Tunnelling in asymmetric double-well potentials: varying initial states

Cordes, J. G.; Das, A. K.

doi:10.1006/spmi.2000.0964

Cited by 14 publications

(12 citation statements)

References 17 publications

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“…As a rule of thumb, the particle remains strongly delocalized if the introduced energetic asymmetry is not larger than the tunneling splitting in the symmetric case [3][4][5]. The description of tunneling in such slightly asymmetric double-minimum potentials continues to draw theoretical interest [6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Hydrogen Delocalization in an Asymmetric Biomolecule: The Curious Case of Alpha-Fenchol

et al. 2021

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Rotational microwave jet spectroscopy studies of the monoterpenol α-fenchol have so far failed to identify its second most stable torsional conformer, despite computational predictions that it is only very slightly higher in energy than the global minimum. Vibrational FTIR and Raman jet spectroscopy investigations reveal unusually complex OH and OD stretching spectra compared to other alcohols. Via modeling of the torsional states, observed spectral splittings are explained by delocalization of the hydroxy hydrogen atom through quantum tunneling between the two non-equivalent but accidentally near-degenerate conformers separated by a low and narrow barrier. The energy differences between the torsional states are determined to be only 16(1) and 7(1) cm−1hc for the protiated and deuterated alcohol, respectively, which further shrink to 9(1) and 3(1) cm−1hc upon OH or OD stretch excitation. Comparisons are made with the more strongly asymmetric monoterpenols borneol and isopinocampheol as well as with the symmetric, rapidly tunneling propargyl alcohol. In addition, the third—in contrast localized—torsional conformer and the most stable dimer are assigned for α-fenchol, as well as the two most stable dimers for propargyl alcohol.

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Section: Introductionmentioning

confidence: 99%

Hydrogen Delocalization in an Asymmetric Biomolecule: The Curious Case of Alpha-Fenchol

et al. 2021

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“…(4) is put back in Eq. (3) and the evolution equations for C n ( t )s are solved, we can compute any quantity of interest 22. It may appear at this point that the tunneling problem is solved in its entirety.…”

Section: Methodsmentioning

confidence: 99%

“…Good reviews covering these issues are available 20, 21. In what follows we propose a practicable tool for calculating a real tunneling time τ av by solving the time‐dependent Schrödinger equation (TDSE) by a simple grid‐based methodology 22, 23. We make use of Ψ( x , t ) so obtained to calculate an average velocity ( v av ) that when used with an idealized estimate of the width of the barrier ( l 0 ) yields a measure of the tunneling time [τ av = ( l 0 / v av )].…”

Section: Introductionmentioning

confidence: 99%

Simple approach to computing tunneling time: Test cases

Mondal¹,

Maji

Bhattacharyya

2003

Int J of Quantum Chemistry

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ABSTRACT:We suggest a recipe for calculating the time taken by a particle to tunnel out from an initially localized state in one of the wells of symmetrical doublewell potential into the other well. We calculate average velocity ͗v ͘ of the tunneling particle by solving the Schrö dinger equation numerically for ⌿(x, t), then estimating ͗v(t)͘ ϭ (d/dt)͗x(t)͘ and time-averaging it. The time taken to tunnel is measured by calculating av ϭ l 0 /͗v ͘ where l 0 is an idealized estimate of the barrier width. We suggest an approximate partitioning of av into an intrinsic decay time ( d ) and a barrier crossing time ( b ), d being obtained from energy spread of the packet. av Ϫ d is shown to be close to the Wentzel-Brillouin-Kramers estimate of barrier crossing time sc . The response of av to an external driving field and nonzero temperatures are tested. We also apply the method to a purely barrier penetration problem as well as to the problem of tunneling through a fluctuating barrier.

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“…At zero temperature the slow spin flip dynamics occurs only due to the tunnelling (kinetic energy) term Γ, and hence the system ceases to have any relaxational dynamics in the limit Γ → 0. It may be mentioned here that in absence of any analytical expression for the tunnelling probability in asymmetric case of the type discussed here, (see e.g., [6]), we employ the asymmetric barrier tunnelling probabilities available [7].…”

Section: Modelmentioning

confidence: 99%

Quantum annealing in a kinetically constrained system

2005

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Classical and quantum annealing is discussed for a kinetically constrained chain of N noninteracting asymmetric double wells, represented by Ising spins in a longitudinal field h. It is shown that in certain cases, where the kinetic constraints may arise from infinitely high but vanishingly narrow barriers appearing in the relaxation path of the system, quantum annealing exploiting the quantum-mechanical penetration of sufficiently narrow barriers may be far more efficient than its thermal counterpart. We have used a semiclassical picture of scattering dynamics to do our simulation for the quantum system.

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Tunnelling in asymmetric double-well potentials: varying initial states

Cited by 14 publications

References 17 publications

Hydrogen Delocalization in an Asymmetric Biomolecule: The Curious Case of Alpha-Fenchol

Hydrogen Delocalization in an Asymmetric Biomolecule: The Curious Case of Alpha-Fenchol

Simple approach to computing tunneling time: Test cases

Quantum annealing in a kinetically constrained system

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