Lindblad dynamics of open multi-mode bosonic systems: Algebra of bilinear superoperators, exceptional points and speed of evolution

• URL: http://arxiv.org/abs/2412.13890v2
• Date: Thu, 19 Jun 2025 15:48:39 GMT
• Title: Lindblad dynamics of open multi-mode bosonic systems: Algebra of bilinear superoperators, exceptional points and speed of evolution
• Abstract summary: We develop the method based on the Lie algebra of quadratic combinations of left and right superoperators associated with matrices.<n>We use our method to derive the low-temperature approximation for the superpropagator and to study the special case of a two mode system representing the photonic polarization modes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop the algebraic method based on the Lie algebra of quadratic combinations of left and right superoperators associated with matrices to study the Lindblad dynamics of multimode bosonic systems coupled a thermal bath and described by the Liouvillian superoperator that takes into account both dynamical (coherent) and environment mediated (incoherent) interactions between the modes. Our algebraic technique is applied to transform the Liouvillian into the diagonalized form by eliminating jump superoperators and solve the spectral problem. The temperature independent effective non-Hermitian Hamiltonian, $\hat{H}_{eff}$, is found to govern both the diagonalized Liouvillian and the spectral properties. It is shown that the Liouvillian exceptional points are represented by the points in the parameter space where the matrix, $H$, associated with $\hat{H}_{eff}$ is non-diagonalizable. We use our method to derive the low-temperature approximation for the superpropagator and to study the special case of a two mode system representing the photonic polarization modes. For this system, we describe the geometry of exceptional points in the space of frequency and relaxation vectors parameterizing the intermode couplings and, for a single-photon state, evaluate the time dependence of the speed of evolution as a function of the angles characterizing the couplings and the initial state.

