Path-integral approach to resonant tunneling

Zohta, Yasuhito

doi:10.1103/physrevb.41.7879

Cited by 23 publications

(15 citation statements)

References 16 publications

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“…The absence of a suitable oscillating solution may come as a surprise when one considers the fact that after bubble nucleation the field inside the bubble oscillates around the local minimum of the potential. However, the surfaces upon which ∂ t φ vanishes are hyperbolae 5 , as opposed to surfaces of constant t, as required by our fourth condition. This condition is crucial because it enables us to match the two MPEPs to the bound state, generating the complete resonant tunneling path.…”

Section: Discussionmentioning

confidence: 96%

“…If the width of the cavity is given by a half-integer number of wavelengths, then the phase of a ray leaving the device does not depend on the number of reflections inside the cavity and so will constructively interfere. A rather direct comparison with quantum mechanics may be seen by studying the phenomenon using path integrals [5]. From this perspective we consider the path integral of the classical paths through a double-barrier system (e.g.…”

Section: Introductionmentioning

confidence: 99%

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No resonant tunneling in standard scalar quantum field theory

Copeland

Padilla

Saffin

2008

J. High Energy Phys.

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Abstract:We investigate the nature of resonant tunneling in standard scalar Quantum Field Theory. Following the pioneering work of Banks, Bender and Wu we describe the quantum field theory in terms of infinite dimensional quantum mechanics and utilize the "Most probable escape path" (MPEP) as the class of paths which dominate the path integral in the classically forbidden region. Considering a 1+1 dimensional field theory example we show that there are five conditions that any associated bound state in the classically allowed region must satisfy if resonant tunnelling is to occur, and we then proceed to show that it is impossible to satisfy all five conditions simultaneously.

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Section: Discussionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

No resonant tunneling in standard scalar quantum field theory

Copeland

Padilla

Saffin

2008

J. High Energy Phys.

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“…Then we will treat the resonant case in detail in sec. VI, where an appropriate incomplete Wick rotation t → e −iθ t provides the key to showing how interference effectsà la Fabry-Pérot between several complex trajectories reproduce the nonexponential behaviour of resonant tunnelling, already at work in open systems with a double barrier [20,21]. After having shown how to adapt our method to the computations of escape rates from a stable island in phase-space (sec.…”

mentioning

confidence: 99%

Instantons re-examined: Dynamical tunneling and resonant tunneling

Deunff

Mouchet²

2010

Phys. Rev. E

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Starting from trace formulae for the tunnelling splittings (or decay rates) analytically continued in the complex time domain, we obtain explicit semiclassical expansions in terms of complex trajectories that are selected with appropriate complex-time paths. We show how this instanton-like approach, which takes advantage of an incomplete Wick rotation, accurately reproduces tunnelling effects not only in the usual double-well potential but also in situations where a pure Wick rotation is insufficient, for instance dynamical tunnelling or resonant tunnelling. Even though only onedimensional autonomous Hamiltonian systems are quantitatively studied, we discuss the relevance of our method for multidimensional and/or chaotic tunnelling.

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“…The simplest way to view resonant tunnelling is with the semi-classical approximation in the path integral formalism [7]. To set the scene, we consider the motion of a quantum particle as it approaches a set of barriers given by Fig.…”

Section: Review Of Resonant Tunnelling In Quantum Mechanicsmentioning

confidence: 99%

“…Within the WKB approximation this requires where p is the momentum. This condition is equivalent to saying that there exists a bound state in region III, and corresponds to paths which oscillate back and forth in this region [7].…”

Section: Review Of Resonant Tunnelling In Quantum Mechanicsmentioning

confidence: 99%

Transmission of an inhomogeneous state via resonant tunnelling

Saffin

Padilla

Copeland

2008

J. High Energy Phys.

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Abstract:We recently investigated the nature of resonant tunnelling in standard scalar Quantum Field Theory, uncovering the conditions required for resonance. It was shown that whereas the homogeneous false vacuum may decay via bubble nucleation, it may not decay in a resonant fashion. The no-go theorem given there is circumvented in this study by considering an initial state other than the homogeneous false vacuum, and we confirm our mechanism by showing in an explicit model how resonant tunnelling occurs. Using this model we demonstrate how the tunnelling rate depends on the energy of specially constructed initial states, with these states corresponding to contracting spherical bubbles of some vacuum that evolve to a minimum radius and then tunnel to another vacuum, instead of the classical motion where the bubble would just start to expand.

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Path-integral approach to resonant tunneling

Cited by 23 publications

References 16 publications

No resonant tunneling in standard scalar quantum field theory

No resonant tunneling in standard scalar quantum field theory

Instantons re-examined: Dynamical tunneling and resonant tunneling

Transmission of an inhomogeneous state via resonant tunnelling

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