An analytical solution of a quantum system with non-Markovian behavior: The Bixon-Jortner system in time domain

• URL: http://arxiv.org/abs/2607.07546v1
• Date: Wed, 08 Jul 2026 15:44:47 GMT
• Title: An analytical solution of a quantum system with non-Markovian behavior: The Bixon-Jortner system in time domain
• Abstract summary: We obtain an exact non-Markovian equation for the dynamics of a simple model system.<n>We demonstrate decay and revival behaviors coming from the delay differential equation.<n>We believe the explicit form of the time-domain non-Markovian equation we obtain and the accessibility the solution techniques we use make our results a useful case study of non-Markovianity in quantum systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Non-Markovian behavior in quantum systems is often studied in the context of bipartite systems consisting of a system of interest and an environment -- tracing over the environment results in non-Markovian behavior for the subsystem of interest. One may get a Markovian limit in certain regimes, which is studied using the Lindblad master equation, and corrections to this behavior can be obtained by techniques such as the Nakajima-Zwanzig formalism. In this paper, we obtain an exact non-Markovian equation for the dynamics of a simple model system that consists of a direct sum rather than a tensor product of two pieces, namely, a discrete state and an infinite ladder. This system, called the Bixon-Jortner model, was first developed in the quantum chemistry literature but has been utilized by the quantum optics community as a model system with interesting behavior, including a Wigner-Weisskopf limit of exponential decay. We attack the time evolution problem of this system directly in time-domain, and start with an integrodifferential equation describing the time evolution of the discrete state. Using tools from mathematical physics, we transform this equation to a delay differential equation, which makes the non-Markovianity completely transparent, and then we solve the delay equation using an intuitive ansatz. This allows us to obtain the analytic form of the dynamics directly in time domain, and demonstrate decay and revival behaviors coming from the aforementioned delay differential equation. We believe the explicit form of the time-domain non-Markovian equation we obtain and the accessibility the solution techniques we use make our results a useful case study of non-Markovianity in quantum systems.

Related papers

• A unifying framework for quantum algorithms for time-dependent non-unitary dynamics [10.241798338676155]
  We introduce an autonomization framework based on the clock-variable formulation.<n>We obtain an explicit time-independent linear system, together with a suitable initial state and a recovery map for the target solution.<n>We combine this framework with Schrdingerization and a Taylor-expansion-based quantum ODE solver.
  arXiv  Detail & Related papers  (2026-08-07T11:47:33Z)
• A time-marching quantum algorithm for simulation of the nonlinear Lorenz dynamics [0.0]
  We develop a quantum algorithm that implements the time evolution of a second order time-discretized version of the Lorenz model.<n> Notably, we showcase that it accurately captures the structural characteristics of the Lorenz system.
  arXiv  Detail & Related papers  (2025-06-26T15:08:00Z)
• 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)
• Going beyond quantum Markovianity and back to reality: An exact master equation study [0.0]
  An analytical depiction of an open quantum system is provided.<n>The steady-state excitation number (AEN) of the system shows rapid escalation with increasing non-Markovianity.<n>The Mpemba effect can be observed in the non-Markovian regime in a surprisingly super-cooling-like effect.
  arXiv  Detail & Related papers  (2024-11-26T08:10:35Z)
• Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
  We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations. We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2024-10-04T18:06:12Z)
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models [0.0]
  We develop a unified framework for open quantum systems composed of many mutually interacting quantum spins.<n>Our framework, based on Schwinger-Keldysh field theory, can handle arbitrary spin value, dimensionality of space, and geometry.<n>It can probe regimes in which non-Markovian dynamics and nonperturbative effects pose formidable challenges.
  arXiv  Detail & Related papers  (2024-05-01T17:57:08Z)
• TANGO: Time-Reversal Latent GraphODE for Multi-Agent Dynamical Systems [43.39754726042369]
  We propose a simple-yet-effective self-supervised regularization term as a soft constraint that aligns the forward and backward trajectories predicted by a continuous graph neural network-based ordinary differential equation (GraphODE) It effectively imposes time-reversal symmetry to enable more accurate model predictions across a wider range of dynamical systems under classical mechanics. Experimental results on a variety of physical systems demonstrate the effectiveness of our proposed method.
  arXiv  Detail & Related papers  (2023-10-10T08:52:16Z)
• Time dependent Markovian master equation beyond the adiabatic limit [0.8192907805418583]
  We derive a Markovian master equation that models the evolution of systems subject to driving and control fields. We demonstrate the reliability and broad scope of our approach by benchmarking the solutions of the derived reduced time evolution against numerically exact simulations.
  arXiv  Detail & Related papers  (2023-04-12T21:33:12Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Different routes to the classical limit of backflow [0.0]
  This work is to analyze the backflow effect in the light of the underlying intrinsic decoherence and the dissipative dynamics. In all the cases treated here, backflow is gradually suppressed as the intrinsic decoherence process is developing.
  arXiv  Detail & Related papers  (2022-11-16T17:18:09Z)
• 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)
• Preserving quantum correlations and coherence with non-Markovianity [50.591267188664666]
  We demonstrate the usefulness of non-Markovianity for preserving correlations and coherence in quantum systems. For covariant qubit evolutions, we show that non-Markovianity can be used to preserve quantum coherence at all times.
  arXiv  Detail & Related papers  (2021-06-25T11:52:51Z)
• Intermediate Times Dilemma for Open Quantum System: Filtered Approximation to The Refined Weak Coupling Limit [0.0]
  A filtered approximation (FA) to the refined weak coupling limit allows capturing the dynamics in the intermediate time regime. We exemplify the performance of the FA equation in the cases of the spin-boson system and qutrit-boson system.
  arXiv  Detail & Related papers  (2021-06-10T14:28:59Z)
• 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)

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.