Exact Ionization Amplitudes for a Delta-Function Well in an Arbitrary-Strength DC Electric Field

• URL: http://arxiv.org/abs/2609.16507v1
• Date: Tue, 15 Sep 2026 01:55:24 GMT
• Title: Exact Ionization Amplitudes for a Delta-Function Well in an Arbitrary-Strength DC Electric Field
• Abstract summary: We investigate finite-time field-induced ionization from a one-dimensional attractive delta-function well in a uniform dc electric field of arbitrary strength.<n>Our aim is to determine the physical bound-state survival amplitude (a_b(t)) at any observation time without constructing the complete time-dependent propagator or wavefunction.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate finite-time field-induced ionization from a one-dimensional attractive delta-function well in a uniform dc electric field of arbitrary strength. Our aim is to determine the physical bound-state survival amplitude \(a_b(t)\) at any observation time without constructing the complete time-dependent propagator or wavefunction. In the gauge-equivalent Kramers--Henneberger representation, the field appears as motion of the contact point, and the resulting dynamics reduces to a closed Volterra equation. Exact endpoint-phase factorization organizes the full chronological rescattering history into a relative-time convolution hierarchy and an exact resolvent. By introducing the accumulated bound-state amplitude and reorganizing its two-time domain in relative and complementary center times, the final contact contribution becomes an explicit boundary integral. All spatial integrations are carried out analytically. The field-driven contact-free term is obtained in closed form using the Faddeeva function, while the direct and repeated-rescattering terms are expressed as explicitly evaluable time integrals. The result applies at arbitrary dc-field strength and finite time, with no weak-field expansion, rescattering truncation, or asymptotic-time approximation. It is verified through the exact field-free limit and an independent numerical solution of the original physical Volterra equation. The formulation gives an exact nonperturbative solution of a fundamental ionization model and reveals otherwise hidden analytical structure in driven quantum dynamics.

Related papers

• Timelike Entanglement from Spacetime Density Matrices: A Lattice Realization [4.363749106659002]
  We investigate timelike entanglement in quantum field theory using spacetime density matrix.<n>We find quantitative agreement in both magnitude and phase across distinct causal regimes.<n>These results provide a microscopic lattice foundation for timelike entanglement and for Lorentzian twist-operator methods beyond equal-time regions.
  arXiv  Detail & Related papers  (2026-09-10T01:37:49Z)
• Stochastic Counterdiabatic Driving via Biorthogonal Liouvillian Eigenmodes [42.668742604089324]
  Escorted free energy simulations address the non-adiabatic lag by engineering control fields $mathbfu$ that eliminate the lag.<n>We construct a complementary numerical framework based on gauge-type transforms instead of generalized coordinate transforms.<n>We show that the counterdiabatic condition is satisfied to machine precision, with the non-adiabatic lag suppressed by roughly twelve orders of magnitude.
  arXiv  Detail & Related papers  (2026-07-27T13:08:14Z)
• Free energy Estimation on Any State Space [49.560935787029564]
  Recent work learns neural transports to significantly accelerate the efficiency in the finite-time regime.<n>In this paper, we generalize this framework to arbitrary state spaces.<n> Experiments validate the effectiveness and efficiency of the proposed method.
  arXiv  Detail & Related papers  (2026-05-29T09:34:53Z)
• Tracing complex zeros of the quantum survival amplitude: How the energy distribution controls dynamical phase transitions [0.0]
  We show that the large-scale properties of the distribution of zeros are governed by the envelope of the energy distribution of the initial state.<n>We prove that the approximate construction becomes exact for BCS ground-state quenches in two-band models.<n>Our results identify the energy envelope as the key ingredient shaping dynamical critical behavior.
  arXiv  Detail & Related papers  (2026-05-07T18:51:28Z)
• Path integral formulation of finite-dimensional quantum mechanics in discrete phase space [0.0]
  We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space.<n>For Hamiltonians linear in the phase-space coordinates, we show that the fluctuation sum factorizes.<n>We show explicitly that the full entanglement dynamics requires the coherent contribution of all fluctuation sectors of the action.
  arXiv  Detail & Related papers  (2026-04-22T17:04:10Z)
• Parallel Complex Diffusion for Scalable Time Series Generation [50.01609741902786]
  PaCoDi is a spectral-native architecture that decouples generative modeling in the frequency domain.<n>We show that PaCoDi outperforms existing baselines in both generation quality and inference speed.
  arXiv  Detail & Related papers  (2026-02-10T14:31:53Z)
• Propagation of Chaos in One-hidden-layer Neural Networks beyond Logarithmic Time [46.15741640288809]
  We study the approximation gap between the dynamics of a-width neural network and its infinite-width counterpart.<n>We demonstrate how to tightly bound this approximation gap through a differential equation governed by the mean-field dynamics.
  arXiv  Detail & Related papers  (2025-04-17T17:24:38Z)
• Time-dependent Neural Galerkin Method for Quantum Dynamics [39.63609604649394]
  We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle.<n>Our scheme computes the entire state trajectory over a finite time window by minimizing a loss function that enforces the Schr"odinger's equation.<n>We showcase the method by simulating global quantum quenches in the paradigmatic Transverse-Field Ising model in both 1D and 2D.
  arXiv  Detail & Related papers  (2024-12-16T13:48:54Z)
• Emptiness Instanton in Quantum Polytropic Gas [49.1574468325115]
  The problem involves determining the probability of the spontaneous formation of an empty interval in the ground state of the gas.<n>By solving the hydrodynamic equations in imaginary time, we derive the analytic form of the emptiness instanton.<n>This solution is expressed as an integral representation analogous to those used for correlation functions in Conformal Field Theory.
  arXiv  Detail & Related papers  (2024-12-16T11:58:51Z)
• Toward quantum tunneling from excited states: Recovering imaginary-time instantons from a real-time analysis [0.0]
  We revisit the path integral description of quantum tunneling and lay the groundwork for its generalization.<n>For clarity, we focus on the simple toy model of a point particle in a double-well potential, for which we perform all steps explicitly.<n>For systems without an explicit time-dependence, our approach reproduces the picture of an instanton-like solution defined on a finite Euclidean-time interval.
  arXiv  Detail & Related papers  (2024-01-31T19:00:00Z)
• Unraveling the bounce: a real time perspective on tunneling [0.0]
  We study tunneling in one-dimensional quantum mechanics using the path integral in real time, where solutions of the classical equation of motion live in the complex plane. We show explicitly how the imaginary time bounce arises as a parameterization of the lowest order term in the energy expansion.
  arXiv  Detail & Related papers  (2023-09-14T10:35:39Z)

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.