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19 pages, 8257 KiB

Open AccessArticle

Basic Cells Special Features and Their Influence on Global Transport Properties of Long Periodic Structures

by Luna R. N. Oliveira and Marcos G. E. da Luz

Entropy 2024, 26(11), 942; https://doi.org/10.3390/e26110942 - 3 Nov 2024

Viewed by 764

Abstract

In this contribution, we address quantum transport in long periodic arrays whose basic cells, localized potentials

U (x)

, display certain particular features. We investigate under which conditions these “local” special characteristics can influence the tunneling behavior through the full structure. [...] Read more.

In this contribution, we address quantum transport in long periodic arrays whose basic cells, localized potentials

U (x)

, display certain particular features. We investigate under which conditions these “local” special characteristics can influence the tunneling behavior through the full structure. As the building blocks, we consider two types of

U (x)

s: combinations of either Pöschl–Teller,

U_{0} / {cosh}^{2} [α x]

, potentials (for which the reflection and transmission coefficients are known analytically) or Gaussian-shaped potentials. For the latter, we employ an improved potential slicing procedure using basic barriers, like rectangular, triangular and trapezoidal, to approximate

U (x)

and thus obtain its scattering amplitudes. By means of a recently derived method, we discuss scattering along lattices composed of a number, N, of these

U (x)

s. We find that near-resonance energies of an isolated

U (x)

do impact the corresponding energy bands in the limit of very large Ns, but only when the cell is spatially asymmetric. Then, there is a very narrow opening (defect or rip) in the system conduction quasi-band, corresponding to the energy of the

U (x)

quasi-state. Also, for specific

U_{0}

’s of a single Pöschl–Teller well, one has 100% transmission for any incident

E > 0

. For the

U (x)

parameters rather close to such a condition, the associated array leads to a kind of “reflection comb” for large Ns;

| T_{N} {(k) |}^{2}

is not close to one only at very specific values of k, when

| T_{N} |^{2} \approx 0

. Finally, the examples here—illustrating how the anomalous transport comportment in finite but long lattices can be inherited from certain singular aspects of the

U (x)

s—are briefly discussed in the context of known effects in the literature, notably for lattices with asymmetric cells. Full article

(This article belongs to the Special Issue Tunneling in Complex Systems)

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11 pages, 2012 KiB

Open AccessArticle

Tunneling Currents in the Hyperbolic Phase Space

by Ivan F. Valtierra and Andrei B. Klimov

Entropy 2024, 26(8), 639; https://doi.org/10.3390/e26080639 - 28 Jul 2024

Viewed by 1164

Abstract

We introduce the quantum currents for quantum systems with an SU(1,1) dynamic symmetry group whose evolution is governed by a non-linear Hamiltonian possessing a continuous spectrum and apply them to the analysis of the tunneling dynamics on the hyperbolic phase space. Full article

(This article belongs to the Special Issue Tunneling in Complex Systems)

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16 pages, 86910 KiB

Open AccessFeature PaperArticle

Chaos-Assisted Dynamical Tunneling in Flat Band Superwires

by Anton M. Graf, Ke Lin, MyeongSeo Kim, Joonas Keski-Rahkonen, Alvar Daza and Eric J. Heller

Entropy 2024, 26(6), 492; https://doi.org/10.3390/e26060492 - 5 Jun 2024

Cited by 3 | Viewed by 1496

Abstract

Recent theoretical investigations have revealed unconventional transport mechanisms within high Brillouin zones of two-dimensional superlattices. Electrons can navigate along channels we call superwires, gently guided without brute force confinement. Such dynamical confinement is caused by weak superlattice deflections, markedly different from the static [...] Read more.

Recent theoretical investigations have revealed unconventional transport mechanisms within high Brillouin zones of two-dimensional superlattices. Electrons can navigate along channels we call superwires, gently guided without brute force confinement. Such dynamical confinement is caused by weak superlattice deflections, markedly different from the static or energetic confinement observed in traditional wave guides or one-dimensional electron wires. The quantum properties of superwires give rise to elastic dynamical tunneling, linking disjoint regions of the corresponding classical phase space, and enabling the emergence of several parallel channels. This paper provides the underlying theory and mechanisms that facilitate dynamical tunneling assisted by chaos in periodic lattices. Moreover, we show that the mechanism of dynamical tunneling can be effectively conceptualized through the lens of a paraxial approximation. Our results further reveal that superwires predominantly exist within flat bands, emerging from eigenstates that represent linear combinations of conventional degenerate Bloch states. Finally, we quantify tunneling rates across various lattice configurations and demonstrate that tunneling can be suppressed in a controlled fashion, illustrating potential implications in future nanodevices. Full article

(This article belongs to the Special Issue Tunneling in Complex Systems)

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20 pages, 893 KiB

Open AccessArticle

The Interplay between Tunneling and Parity Violation in Chiral Molecules

by Daniel Martínez-Gil, Pedro Bargueño and Salvador Miret-Artés

Entropy 2024, 26(6), 456; https://doi.org/10.3390/e26060456 - 27 May 2024

Cited by 1 | Viewed by 1214

Abstract

In this review, the concepts of quantum tunneling and parity violation are introduced in the context of chiral molecules. A particle moving in a double well potential provides a good model to study the behavior of chiral molecules, where the left well and [...] Read more.

