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Tunneling in Complex Systems
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Tunneling in Complex Systems

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Multidisciplinary Applications".

Deadline for manuscript submissions: 31 July 2024 | Viewed by 3197

Special Issue Editors

Prof. Dr. Eric J. Heller

E-Mail Website
Guest Editor
Department of Physics and Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA
Interests: time dependent and semi-classical quantum mechanics of molecules and devices; tunneling in complex systems, imaging of electrons in molecules, graphene, and semiconductors; classical–quantum correspondence in nonlinear dynamical systems
Dr. Micheline Soley

E-Mail Website
Co-Guest Editor
Department of Chemistry and Department of Physics-Affiliate; University of Wisconsin-Madison, Madison, WI 53706, USA
Interests: quantum computing algorithm development; atomic and molecular physics; ultracold chemistry and collisions; quantum reflection; PT symmetry; tensor networks; quantum dynamics

Special Issue Information

Dear Colleagues,

Quantum tunneling is a well-known fundamental effect in quantum mechanics that has become increasingly important since its first description nearly a century ago. Today its importance ranges from cold atoms and molecules to biology, chemistry, and quantum field theory. Its further development could continue to impact a wide range of applications such as quantum computing, scanning tunneling microscopy, single molecule magnets, and nanoscale devices. This Special Issue aims to bring together discussions of quantum tunneling from different fields to address the questions of what constitutes tunneling, how it relates to its counterparts such as Anderson localization and quantum reflection, in addition to generating further knowledge and innovations and highlighting what unites tunneling across disciplines.

Prof. Dr. Eric J. Heller
Dr. Micheline Soley
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • tunneling in thermal systems
  • many-body tunneling
  • tunneling time
  • dynamical tunneling
  • chaos-assisted tunneling
  • coherent vs incoherent tunneling
  • role of Planckian times
  • tunneling in glassy systems
  • tunneling in quantum solids like H2 below 13 K
  • tunneling in molecules
  • tunneling in biological systems

Published Papers (3 papers)

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Research

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15 pages, 2968 KiB  
Article
Accelerating Quantum Decay by Multiple Tunneling Barriers
by Ermanno Pinotti and Stefano Longhi
Entropy 2023, 25(9), 1345; https://doi.org/10.3390/e25091345 - 16 Sep 2023
Viewed by 1007
Abstract
A quantum particle constrained between two high potential barriers provides a paradigmatic example of a system sustaining quasi-bound (or resonance) states. When the system is prepared in one of such quasi-bound states, the wave function approximately maintains its shape but decays in time [...] Read more.
A quantum particle constrained between two high potential barriers provides a paradigmatic example of a system sustaining quasi-bound (or resonance) states. When the system is prepared in one of such quasi-bound states, the wave function approximately maintains its shape but decays in time in a nearly exponential manner radiating into the surrounding space, the lifetime being of the order of the reciprocal of the width of the resonance peak in the transmission spectrum. Naively, one could think that adding more lateral barriers would preferentially slow down or prevent the quantum decay since tunneling is expected to become less probable and due to quantum backflow induced by multiple scattering processes. However, this is not always the case and in the early stage of the dynamics quantum decay can be accelerated (rather than decelerated) by additional lateral barriers, even when the barrier heights are arbitrarily large. The decay acceleration originates from resonant tunneling effects and is associated to large deviations from an exponential decay law. We discuss such a counterintuitive phenomenon by considering the hopping dynamics of a quantum particle on a tight-binding lattice with on-site potential barriers. Full article
(This article belongs to the Special Issue Tunneling in Complex Systems)
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Review

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21 pages, 13702 KiB  
Review
Dynamical Tunneling in More than Two Degrees of Freedom
by Srihari Keshavamurthy
Entropy 2024, 26(4), 333; https://doi.org/10.3390/e26040333 - 14 Apr 2024
Viewed by 427
Abstract
Recent progress towards understanding the mechanism of dynamical tunneling in Hamiltonian systems with three or more degrees of freedom (DoF) is reviewed. In contrast to systems with two degrees of freedom, the three or more degrees of freedom case presents several challenges. Specifically, [...] Read more.
Recent progress towards understanding the mechanism of dynamical tunneling in Hamiltonian systems with three or more degrees of freedom (DoF) is reviewed. In contrast to systems with two degrees of freedom, the three or more degrees of freedom case presents several challenges. Specifically, in higher-dimensional phase spaces, multiple mechanisms for classical transport have significant implications for the evolution of initial quantum states. In this review, the importance of features on the Arnold web, a signature of systems with three or more DoF, to the mechanism of resonance-assisted tunneling is illustrated using select examples. These examples represent relevant models for phenomena such as intramolecular vibrational energy redistribution in isolated molecules and the dynamics of Bose–Einstein condensates trapped in optical lattices. Full article
(This article belongs to the Special Issue Tunneling in Complex Systems)
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16 pages, 18316 KiB  
Review
Chaos-Assisted Tunneling
by Linda E. Reichl
Entropy 2024, 26(2), 144; https://doi.org/10.3390/e26020144 - 07 Feb 2024
Cited by 1 | Viewed by 715
Abstract
The ability of particles to “tunnel” through potential energy barriers is a purely quantum phenomenon. A classical particle in a symmetric double-well potential, with energy below the potential barrier, will be trapped on one side of the potential well. A quantum particle, however, [...] Read more.
The ability of particles to “tunnel” through potential energy barriers is a purely quantum phenomenon. A classical particle in a symmetric double-well potential, with energy below the potential barrier, will be trapped on one side of the potential well. A quantum particle, however, can sit on both sides, in either a symmetric state or an antisymmetric state. An analogous phenomenon occurs in conservative classical systems with two degrees of freedom and no potential barriers. If only the energy is conserved, the phase space will be a mixture of regular “islands” embedded in a sea of chaos. Classically, a particle sitting in one regular island cannot reach another symmetrically located regular island when the islands are separated by chaos. However, a quantum particle can sit on both regular islands, in symmetric and antisymmetric states, due to chaos-assisted tunneling. Here, we give an overview of the theory and recent experimental observations of this phenomenon. Full article
(This article belongs to the Special Issue Tunneling in Complex Systems)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.


1. Authors: Andrei B. Klimov and Iván F. Valtierra
Tentative title: Tunneling Wigner Currents in the Hyperbolic Phase-Space

2. Authors: Daniel Martínez-Gil, Salvador Miret-Artes and Pedro Bargueno
Tentative title: The Interplay Between Tunnelling and Parity Violation in Chiral Molecules

3. Authors: Jens Poulsen and Gunnar Nyman 
Tentative title: Fulfilling the Uncertainty Principle in Temperature Dependent Tunneling Using Variational Wigner Functions
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