Related papers

• Collective dressed states for inelastic light scattering by atomic ensembles [0.0]
  We develop a general dressed-state framework for computing fluorescence spectra, absorption probe spectra, and photon-photon correlations of light scattered by ensembles.<n>The approach employs a full vectorial treatment of the electromagnetic field, handles any atomic geometries, illumination directions, and polarizations, and yields optical observables as explicit sums of Lorentzian lines.
  arXiv  Detail & Related papers  (2026-08-31T18:00:04Z)
• Effective Geometry and Position-Dependent Mass in Dual-$q$ Quantum Mechanics [0.0]
  This work investigates the deformed-derivative formalism introduced by Borges.<n>It focuses on the relation between the linear operator $D_(q)$ and its nonlinear dual counterpart $D(q)$.<n>We show that this nonlinearity can be removed by a simultaneous transformation of the coordinate and of the wave function.
  arXiv  Detail & Related papers  (2026-05-27T11:29:44Z)
• 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)
• Wigner and Gabor phase-space analysis of propagators for evolution equations [0.0]
  We study the Wigner kernel and the Gabor matrix associated with the propagators of a broad class of linear evolution equations.<n>We derive explicit expressions for the Wigner kernels of Fourier multipliers and establish quantitative decay estimates for the corresponding Gabor matrices.
  arXiv  Detail & Related papers  (2025-11-24T18:36:04Z)
• On the Schrödingerization method for linear non-unitary dynamics with optimal dependence on matrix queries [42.104910612491885]
  The Schr"odingerization method converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schr"odinger-type equations with unitary evolution.<n>The original proposal used a particular initial function in the auxiliary space that did not achieve optimal scaling in precision.<n>Here we show that, by choosing smoother initial functions in auxiliary space, Schr"odingerization textitcan in fact achieve near optimal and even optimal scaling in matrix queries.
  arXiv  Detail & Related papers  (2025-05-01T07:46:50Z)
• Variational formulation based on duality to solve partial differential equations: Use of B-splines and machine learning approximants [0.0]
  Partial differential equations (PDEs) in fluid mechanics, inelastic deformation in solids, and transient parabolic and hyperbolic equations do not have an exact, primal variational structure.<n>A variational principle based on the dual (Lagrange multiplier) field was proposed to treat the given PDE as constraints.<n>The vanishing of the first variation of the dual functional is, up to Dirichlet boundary conditions on dual fields, the weak form of the primal PDE problem.<n>We derive the dual weak form for the linear, one-dimensional, transient convection-diffusion equation.
  arXiv  Detail & Related papers  (2024-12-02T07:53:47Z)
• Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space [49.1574468325115]
  We find an exceptional point at a critical dissipation strength that separates oscillating and non-oscillating decay. We also describe a different type of dissipation that leads to a single decay mode in the whole operator subspace.
  arXiv  Detail & Related papers  (2024-05-27T16:11:39Z)
• The entanglement membrane in exactly solvable lattice models [0.0]
  Entanglement membrane theory describes entanglement dynamics in chaotic quantum many-body systems. We compute the entanglement line tension in a class of exactly solvable yet chaotic unitary circuits. Our results shed light on entanglement membrane theory in microscopic Floquet lattice models.
  arXiv  Detail & Related papers  (2023-12-19T19:00:02Z)
• Quench dynamics in higher-dimensional Holstein models: Insights from Truncated Wigner Approaches [41.94295877935867]
  We study the melting of charge-density waves in a Holstein model after a sudden switch-on of the electronic hopping. A comparison with exact data obtained for a Holstein chain shows that a semiclassical treatment of both the electrons and phonons is required in order to correctly describe the phononic dynamics.
  arXiv  Detail & Related papers  (2023-12-19T16:14:01Z)
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search [77.34726150561087]
  We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
  arXiv  Detail & Related papers  (2023-02-28T07:36:02Z)
• 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)
• An Accurate Pentadiagonal Matrix Solution for the Time-Dependent Schr\"{o}dinger Equation [2.480301925841752]
  We invoke the highly accurate five-point stencil to discretize the wave function onto an Implicit-Explicit pentadiagonal Crank-Nicolson scheme. It is demonstrated that the resultant solutions are significantly more accurate than the standard ones.
  arXiv  Detail & Related papers  (2022-05-26T16:16:56Z)
• On optimization of coherent and incoherent controls for two-level quantum systems [77.34726150561087]
  This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr"odinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
  arXiv  Detail & Related papers  (2022-05-05T09:08:03Z)
• Non-diagonal Lindblad master equations in quantum reservoir engineering [0.0]
  We present a set of dynamical equations for the first and second moments of canonical variables for bosonic and fermionic linear Gaussian systems. Our method is efficient and allows one to obtain analytical solutions for the steady state. Our exploration yields a surprising byproduct: the Duan criterion, commonly applied to bosonic systems for verification of entanglement, is found to be equally valid for fermionic systems.
  arXiv  Detail & Related papers  (2021-11-07T09:55:04Z)
• Deep Learning Approximation of Diffeomorphisms via Linear-Control Systems [91.3755431537592]
  We consider a control system of the form $dot x = sum_i=1lF_i(x)u_i$, with linear dependence in the controls. We use the corresponding flow to approximate the action of a diffeomorphism on a compact ensemble of points.
  arXiv  Detail & Related papers  (2021-10-24T08:57:46Z)
• Self-consistent microscopic derivation of Markovian master equations for open quadratic quantum systems [0.0]
  We provide a rigorous construction of Markovian master equations for a wide class of quantum systems. We show that, for non-degenerate systems under a full secular approximation, the effective Lindblad operators are the normal modes of the system. We also address the particle and energy current flowing through the system in a minimal two-bath scheme and find that they hold the structure of Landauer's formula.
  arXiv  Detail & Related papers  (2021-01-22T19:25:17Z)
• New approach to describe two coupled spins in a variable magnetic field [55.41644538483948]
  We describe the evolution of two spins coupled by hyperfine interaction in an external time-dependent magnetic field. We modify the time-dependent Schr"odinger equation through a change of representation. The solution is highly simplified when an adiabatically varying magnetic field perturbs the system.
  arXiv  Detail & Related papers  (2020-11-23T17:29:31Z)

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.