Markovian Embeddings of Non-Markovian Open System Dynamics

• URL: http://arxiv.org/abs/2602.21430v1
• Date: Tue, 24 Feb 2026 23:07:43 GMT
• Title: Markovian Embeddings of Non-Markovian Open System Dynamics
• Authors: Meng Xu, J. T. Stockburger, J. Ankerhold,
• Abstract summary: Embedding non-Markovian open quantum dynamics into an enlarged Markovian space offers a powerful route to nonperturbative simulations.<n>We show that these distinct embeddings arise from different unravelings of Gaussian bath self-energies, generating a family of deterministic, time-local equations.<n>This work provides both a transparent theoretical foundation for embedding techniques and a flexible platform for developing new methods to simulate non-Markovian quantum dynamics.
• Score: 1.0747226579580043
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Embedding non-Markovian open quantum dynamics into an enlarged Markovian space offers a powerful route to nonperturbative simulations, where the dynamics of the extended space can be governed by multiple distinct Markovian equations. We show that these distinct embeddings arise from different unravelings of Gaussian bath self-energies, generating a family of deterministic, time-local equations for the extended system. Using the Brownian-oscillator spectral density as an illustrative example, we clarify the relationships among existing approaches, including the Hierarchical Equations of Motion (HEOM) and the Lindblad--pseudomode formalism, and demonstrate how this framework enables numerically stable and efficient simulations. This work provides both a transparent theoretical foundation for embedding techniques and a flexible platform for developing new methods to simulate non-Markovian quantum dynamics.

Related papers

• Projection-Based Memory Kernel Coupling Theory for Quantum Dynamics: A Stable Framework for Non-Markovian Simulations [13.09851912426216]
  We present a projection-based, stability-preserving methodology for computing time correlation functions in open quantum systems.<n>This approach provides a versatile and reliable framework for non-Markovian dynamics in complex systems.
  arXiv  Detail & Related papers  (2026-02-11T08:22:00Z)
• Stochastic unravelings for trace-nonpreserving open quantum system dynamics [0.0]
  We introduce a general framework that extends piecewise-deterministic unravelings to arbitrary trace-nonpreserving master equations.<n>Our approach includes, as special cases, unravelings of arbitrary dynamics in the Heisenberg picture.<n>It is compatible with different unraveling schemes and with reverse jumps in the non-Markovian regime.
  arXiv  Detail & Related papers  (2025-11-19T15:10:27Z)
• Realization of Trapped Ion Dynamics in the Strong-Field Regime and Non-Markovianity [33.781064984238775]
  We experimentally investigate the dynamics of a trapped ion where the Rabi frequency (Omega) approaches the vibrational mode frequency (nu)<n>Using quantum state tomography, we reconstruct the density matrix and track its evolution to assess non-Markovianity.<n>Our findings establish a pathway for using trapped-ion platforms to investigate non-Markovianity, coherent control, and the fundamental behavior of open quantum systems in extreme regimes.
  arXiv  Detail & Related papers  (2025-10-23T11:25:09Z)
• Flexible Language Modeling in Continuous Space with Transformer-based Autoregressive Flows [46.673228292287895]
  We propose a novel framework that employs transformer-based autoregressive normalizing flows to model continuous representations.<n>This approach unlocks substantial flexibility, enabling the construction of models that can capture global bi-directional context.<n>We propose new mixture-based coupling transformations designed to capture complex dependencies within the latent space shaped by discrete data.
  arXiv  Detail & Related papers  (2025-07-01T04:51:25Z)
• Extended Non-Markovian Stochastic Schrödinger Equation with Complex Frequency Modes for General Basis Functions [6.836013275880708]
  We introduce an extended formulation of the non-Markovian Schr"odinger equation with complex frequency modes (extended cNMSSE)<n>This extension employs non-exponential basis sets to expand the bath correlation functions.<n>It is applicable to environments beyond those characterized by Debye-type spectral densities.
  arXiv  Detail & Related papers  (2025-06-28T02:47:14Z)
• Lie symmetries and ghost-free representations of the Pais-Uhlenbeck model [44.99833362998488]
  We investigate the Pais-Uhlenbeck (PU) model, a paradigmatic example of a higher time-derivative theory.<n>Exploiting Lie symmetries in conjunction with the model's Bi-Hamiltonian structure, we construct distinct Poisson bracket formulations.<n>Our approach yields a unified framework for interpreting and stabilising higher time-derivative dynamics.
  arXiv  Detail & Related papers  (2025-05-09T15:16:40Z)
• Post-Markovian master equation à la microscopic collisional model [0.0]
  We derive a positive post-Markovian master equation (PMME) from a microscopic Markovian collisional model framework. We also investigate thermalization using the derived equation, revealing that the post-Markovian dynamics accelerates the thermalization process.
  arXiv  Detail & Related papers  (2024-11-25T19:18:10Z)
• Hybrid Stabilizer Matrix Product Operator [44.99833362998488]
  We introduce a novel hybrid approach combining tensor network methods with the stabilizer formalism to address the challenges of simulating many-body quantum systems. We demonstrate the effectiveness of our method through applications to random Clifford T-doped circuits and Random Clifford Floquet Dynamics.
  arXiv  Detail & Related papers  (2024-05-09T18:32:10Z)
• 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)
• Variational Inference for Continuous-Time Switching Dynamical Systems [29.984955043675157]
  We present a model based on an Markov jump process modulating a subordinated diffusion process. We develop a new continuous-time variational inference algorithm. We extensively evaluate our algorithm under the model assumption and for real-world examples.
  arXiv  Detail & Related papers  (2021-09-29T15:19:51Z)
• QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics [51.15339237964982]
  "hierarchical equations of motion" (HEOM) is a powerful exact numerical approach to solve the dynamics. It has been extended and applied to problems in solid-state physics, optics, single-molecule electronics, and biological physics. We present a numerical library in Python, integrated with the powerful QuTiP platform, which implements the HEOM for both bosonic and fermionic environments.
  arXiv  Detail & Related papers  (2020-10-21T07:54:56Z)
• Phase space theory for open quantum systems with local and collective dissipative processes [0.0]
  We investigate driven dissipative quantum dynamics of an ensemble of two-level systems given by a Markovian master equation with collective and noncollective dissipators. Our results expose, utilize and promote pioneered techniques in the context of laser theory.
  arXiv  Detail & Related papers  (2020-06-05T07:22:02Z)
• Method of spectral Green functions in driven open quantum dynamics [77.34726150561087]
  A novel method based on spectral Green functions is presented for the simulation of driven open quantum dynamics. The formalism shows remarkable analogies to the use of Green functions in quantum field theory. The method dramatically reduces computational cost compared with simulations based on solving the full master equation.
  arXiv  Detail & Related papers  (2020-06-04T09:41:08Z)
• Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes [0.0]
  We develop an exact framework to describe the non-Markovian dynamics of an open quantum system. We show how expanding the system using discrete modes allows for the full inclusion of non-Markovian effects.
  arXiv  Detail & Related papers  (2020-02-22T17:45:34Z)

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.