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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183 views

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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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 ...
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Is there any chance that the EM drive thrust could be caused by quantum tunnelling? [duplicate]

So, I know you guys probably hate this topic, but I don't think stop looking into it is the solution. Figuring out what's wrong with the experiments would also bring new knowledge to the table, and ...
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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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Relation between Casimir Effect and Quantum Tunnelling

Are Casimir Effect and Quantum Tunnelling dependent on each other? Also, is it reasonable to conclude that if Casimir Effect is already observed in a system, then Quantum Tunnelling has also taken ...
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Tunnel Effect and wave in classical mechanics and in quantum mechanical

My question is: from the point of view of classical mechanics, when a wave encounters a barrier, it is totally transmitted through the barrier, while in quantum mechanical there is also a part of the ...
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553 views

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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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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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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How does light travel through an optical fibre of diameter less than the distance between the wave's crest and the trough?

It is known that optical fibres use light waves for faster communications and also in many other things like measuring and all.....everything is fine till the wave just fits into the fibre ....but ...
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Delta potential, negative energy, quantum particle

I was solving a task involving bound states of an electron : We have a delta potential $V(x) = -\lambda \space \delta(x)$, find the energy of the only bound state. So I get $\sqrt{k}e^{i k x} , \space ...
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How can the levels of an asymmetric double well be understood qualitatively?

Consider the potential energy profile above (blue). There are two minima which can be thought of as wells, one much deeper than the other. In the diagram there are a few energy levels that I drew in ...
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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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Quantum Tunnelling and $c$

What prevents a particle travelling at a speed infinitesimally smaller than that of $c$ tunnelling a slightly further distance than it would have otherwise and thus have travelled faster than the ...
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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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386 views

Transmission reflection at step potential mass independent?

I was reading the Wikipedia page about transmission and reflection, and to my surprise, the transmission and reflection coefficients do not depend on the mass of the particle. So in consequence the ...
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863 views

Evanescent waves and photon tunneling

Context I am reading about near-field heat transfer. Generally this phenomena is describes using (classical) Maxwell equations. In vacuum heat transfer from a body A to a body B such that $T_A > ...
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552 views

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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Mechanism for collapse of iron stars into black holes via quantum tunnelling

In the wikipedia page "Future of an expanding universe" it refers to the scenario of a future without proton decay. The page talks about how processes would lead to stellar-mass cold spheres of iron, ...
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931 views

Why we can't use quantum tunnelling still in nuclear fusion where sun uses this trick of nature easily?

Sun haven't enough temperature to break down coulomb barrier between two protons to be fussed.But yet nuclear fusion occurs through quantum tunnelling process.So,why we can't use quantum tunnelling in ...
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598 views

Scattering from a step potential barrier

Suppose a potential barrier of the form $$ V(x) = \begin{cases} V_0 & x>0 \\ 0 & x<0 \end{cases} $$ Then, for energy $E$ such that $E < V_0$, we have that the transmission and ...
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What does it mean to have a transmission coefficient 1.03*10^-3

I solved a potential barrier problem. E=4.5ev V0=5eV barrier width a=950pm The transmission coefficient came out to be 1.03*10^-3 I was wondering what this means? isn't the transmission probability ...
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498 views

Potential step and tunnelling

Imagine a particle with energy $E$ heading towards a potential step with height $V_0$ where $E<V_0$. The particle's wave function is oscillatory before the boundary and exponentially decaying in ...
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Applicability of wavefunction matching when Hamiltonian (not just potential) varies

A simple tunnelling calculation can be performed for a potential step by calculating the eigenfunctions for the Hamiltonian on either side of the step and matching the wavefunctions (and using ...
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How to calculate tunneling current between two metals separated by a dielectric?

If I have two metallic electrodes (e.g. Al, Cr) separated by a dielectric (ε, d; e.g. SiO2), how can I calculate the tunneling current as a function of applied voltage?
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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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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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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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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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Showing the transmission coefficient is valid

In a semiconductor device, electrons accelerated through a potential difference of 7V attempts to tunnel through a barrier of width 0.5nm and height 10V. Assume the potential is zero outside the ...
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549 views

Single particle tunneling Hamiltonian

In reference to Problem 9, Chapter 2 in Modern Quantum Mechanics by JJ Sakurai, For a single particle tunneling in a 1D double well potential, with position eigenkets $\mid R\rangle$, $\mid L\rangle$....
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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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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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What exactly is Quantum Tunneling? [closed]

What is quantum tunneling How is it possible? I tried reading up on itbut i couldn't exactly grasp the concept.
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743 views

Tunneling in classical mechanics

According to a classical mechanics a particle that do not have enough energy will not be able to surmount a potential barrier. But what if we have a lot of particles(e.g. electrons)? They can ...
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921 views

Can photons undergo quantum tunneling? [duplicate]

Most leptons can do this so I'm curious to see if photons or any bosons at all can.
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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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510 views

Are coherent tunneling and incoherent hopping belong to quantum interference?

What the accurate definition of quantum interference in molecule or molecules? In some case, there is coherent tunneling in a molecule junction while sometime it is incoherent hopping, or even the ...
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Will using the WKB method for tunneling current give incorrect results for specifically low applied voltages?

I am simulating quantum tunneling through a rectangular potential barrier, as a function of applied voltage across the barrier as well as barrier thickness. I am following the theory from the book "...
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189 views

What's the bubble's wall made up of in false vacuum decay? [closed]

It is well known that for some kind of double well potentials, there are two minima with one is unstable called the false vacuum while the other stable one called the true vacuum. The tunneling is ...
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Two-Band k.p Model is not Hermitian for imaginary wavevectors

In E. O. Kane's original work on Zener Tunneling, he uses a two-band $k\cdot p$ model for the semiconductor bandstructure: $$H=\begin{pmatrix}E_g+\frac{\hbar^2k^2}{2m_0}&(\hbar/m)kp\\(\hbar/m)kp&...
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Tunnelling from a normal metal into a superconductor

a similar question has already been asked in the forum but unfortunately I cannot yet comment and still think that some things left unanswered. My question is in general concerning the tunnelling ...
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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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651 views

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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Does quantum tunnelling drill holes in solid state drives?

The solid state drive (SSD) consists of numerous data storage elements. Each element (NAND flash memory element) reminds me of a microscopic battery. An electron is supposed to enter the element ...
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Why do wider double wells have a lower $\Delta E$ than thinner ones?

In this diagram, in which an $n=1 (E_{1})$ and $n=2 (E_{2})$ wave have been superimposed, the probability density of the new, combined wave changes with time. The period of its shifting density is ...
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Can the internal energy of a system change by itself?

Thermodynamically it is not possible. Internal energy of a system can not change until and unless an external work is done on the system or by the system. But I came across a very strange process of ...
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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 ...