Dynamical system analysis of quantum tunneling in an asymmetric double-well potential

• URL: http://arxiv.org/abs/2510.24100v1
• Date: Tue, 28 Oct 2025 06:11:28 GMT
• Title: Dynamical system analysis of quantum tunneling in an asymmetric double-well potential
• Authors: Swetamber Das, Arghya Dutta,
• Abstract summary: We study quantum tunneling in an asymmetric double-well potential using a dynamical systems--based approach rooted in the Ehrenfest formalism.<n>An approximate closure, required to render the system tractable, yields a reduced dynamical system for the mean and variance, with skewness entering explicitly due to the potential's asymmetry.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study quantum tunneling in an asymmetric double-well potential using a dynamical systems--based approach rooted in the Ehrenfest formalism. In this framework, the time evolution of a Gaussian wave packet is governed by a hierarchy of coupled equations linking lower- and higher-order position moments. An approximate closure, required to render the system tractable, yields a reduced dynamical system for the mean and variance, with skewness entering explicitly due to the potential's asymmetry. Stability analysis of this system identifies energy thresholds for detectable tunneling across the barrier and reveals regimes where tunneling, though theoretically allowed, remains practically undetectable. Comparison with full numerical solutions of the time-dependent Schr\"odinger equation shows that, beyond reproducing key tunneling features, the dynamical systems approach provides an interpretable description of quantum transport through tunneling in an effective asymmetric two-level system.

Related papers

• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment.<n>We find sufficient conditions under which dynamical decoupling works for such systems.<n>Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• Probing entanglement of a continuous basis system [0.0]
  We propose a method to probe entanglement in a theoretically inaccessible quantum system with either a discrete or continuous basis.<n>Our approach leverages insights into the entanglement distribution within a four-partite quantum system.<n>Our findings reveal an intriguing conservative flow-like behavior in the redistribution of entanglement among subsystems, suggesting that entanglement may exhibit conservative properties in pure composite quantum systems.
  arXiv  Detail & Related papers  (2024-09-12T19:59:06Z)
• Three perspectives on entropy dynamics in a non-Hermitian two-state system [41.94295877935867]
  entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping.
  arXiv  Detail & Related papers  (2024-04-04T14:45:28Z)
• Machine Learning Catalysis of Quantum Tunneling [0.07281763676971992]
  We show that, by applying Machine Learning techniques when the system is coupled to ancilla, one optimize the parameters of both the ancillary component and the coupling. We provide illustrative examples for the paradigmatic scenario involving a two-mode system and a two-mode ancilla. The increase of the tunneling probability is rooted in the decrease of the two-well asymmetry due to the coherent oscillations induced by the coupling to the ancilla.
  arXiv  Detail & Related papers  (2023-10-16T08:10:41Z)
• Catalysis of quantum tunneling by ancillary system learning [0.0]
  We show that an effective solution can be achieved by coupling the tunneling system with an ancillary system of the same kind. We provide examples for the paradigmatic scenario involving a two-mode system and a two-mode ancilla with arbitrary couplings. Importantly, the enhancement of the tunneling probability appears to be minimally affected by noise and decoherence in both the system and the ancilla.
  arXiv  Detail & Related papers  (2023-08-11T10:21:14Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Trajectories without quantum uncertainties in composite systems with disparate energy spectra [0.0]
  measurement-induced quantum back action can be eliminated in composite systems by engineering quantum-mechanics-free subspaces. The utility of the concept has been limited by the requirement of close proximity of the resonance frequencies of the system of interest and the negative-mass reference system. Here we propose a general approach which overcomes these limitations by employing periodic modulation of the driving fields.
  arXiv  Detail & Related papers  (2021-11-04T09:12:28Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
  We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation. We describe quantum decays in a 2-level system as coherent and continuous processes.
  arXiv  Detail & Related papers  (2021-07-29T18:27:38Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Feedback-induced instabilities and dynamics in the Jaynes-Cummings model [62.997667081978825]
  We investigate the coherence and steady-state properties of the Jaynes-Cummings model subjected to time-delayed coherent feedback. The introduced feedback qualitatively modifies the dynamical response and steady-state quantum properties of the system.
  arXiv  Detail & Related papers  (2020-06-20T10:07:01Z)

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.