Approximate Reduced Lindblad Dynamics via Algebraic and Adiabatic Methods

• URL: http://arxiv.org/abs/2603.11982v1
• Date: Thu, 12 Mar 2026 14:34:19 GMT
• Title: Approximate Reduced Lindblad Dynamics via Algebraic and Adiabatic Methods
• Abstract summary: We show that projecting a Lindblad generator on its center manifold yields an exact reduced quantum dynamical semigroup whose dynamics is unitary.<n>For analytics of a Lindblad generator with a tractable center manifold, we propose a perturbative reduction that keeps the reduced space fixed at the unperturbed center manifold.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present an algebraic framework for approximate model reduction of Markovian open quantum dynamics that guarantees complete positivity and trace preservation by construction. First, we show that projecting a Lindblad generator on its center manifold -- the space spanned by eigenoperators with purely imaginary eigenvalue -- yields an asymptotically exact reduced quantum dynamical semigroup whose dynamics is unitary, with exponentially decaying transient error controlled by the generator's spectral gap. Second, for analytic perturbations of a Lindblad generator with a tractable center manifold, we propose a perturbative reduction that keeps the reduced space fixed at the unperturbed center manifold. The resulting generator is shown to remain a valid Lindbladian for arbitrary perturbation strengths, and explicit finite-time error bounds, that quantify leakage from the unperturbed center sector, are provided. We further clarify the connection to adiabatic elimination methods, by both showing how the algebraic reduction can be directly related to a first-order adiabatic-elimination and by providing sufficient conditions under which the latter method can be applied while preserving complete positivity. We showcase the usefulness of our techniques in dissipative many-body quantum systems exhibiting non-stationary long-time dynamics.

Related papers

• Basin-Preserving Discretizations of Modern Hopfield Retrieval Dynamics: Energy Cells, Dissipation, and the Attention Limit [0.0]
  We show that every finite energy cell below the escape energy is contained simultaneously in the basins the continuous flow, attracting every relaxed attention.<n>We also derive explicit local bounds, with certified optimal tunneling preservation patterns.
  arXiv  Detail & Related papers  (2026-08-21T17:06:43Z)
• 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)
• Symmetry-protected topology and deconfined solitons in a multi-link $\mathbb{Z}_2$ gauge theory [45.88028371034407]
  We study a $mathbbZ$ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell.<n>We show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability.<n>By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization.
  arXiv  Detail & Related papers  (2026-03-02T22:59:25Z)
• Extracting quantum field theory dynamics from an approximate ground state [0.0]
  We develop a linear-programming method to extract information from static ground-state correlators in quantum field theory.<n>We test the method on the $1+1$-dimensional $4$ model, using a variational approximation to the vacuum.<n>The resulting mass gaps agree with renormalized Hamiltonian truncation and Borel-resummed perturbation theory.
  arXiv  Detail & Related papers  (2025-12-22T17:25:24Z)
• Graph-based Clustering Revisited: A Relaxation of Kernel $k$-Means Perspective [73.18641268511318]
  We propose a graph-based clustering algorithm that only relaxes the orthonormal constraint to derive clustering results.<n>To ensure a doubly constraint into a gradient, we transform the non-negative constraint into a class probability parameter.
  arXiv  Detail & Related papers  (2025-09-23T09:14:39Z)
• Operator-space fragmentation and integrability in Pauli-Lindblad models [0.0]
  In closed quantum systems Hilbert-space fragmentation is an effective mechanism for slowing decoherence in the presence of constrained interactions.<n>We develop a general mechanism for operator-space fragmentation of mixed states, undergoing Lindbladian evolution.<n>Using these methods we uncover a range of universal dynamical regimes in Pauli-Lindblad models.
  arXiv  Detail & Related papers  (2025-06-19T18:01:25Z)
• Recursive perturbation approach to time-convolutionless master equations: Explicit construction of generalized Lindblad generators for arbitrary open systems [44.99833362998488]
  We develop a perturbative expansion for the time-convolutionless (TCL) generator of an open quantum system in a generalized Lindblad form.<n>This formulation provides a systematic approach to derive the generator at arbitrary order while preserving a Lindblad-like structure.<n>To validate the method and show its effectiveness in addressing non-Markovian dynamics and strong-coupling effects, we compute the generator explicitly up to fourth order.
  arXiv  Detail & Related papers  (2025-06-04T15:51:26Z)
• Weak coupling limit for quantum systems with unbounded weakly commuting system operators [50.24983453990065]
  This work is devoted to a rigorous analysis of the weak coupling limit (WCL) for the reduced dynamics of an open infinite-dimensional quantum system interacting with electromagnetic field or a reservoir formed by Fermi or Bose particles.<n>We derive in the weak coupling limit the reservoir statistics, which is determined by whose terms in the multi-point correlation functions of the reservoir are non-zero in the WCL.<n>We prove that the resulting reduced system dynamics converges to unitary dynamics with a modified Hamiltonian which can be interpreted as a Lamb shift to the original Hamiltonian.
  arXiv  Detail & Related papers  (2025-05-13T05:32:34Z)
• Hilbert space fragmentation at the origin of disorder-free localization in the lattice Schwinger model [0.0]
  Recent works have reported the possibility of disorder-free localization in the lattice Schwinger model.<n>We perform a detailed characterization of thermalization breakdown in the Schwinger model.<n>We identify the origin of this ultraslow growth of entanglement as due to approximate Hilbert space fragmentation.
  arXiv  Detail & Related papers  (2024-09-12T18:00:00Z)
• Lindbladian reverse engineering for general non-equilibrium steady states: A scalable null-space approach [49.1574468325115]
  We introduce a method for reconstructing the corresponding Lindbaldian master equation given any target NESS. The kernel (null-space) of the correlation matrix corresponds to Lindbladian solutions. We illustrate the method in different systems, ranging from bosonic Gaussian to dissipative-driven collective spins.
  arXiv  Detail & Related papers  (2024-08-09T19:00:18Z)
• Sufficient condition for gapless spin-boson Lindbladians, and its connection to dissipative time-crystals [64.76138964691705]
  We discuss a sufficient condition for gapless excitations in the Lindbladian master equation for collective spin-boson systems. We argue that gapless modes can lead to persistent dynamics in the spin observables with the possible formation of dissipative time-crystals.
  arXiv  Detail & Related papers  (2022-09-26T18:34:59Z)
• Lindbladian dissipation of strongly-correlated quantum matter [0.9290757451344674]
  The Sachdev-Ye-Kitaev Lindbladian is a paradigmatic solvable model of dissipative many-body quantum chaos. Analytical progress is possible by developing a mean-field theory for the Liouvillian time evolution on the Keldysh contour.
  arXiv  Detail & Related papers  (2021-12-22T18:17:52Z)

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.