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A Brief Review of Quantum Tunneling: Computational Approaches and Experimental Evidence

Sareh Eslamzadeh, Saheb Soroushfar

TL;DR

The paper surveys the quantum tunneling approach to Hawking radiation, distinguishing stationary and dynamical horizons. It presents two semi-classical methods, the Parikh-Wilczek null-geodesic approach and the Hamilton-Jacobi method, linking the imaginary part of the action to the emission rate and Hawking temperature. The extension to dynamical horizons introduces trapping horizons, Kodama vectors, and dynamical surface gravity, with two tunneling paths and a key Im S expression for the relevant channel. Experimentally, while direct detection is challenging, analogue systems, quantum simulations, and astrophysical searches provide indirect evidence supporting the tunneling picture.

Abstract

This paper presents a concise review of the quantum tunneling approach to Hawking radiation, covering its theoretical foundations, extensions, and experimental efforts. We begin by outlining the Hamilton-Jacobi and Parikh-Wilczek methods, which provide a semi-classical framework for deriving Hawking radiation from stationary black holes. The discussion is then extended to dynamical black holes, where evolving horizons require modified treatments incorporating trapping horizons, Kodama vectors, and dynamical surface gravity. We explored the possible tunneling paths for particles crossing the horizon in dynamical black holes and emphasized the crucial role of the imaginary part of the action in determining the Hawking temperature. In the second part, we review experimental investigations of Hawking radiation, including analogue black hole experiments, quantum simulations, and astrophysical searches for primordial black hole evaporation. While no direct detection of Hawking radiation has been achieved, recent advances in Bose-Einstein condensates, optical analogues, and superconducting qubits offer indirect support for the tunneling interpretation of black hole evaporation.

A Brief Review of Quantum Tunneling: Computational Approaches and Experimental Evidence

TL;DR

The paper surveys the quantum tunneling approach to Hawking radiation, distinguishing stationary and dynamical horizons. It presents two semi-classical methods, the Parikh-Wilczek null-geodesic approach and the Hamilton-Jacobi method, linking the imaginary part of the action to the emission rate and Hawking temperature. The extension to dynamical horizons introduces trapping horizons, Kodama vectors, and dynamical surface gravity, with two tunneling paths and a key Im S expression for the relevant channel. Experimentally, while direct detection is challenging, analogue systems, quantum simulations, and astrophysical searches provide indirect evidence supporting the tunneling picture.

Abstract

This paper presents a concise review of the quantum tunneling approach to Hawking radiation, covering its theoretical foundations, extensions, and experimental efforts. We begin by outlining the Hamilton-Jacobi and Parikh-Wilczek methods, which provide a semi-classical framework for deriving Hawking radiation from stationary black holes. The discussion is then extended to dynamical black holes, where evolving horizons require modified treatments incorporating trapping horizons, Kodama vectors, and dynamical surface gravity. We explored the possible tunneling paths for particles crossing the horizon in dynamical black holes and emphasized the crucial role of the imaginary part of the action in determining the Hawking temperature. In the second part, we review experimental investigations of Hawking radiation, including analogue black hole experiments, quantum simulations, and astrophysical searches for primordial black hole evaporation. While no direct detection of Hawking radiation has been achieved, recent advances in Bose-Einstein condensates, optical analogues, and superconducting qubits offer indirect support for the tunneling interpretation of black hole evaporation.

Paper Structure

This paper contains 10 sections, 14 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Tunneling from Horizon of the Stationary Black Hole
  3. Parikh-Wilczek Method
  4. Hamilton-Jacobi Method
  5. Extension of Tunneling Methods to Dynamical Black Hole
  6. Experimental Evidence of Hawking Radiation
  7. Analogue Black Hole Experiments
  8. Quantum Simulations of Hawking Radiation
  9. Astrophysical Observations of Hawking Radiation
  10. Summary

Figures (2)

  • Figure 1: The spherical wave passing through the horizon of Schwarzschild black hole. ($\vec{abc}$) is a light-like geodesic as a continuous path from the inside to the outside of the black hole, where ($\vec{ab}$) is the classical forbidden path and, therefore, in the reverse time direction.
  • Figure 2: Two types of paths for escaping particles from dynamical black holes.