Extended Non-Markovian Stochastic Schrödinger Equation with Complex Frequency Modes for General Basis Functions

• URL: http://arxiv.org/abs/2506.22738v2
• Date: Tue, 15 Jul 2025 08:49:41 GMT
• Title: Extended Non-Markovian Stochastic Schrödinger Equation with Complex Frequency Modes for General Basis Functions
• Authors: Yukai Guo, Zeyu Huang, Xing Gao,
• Abstract summary: 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.
• Score: 6.836013275880708
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce an extended formulation of the non-Markovian stochastic Schr\"odinger equation with complex frequency modes (extended cNMSSE), designed for simulating open quantum system dynamics under arbitrary spectral densities. This extension employs non-exponential basis sets to expand the bath correlation functions, overcoming the reliance of the original cNMSSE on exponential decompositions of the spectral density. Consequently, the extended cNMSSE is applicable to environments beyond those characterized by Debye-type spectral densities. The flexibility to employ general basis functions is particularly advantageous for handling spectral densities with higher-order poles, for which exponential decompositions are often inaccurate or unavailable. The extended cNMSSE is implemented in a pseudo-Fock space using conventional ladder operators and solved efficiently via matrix product state (MPS) techniques, preserving the favorable linear-scaling and wavefunction-based nature of the original method. Benchmark simulations across four representative cases, including discrete spectral density, Ohmic spectral density with exponential and algebraic cutoffs, and critically damped Brownian spectral density, demonstrate excellent agreement with results of hierarchy of forward-backward stochastic Schr\"odinger equations (HFB-SSE) and extended hierarchical equation of motion (HEOM).

