Recent Advances in Semiclassical Methods Inspired by Supersymmetric Quantum Mechanics

• URL: http://arxiv.org/abs/2408.15424v2
• Date: Thu, 29 Aug 2024 02:48:44 GMT
• Title: Recent Advances in Semiclassical Methods Inspired by Supersymmetric Quantum Mechanics
• Authors: Asim Gangopadhyaya, Jonathan Bougie, Constantin Rasinariu,
• Abstract summary: Recent research has demonstrated a deep connection between supersymmetric quantum mechanics and the exactness of semiclassical methods. Specifically, the mathematical form of conventional shape-invariant potentials guarantees exactness in several related situations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Semiclassical methods are essential in analyzing quantum mechanical systems. Although they generally produce approximate results, relatively rare potentials exist for which these methods are exact. Such intriguing potentials serve as crucial test cases for semiclassical approximations. Recent research has demonstrated a deep connection between supersymmetric quantum mechanics and the exactness of semiclassical methods. Specifically, the mathematical form of conventional shape-invariant potentials guarantees exactness in several related situations. In this manuscript, we review these recent results and discuss their significance.

Related papers

• Exploring Supersymmetry: Interchangeability Between Jaynes-Cummings and Anti-Jaynes-Cummings Models [39.58317527488534]
  The supersymmetric connection that exists between the Jaynes-Cummings (JC) and anti-Jaynes Cummings (AJC) models in quantum optics is unraveled. A new method is proposed to obtain the temporal evolution of observables in the AJC model using supersymmetric techniques.
  arXiv  Detail & Related papers  (2024-04-18T18:00:34Z)
• Classical Invasive Description of Informationally-Complete Quantum Processes [0.0]
  In classical theory, the joint probability distributions of a process obey by definition the Kolmogorov consistency conditions. Here, we derive conditions that characterize uniquely classical processes that are probed by a reasonable class of invasive measurements. We then analyse under what circumstances such classical processes can simulate the statistics arising from quantum processes associated with informationally-complete measurements.
  arXiv  Detail & Related papers  (2023-12-11T17:31:32Z)
• Symmetry breaking and restoration for many-body problems treated on quantum computers [0.0]
  This thesis explores the application of the Symmetry-Breaking/Symmetry-Restoration methodology on quantum computers. It involves intentionally breaking and restoring the symmetries of the wave function ansatz at different stages of the variational search for the ground state. In the final part, hybrid quantum-classical techniques were introduced to extract an approximation of the low-lying spectrum of a Hamiltonian.
  arXiv  Detail & Related papers  (2023-10-27T09:12:38Z)
• Anticipative measurements in hybrid quantum-classical computation [68.8204255655161]
  We present an approach where the quantum computation is supplemented by a classical result. Taking advantage of its anticipation also leads to a new type of quantum measurements, which we call anticipative. In an anticipative quantum measurement the combination of the results from classical and quantum computations happens only in the end.
  arXiv  Detail & Related papers  (2022-09-12T15:47:44Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Exactness of Semiclassical Quantization Rule for Broken Supersymmetry [0.0]
  We show that the long-conjectured exactness of the supersymmetry-based semiclassical quantization condition for broken supersymmetry is a consequence of the additive shape invariance for the corresponding potentials.
  arXiv  Detail & Related papers  (2020-12-03T13:48:46Z)
• Comparison of the mean field and Bohmian semi-classical approximations to the Rabi model [0.0]
  Bohmian mechanics is an alternative to standard quantum mechanics that does not suffer from the measurement problem. We analyse the Rabi model using a different semi-classical approximation based on Bohmian mechanics. Both semi-classical approximations tend to reproduce the collapse of the population inversion, but fail to reproduce the revival, which is characteristic of the full quantum description.
  arXiv  Detail & Related papers  (2020-11-10T18:36:17Z)
• Old Quantization, Angular Momentum, and Nonanalytic Problems [1.933681537640272]
  We show that old quantization leads to qualitatively and quantitatively useful information about systems with spherically symmetric potentials. We analyze systems with logarithmic and Yukawa potentials, and compare the results of old quantization to those from solving Schrodinger's equation.
  arXiv  Detail & Related papers  (2020-08-31T19:35:25Z)
• Optimal non-classical correlations of light with a levitated nano-sphere [34.82692226532414]
  Nonclassical correlations provide a resource for many applications in quantum technology. Optomechanical systems can generate nonclassical correlations between the mechanical mode and a mode of travelling light. We propose automated optimization of the production of quantum correlations in such a system.
  arXiv  Detail & Related papers  (2020-06-26T15:27:47Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)
• Theoretical methods for ultrastrong light-matter interactions [91.3755431537592]
  This article reviews theoretical methods developed to understand cavity quantum electrodynamics in the ultrastrong-coupling regime. The article gives a broad overview of the recent progress, ranging from analytical estimate of ground-state properties to proper computation of master equations. Most of the article is devoted to effective models, relevant for the various experimental platforms in which the ultrastrong coupling has been reached.
  arXiv  Detail & Related papers  (2020-01-23T18:09:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.