result in a supernova? states that a small black hole of mass approximately $10^...
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Why can't a particle penetrate an infinite potential barrier?

I am studying basic quantum theory. My question is: Why can't a particle penetrate an infinite potential barrier? The reasoning that I have applied is that particles under consideration have finite ...
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How are our enzymes able to perform quantum tunnelling?

The hydrogen protons undergo quantum tunnelling in the the sun to fuse into helium, but are only able to do so as they are under immense heat and pressure and the protons and electrons get separated. ...
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Quantum tunneling probability for a 3d potential

I have an electron potential energy landscape for a metal surface to vacuum transition from a DFT calculation. The following pictures show a 2D slice of the potential, where potential energy is given ...
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Weak gravity limit of (Einstein-Hilbert + matter) action

The problem Consider the following euclidean action $$ S_E = - \int_{\mathcal{M}} d^4x \sqrt{g} \left [\frac{R}{2 \kappa} +\mathcal{L}_M \right ] + S_{GHY},$$ where $S_{GHY} = -\int_{\partial \...
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In semiconductor devices, why is quantum tunneling “fast”?

I'm reading up on semiconductor devices that rely on quantum tunneling, such as the tunnel diode and the TFET. The big advantage of these devices is apparently that "quantum tunneling is extremely ...
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Quantum barrier for photons [closed]

In quantum mechanics, a particle may tunnel through a barrier it would not be able to surmount in a classical sense. My question is this: What are all the factors that may prevent a photon from ...
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In principle, can energy “tunnel” directly out of a black hole? If not, why not?

Energy seems to quantum tunnel through normally impenetrable barriers, so I wonder why not the back side of an event horizon?
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What's the difference between hopping and tunneling?

My professor made a distinction between electron hopping (the closest wikipedia had an article on) and tunneling, saying that one (he didn't say which, but I assume hopping) was temperature dependent ...
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Quantum Tunneling and Conservation of Energy

According to my understanding quantum mechanics, the probability of any particular particle in the universe being at any specific location in the universe is very small but never actually becomes zero....
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Virtual particles/quantum tunneling - conservation of energy?

I'm confused as to how the above phenomena can take place since arent they breaking the law of conservation of energy (even, if temporarily)?
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Chance of “macro tunneling”?

We know that subatomic particles can and do tunnel through barriers, so it is theoretically "possible" somewhat that a grain of sand could tunnel through a paper, but Id like to get some perspective ...
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Calculation of Berry's phase due to monopole tunneling event of $O(3)$ NLSM on square lattice

I am currently reading the seminal paper by Duncan Haldane: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.61.1029 In this paper, he asserts that for a unit-vector field $\hat{\Omega}(x,y,t)...
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Quantum tunneling effect in a potential of the kind $V(x)=A\frac{x^2}{1+x^4}$ [closed]

Given a potential: $$V(x)=A\frac{x^2}{1+x^4}$$ with $A\gt 1$ and a quantum particle inside the well around the point $x=0$. I'm stuck on the calculation of the transmission and reflection coefficients ...
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Does tunneling transmission probability depend on the density of states or velocity?

In some quantum text books [1], the tunneling transmission formula depends only on the density of states of 2 regions (DOS) involved in tunneling. ($T(E) = C \times DOS_1(E) \times DOS_2(E)$, where C ...
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Where is the particle during a tunneling event?

If, say, a particle with energy $E<V_0$, approaches a finite potential barrier with height $V_0$, and happens to tunnel through, where would the particle be during the time period when it is to the ...
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What sets the half life of unstable nuclei/nucleons?

A chemist friend asked me what sets the half life for free neutrons, unstable nuclei, etc. He said in chemistry half lives of molecules can often be calculated based on concentrations and molecular ...
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Can Half Lives (hypothetically) be Measured by Wave-functions?

I understand that half-lives are measured over several days/months/years of observing a certain amount of an element and seeing how long it takes to decay a certain amount, but I'm curious as to ...
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Why is the WKB tunneling amplitude a non-perturbative result?

The tunneling amplitude obtained from WKB aprroximation is given by $$|T(E)|=\exp\Big\{-\frac{1}{\hbar}\int\limits_{x_1}^{x_2}dx[2(V(x)-E)]^{1/2}\Big\}[1+O(\hbar)]$$ where $x_1$ and $x_2$ are the ...
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Hamiltionian spectrum in unstable systems

I have heard that the eigenvalue of Hamiltonian in an unstable system can contain an imaginary part corresponding the tunneling. Is that true? If it is the case, then I am very confused about it. Let ...
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How can I understand the tunneling problem by Euclidean path integral where the quadratic fluctuation has a negative eigenvalue?

I came across the S. Coleman's seminal papers 'Fate of the false vacuum' (http://dx.doi.org/10.1103/PhysRevD.15.2929, http://dx.doi.org/10.1103/PhysRevD.16.1762) where he describes the tunneling ...
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Refraction: Energy flow, tunneling and Evanescent EM waves

In the full internal reflection case where we have a refracted evanescent wave, If another object is nearby, then we could have wave tunneling phenomenon(frustrated total internal reflection). I am ...
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How is quantum tunneling possible?

How is quantum tunneling possible? According to quantum mechanics, each particle is represented by a probability density function. This function must be continuous, and therefore when we look at a ...
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Macroscopic quantum phenomena and tunneling

Wikipedia's article on macroscopic quantum tunneling says Quantum phenomena are generally classified as macroscopic when the quantum states are occupied by a large number of particles (typically ...
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What happens when there are different classical trajectories before and after Wick rotation? [duplicate]

Recently I read the path integral of double well tunnelling. I am puzzled about the Wick rotation calculation. For example, I choose potential like $V(x)=(x^2-1)^2$ and Lagragian $L= \frac{1}{2} \dot ...
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What was the largest object/particle tunneling observed?

What is a current record? Reference to that would be nice. and what can be expected in near future? what are the theoretical limits?
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Quantum Mechanics Tunneling

My understanding is that QM tunneling tells us how likely it is that a photon, electron, etc. will make it through a barrier. In layman's terms, is this true/correct?
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1st Law of thermodynamics (conservation of energy) and quantum tunneling

Doesn't quantum tunneling contradict the 1st Law of thermodynamics? As far as I remember my school physics teacher told us that quantum tunneling is the reason why we can observe the alpha decay, as ...
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A microscopic derivation of the Josephson effect

It is a little bit surprising to me that it seems hard to find a detailed, microscopic derivation of the Josephson effect. Generally, you see a hand-waving derivation based on the macroscopic ...
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Why do tunneling photons outrace their non tunneling counterparts in vacuum?

If we describe a photons with a wave packet, moving towards a potential barrier and E smaller than V, there is a finite chance that it will tunnel to the other side. In this process it is likely that ...
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Vacuum Stability

I am studying one of the paper of Sidney Coleman, "Fate of the False Vacuum. II. First quantum corrections". Just before eq. (2.18) he says "Because of time translation invariance, this equation ...
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What are good ways to check the validity of code to simulate the time-dependent Schrödinger equation?

Recently, I've made some code that can do simple quantum mechanics simulation as written in the title. I wanna check if this code correctly solves time-dependent Schrödinger equation and satisfies ...
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How this quantum tunneling formula is approximated?

Transmission coefficient '$T$' of a barrier of constant potential $V$ having length $a$ is approximated to $16\frac{E}{V}e^{-2qa}$ where $E<<V$ & $q=\sqrt{\frac{2m}{(\hbar)^2}(V-E)}$. $E$ is ...