Related papers

• Plug-and-Play Diffusion Meets ADMM: Dual-Variable Coupling for Robust Medical Image Reconstruction [45.25461515976432]
  Plug-and-Play diffusion prior (DP) frameworks have emerged as a powerful paradigm for imaging reconstruction.<n>We present a novel approach to resolving bias-hallucination trade-off, achieving state-of-the-art gradients with significantly accelerated convergence.
  arXiv  Detail & Related papers  (2026-02-26T16:58:43Z)
• 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)
• Quantum spectroscopy of topological dynamics via a supersymmetric Hamiltonian [0.0]
  We estimate topological descriptors through quantum spectroscopy.<n>We show that low-lying excited states quantify the stability of topological features.<n>This framework suggests that quantum hardware can function as a spectrometer for data topologies beyond classical reach.
  arXiv  Detail & Related papers  (2025-11-28T13:25:26Z)
• Fast spectral separation method for kinetic equation with anisotropic non-stationary collision operator retaining micro-model fidelity [13.462104954140088]
  We present a data-driven collisional operator for one-component plasmas, learned from molecular dynamics simulations.<n>The proposed operator features an anisotropic, non-stationary collision kernel that accounts for particle correlations.<n> Numerical experiments demonstrate that the proposed model accurately captures plasma dynamics in the moderately coupled regime.
  arXiv  Detail & Related papers  (2025-10-16T19:27:03Z)
• Zassenhaus Expansion in Solving the Schrödinger Equation [0.0]
  A fundamental challenge lies in approximating the unitary evolution operator ( e-imathcalHt ) where ( mathcalH ) is a large, typically non-commuting, Hermitian operator.<n>We present a refinement of the fixed-depth simulation framework introduced by E. K"okc"u et al, incorporating the second-order Zassenhaus expansion.<n>This yields a controlled, non-unitary approximation with error scaling as ( mathcalO(t
  arXiv  Detail & Related papers  (2025-05-14T14:48:47Z)
• Avoided-crossings, degeneracies and Berry phases in the spectrum of quantum noise through analytic Bloch-Messiah decomposition [49.1574468325115]
  "analytic Bloch-Messiah decomposition" provides approach for characterizing dynamics of quantum optical systems.<n>We show that avoided crossings arise naturally when a single parameter is varied, leading to hypersensitivity of the singular vectors.<n>We highlight the possibility of programming the spectral response of photonic systems through the deliberate design of avoided crossings.
  arXiv  Detail & Related papers  (2025-04-29T13:14:15Z)
• Rigged Dynamic Mode Decomposition: Data-Driven Generalized Eigenfunction Decompositions for Koopman Operators [0.0]
  We introduce the Rigged Dynamic Mode Decomposition (Rigged DMD) algorithm, which computes generalized eigenfunction decompositions of Koopman operators.<n>We provide examples, including systems with a Lebesgue spectrum, integrable Hamiltonian systems, the Lorenz system, and a high-Reynolds number lid-driven flow in a two-dimensional square cavity.
  arXiv  Detail & Related papers  (2024-05-01T18:00:18Z)
• Dynamically Emergent Quantum Thermodynamics: Non-Markovian Otto Cycle [49.1574468325115]
  We revisit the thermodynamic behavior of the quantum Otto cycle with a focus on memory effects and strong system-bath couplings. Our investigation is based on an exact treatment of non-Markovianity by means of an exact quantum master equation.
  arXiv  Detail & Related papers  (2023-08-18T11:00:32Z)
• About the performance of perturbative treatments of the spin-boson dynamics within the hierarchical equations of motion approach [7.573209631509984]
  We show that FP-HEOM can be systematically employed to investigate higher-order master equations. We focus on the challenging scenario of the spin-boson problem with a sub-Ohmic spectral distribution at zero temperature. We compare the memory kernel for population dynamics obtained from the exact FP-HEOM dynamics with that of the approximate NIBA.
  arXiv  Detail & Related papers  (2023-08-03T20:01:40Z)
• A quantum-classical decomposition of Gaussian quantum environments: a stochastic pseudomode model [0.8258451067861933]
  We show that the effect of a Bosonic environment linearly coupled to a quantum system can be simulated by a Gaussian Lindblad master equation. For a subset of rational spectral densities, all parameters are explicitly specified without the need of any fitting procedure.
  arXiv  Detail & Related papers  (2023-01-18T14:17:17Z)
• NAG-GS: Semi-Implicit, Accelerated and Robust Stochastic Optimizer [45.47667026025716]
  We propose a novel, robust and accelerated iteration that relies on two key elements. The convergence and stability of the obtained method, referred to as NAG-GS, are first studied extensively. We show that NAG-arity is competitive with state-the-art methods such as momentum SGD with weight decay and AdamW for the training of machine learning models.
  arXiv  Detail & Related papers  (2022-09-29T16:54:53Z)
• Blending Neural Operators and Relaxation Methods in PDE Numerical Solvers [3.2712166248850685]
  HINTS is a hybrid, iterative, numerical, and transferable solver for partial differential equations. It balances the convergence behavior across the spectrum of eigenmodes by utilizing the spectral bias of DeepONet. It is flexible with regards to discretizations, computational domain, and boundary conditions.
  arXiv  Detail & Related papers  (2022-08-28T19:07:54Z)
• Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion [68.8204255655161]
  We present a methodology for simulating multi-dimensional electronic spectra of molecular aggregates with coupling electronic excitation to a structured environment. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space but with the same noise.
  arXiv  Detail & Related papers  (2022-07-06T15:30:38Z)
• 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)
• Hyperspectral Image Denoising Using Non-convex Local Low-rank and Sparse Separation with Spatial-Spectral Total Variation Regularization [49.55649406434796]
  We propose a novel non particular approach to robust principal component analysis for HSI denoising. We develop accurate approximations to both rank and sparse components. Experiments on both simulated and real HSIs demonstrate the effectiveness of the proposed method.
  arXiv  Detail & Related papers  (2022-01-08T11:48:46Z)
• Simulation of absorption spectra of molecular aggregates: a Hierarchy of Stochastic Pure States approach [68.8204255655161]
  hierarchy of pure states (HOPS) provides a formally exact solution based on local, trajectories. Exploiting the localization of HOPS for the simulation of absorption spectra in large aggregares requires a formulation in terms of normalized trajectories.
  arXiv  Detail & Related papers  (2021-11-01T16:59:54Z)
• Pseudomode description of general open quantum system dynamics: non-perturbative master equation for the spin-boson model [0.0]
  We outline a non-perturbative approach for simulating the behavior of open quantum systems interacting with a bosonic environment. Our framework can be used as a powerful and versatile tool for analyzing non-Markovian open system dynamics.
  arXiv  Detail & Related papers  (2021-08-12T13:49:22Z)
• 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.