A Brief History of Quantum Tunneling Some Basic Questions Concerning Quantum Tunneling Simple Solvable Problems Time-Dependence of the Wave Function in One-Dimensional Tunneling Semiclassical Approximations Generalization of the Bohr - Sommerfeld Quantization Rule and its Application to Quantum Tunneling Gamow's Theory, Complex Eigenvalues, and the Wave Function of a Decaying State Tunneling in Symmetric and Asymmetric Local Potentials and Tunneling in Nonlocal and Quasi-Solvable Barriers Classical Descriptions of Tunneling Tunneling in Time-Dependent Barriers Decay Width and Scattering Theory The Method of Variable Reflection Amplitude Applied to Solve Multichannel Tunneling Problems Path Integral and Its Semi-Classical Approximation in Quantum Tunneling Heisenberg's Equations of Motion for Tunneling Wigner Distribution Function in Quantum Tunneling Decay Widths of Siegert States, Complex Scaling and Dilatation Transformation Multidimensional Quantum Tunneling Group and Signal Velocities Time-Delay, Reflection Time Operator and Minimum Tunneling Time More about Tunneling Time Tunneling of a System with Internal Degrees of Freedom Motion of a Particle in a Waveguide with Variable Cross Section and in a Space Bounded by a Dumbbell-Shaped Object Relativistic Formulation of Quantum Tunneling Inverse Problems of Quantum Tunneling Some Examples of Quantum Tunneling in Atomic and Molecular Physics Some Examples from Condensed Matter Physics Alpha Decay.A Brief History of Quantum Tunneling Some Basic Questions Concerning Quantum Tunneling Simple Solvable Problems Time-Dependence of the Wave Function in One-Dimensional Tunneling Semiclassical Approximations Generalization of the Bohr - Sommerfeld Quantization Rule and its Application to Quantum Tunneling Gamow's Theory, Complex Eigenvalues, and the Wave Function of a Decaying State Tunneling in Symmetric and Asymmetric Local Potentials and Tunneling in Nonlocal and Quasi-Solvable Barriers Classical Descriptions of Tunneling Tunneling in Time-Dependent Barriers Decay Width and Scattering Theory The Method of Variable Reflection Amplitude Applied to Solve Multichannel Tunneling Problems Path Integral and Its Semi-Classical Approximation in Quantum Tunneling Heisenberg's Equations of Motion for Tunneling Wigner Distribution Function in Quantum Tunneling Decay Widths of Siegert States, Complex Scaling and Dilatation Transformation Multidimensional Quantum Tunneling Group and Signal Velocities Time-Delay, Reflection Time Operator and Minimum Tunneling Time More about Tunneling Time Tunneling of a System with Internal Degrees of Freedom Motion of a Particle in a Waveguide with Variable Cross Section and in a Space Bounded by a Dumbbell-Shaped Object Relativistic Formulation of Quantum Tunneling Inverse Problems of Quantum Tunneling Some Examples of Quantum Tunneling in Atomic and Molecular Physics Some Examples from Condensed Matter Physics Alpha Decay.

WORLD SCIENTIFIC eBooksJan 1, 2003259 citations

Breaking rotational symmetry in a trapped-ion quantum tunneling rotor

Ryutaro Ohira, Takashi Mukaiyama, Kenji Toyoda

A trapped-ion quantum tunneling rotor (QTR) is in a quantum superposition of two different Wigner crystal orientations. In a QTR system, quantum tunneling drives the coherent transition between the two different Wigner crystal orientations. We theoretically study the quantum dynamics of a QTR, particularly when the spin state of one of the ions is flipped. We show that the quantum dynamics of an $\mathit{N}$ -ion QTR can be described by continuous-time cyclic quantum walks. We also investigate the quantum dynamics of the QTR in a magnetic field. Flipping the spin state breaks the rotational symmetry of the QTR, making the quantum-tunneling-induced rotation distinguishable. This symmetry breaking creates coupling between the spin state of the ions and the rotational motion of the QTR, resulting in different quantum tunneling dynamics.A trapped-ion quantum tunneling rotor (QTR) is in a quantum superposition of two different Wigner crystal orientations. In a QTR system, quantum tunneling drives the coherent transition between the two different Wigner crystal orientations. We theoretically study the quantum dynamics of a QTR, particularly when the spin state of one of the ions is flipped. We show that the quantum dynamics of an $\mathit{N}$-ion QTR can be described by continuous-time cyclic quantum walks. We also investigate the quantum dynamics of the QTR in a magnetic field. Flipping the spin state breaks the rotational symmetry of the QTR, making the quantum-tunneling-induced rotation distinguishable. This symmetry breaking creates coupling between the spin state of the ions and the rotational motion of the QTR, resulting in different quantum tunneling dynamics.

arXiv:1907.07404Physical Review AFeb 14, 20202 citations

Quantum Tunneling

CRC Press eBooksOct 4, 20164 citations

Quantum Tunneling

Benjamin Bähr, Boris Lemmer, Rina Piccolo

Springer eBooksJan 1, 20160 citations

A Model of Quantum Tunneling with Knots and Braid Operators

Phuong-Nam Nguyen

Topological quantum computing is an emerging field that leverages the mathematical structures of knots and braids to encode and manipulate quantum information. However, the topological nature of quantum tunneling remains largely unexplored. In this work, we introduce a novel paradigm for quantum tunneling based on the knot representation of quantum wavefunctions, where Reidemeister moves—interpreted as braid group operators—govern the wavefunction’s evolution. Specifically, we propose four distinct models for topological quantum tunneling: (1) tunneling via Reidemeister transitions, (2) tunneling on a ring-domain, (3) tunneling under space-time curvature, and (4) tunneling influenced by gravitational potential. By establishing a rigorous connection between knot theory, braid group structures, and quantum tunneling, our approach provides a new framework for understanding quantum transport in complex environments. The broader impact of this work lies in bridging topological quantum mechanics with quantum biology and life sciences, opening new avenues for interdisciplinary research in quantum information processing and biophysical modeling.Topological quantum computing is an emerging field that leverages the mathematical structures of knots and braids to encode and manipulate quantum information. However, the topological nature of quantum tunneling remains largely unexplored. In this work, we introduce a novel paradigm for quantum tunneling based on the knot representation of quantum wavefunctions, where Reidemeister moves—interpreted as braid group operators—govern the wavefunction’s evolution. Specifically, we propose four distinct models for topological quantum tunneling: (1) tunneling via Reidemeister transitions, (2) tunneling on a ring-domain, (3) tunneling under space-time curvature, and (4) tunneling influenced by gravitational potential. By establishing a rigorous connection between knot theory, braid group structures, and quantum tunneling, our approach provides a new framework for understanding quantum transport in complex environments. The broader impact of this work lies in bridging topological quantum mechanics with quantum biology and life sciences, opening new avenues for interdisciplinary research in quantum information processing and biophysical modeling.

International Conference on Cryptography and Information Security (VCRIS)Oct 30, 20250 citations

\mathit{N}

-ion QTR can be described by continuous-time cyclic quantum walks. We also investigate the quantum dynamics of the QTR in a magnetic field. Flipping the spin state breaks the rotational symmetry of the QTR, making the quantum-tunneling-induced rotation distinguishable. This symmetry breaking creates coupling between the spin state of the ions and the rotational motion of the QTR, resulting in different quantum tunneling dynamics.