In this review, the concepts of quantum tunneling and parity violation are introduced in the context of chiral molecules. A particle moving in a double well potential provides a good model to study the behavior of chiral molecules, where the left well and right well represent the L and R enantiomers, respectively. If the model considers the quantum behavior of matter, the concept of quantum tunneling emerges, giving place to stereomutation dynamics between left- and right-handed chiral molecules. Parity-violating interactions, like the electroweak one, can be also considered, making possible the existence of an energy difference between the L and R enantiomers, the so-called parity-violating energy difference (PVED). Here we provide a brief account of some theoretical methods usually employed to calculate this PVED, also commenting on relevant experiments devoted to experimentally detect the aforementioned PVED in chiral molecules. Finally, we comment on some ways of solving the so-called Hund’s paradox, with emphasis on mean-field theory and decoherence. Full article

(This article belongs to the Special Issue Tunneling in Complex Systems)

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16 pages, 3749 KiB

Open AccessFeature PaperArticle

Quantum Tunneling and Complex Dynamics in the Suris’s Integrable Map

by Yasutaka Hanada and Akira Shudo

Entropy 2024, 26(5), 414; https://doi.org/10.3390/e26050414 - 11 May 2024

Viewed by 1706

Abstract

Quantum tunneling in a two-dimensional integrable map is studied. The orbits of the map are all confined to the curves specified by the one-dimensional Hamiltonian. It is found that the behavior of tunneling splitting for the integrable map and the associated Hamiltonian system [...] Read more.

Quantum tunneling in a two-dimensional integrable map is studied. The orbits of the map are all confined to the curves specified by the one-dimensional Hamiltonian. It is found that the behavior of tunneling splitting for the integrable map and the associated Hamiltonian system is qualitatively the same, with only a slight difference in magnitude. However, the tunneling tails of the wave functions, obtained by superposing the eigenfunctions that form the doublet, exhibit significant differences. To explore the origin of the difference, we observe the classical dynamics in the complex plane and find that the existence of branch points appearing in the potential function of the integrable map could play the role of yielding non-trivial behavior in the tunneling tail. The result highlights the subtlety of quantum tunneling, which cannot be captured in nature only by the dynamics in the real plane. Full article

(This article belongs to the Special Issue Tunneling in Complex Systems)

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15 pages, 349 KiB

Open AccessArticle

Finite-Temperature Correlation Functions Obtained from Combined Real- and Imaginary-Time Propagation of Variational Thawed Gaussian Wavepackets

by Jens Aage Poulsen and Gunnar Nyman

Entropy 2024, 26(5), 412; https://doi.org/10.3390/e26050412 - 10 May 2024

Cited by 1 | Viewed by 1090

Abstract

We apply the so-called variational Gaussian wavepacket approximation (VGA) for conducting both real- and imaginary-time dynamics to calculate thermal correlation functions. By considering strongly anharmonic systems, such as a quartic potential and a double-well potential at high and low temperatures, it is shown [...] Read more.

We apply the so-called variational Gaussian wavepacket approximation (VGA) for conducting both real- and imaginary-time dynamics to calculate thermal correlation functions. By considering strongly anharmonic systems, such as a quartic potential and a double-well potential at high and low temperatures, it is shown that this method is partially able to account for tunneling. This is contrary to other popular many-body methods, such as ring polymer molecular dynamics and the classical Wigner method, which fail in this respect. It is a historical peculiarity that no one has considered the VGA method for representing both the Boltzmann operator and the real-time propagation. This method should be well suited for molecular systems containing many atoms. Full article

(This article belongs to the Special Issue Tunneling in Complex Systems)

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15 pages, 2968 KiB

Open AccessArticle

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

Cited by 1 | Viewed by 2244

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

Open AccessReview

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

Cited by 1 | Viewed by 1553

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

Open AccessReview

Chaos-Assisted Tunneling

by Linda E. Reichl

Entropy 2024, 26(2), 144; https://doi.org/10.3390/e26020144 - 7 Feb 2024

Cited by 2 | Viewed by 1461

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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