Linear and integrable nonlinear evolution of the qutrit

• URL: http://arxiv.org/abs/2006.10322v1
• Date: Thu, 18 Jun 2020 07:25:19 GMT
• Title: Linear and integrable nonlinear evolution of the qutrit
• Authors: Krzysztof Kowalski
• Abstract summary: The analyzed dynamics of the qutrit is rich and includes quasiperiodic motion, multiple equilibria and limit cycles. The generalization of the von Neumann equation preserving convexity of the state space is studied in the nontrivial case of the qutrit.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The nonlinear generalization of the von Neumann equation preserving convexity of the state space is studied in the nontrivial case of the qutrit. This equation can be cast into the integrable classical Riccati system of nonlinear ordinary differential equations. The solutions of such system are investigated in both the linear case corresponding to the standard von Neumann equation and the nonlinear one referring to the generalization of this equation. The analyzed dynamics of the qutrit is rich and includes quasiperiodic motion, multiple equilibria and limit cycles.

Related papers

• Alleviating Post-Linearization Challenges for Solving Nonlinear Systems on a Quantum Computer [0.0]
  Carleman linearization provides a high dimensional infinite linear system corresponding to a finite nonlinear system.<n>We decompose the Hamiltonian into the weighted sum of non-unitary operators, namely the Sigma basis.<n>Once the Hamiltonian is decomposed, we then use the concept of unitary completion to construct the circuit.
  arXiv  Detail & Related papers  (2026-02-06T14:56:39Z)
• Explicit Discovery of Nonlinear Symmetries from Dynamic Data [50.20526548924647]
  LieNLSD is the first method capable of determining the number of infinitesimal generators with nonlinear terms and their explicit expressions.<n>LieNLSD shows qualitative advantages over existing methods and improves the long rollout accuracy of neural PDE solvers by over 20%.
  arXiv  Detail & Related papers  (2025-10-02T09:54:08Z)
• Two-Point Deterministic Equivalence for Stochastic Gradient Dynamics in Linear Models [76.52307406752556]
  We derive a novel deterministic equivalence for the two-point function of a random resolvent. We give a unified derivation of the performance of a wide variety of high-dimensional trained linear models with gradient descent.
  arXiv  Detail & Related papers  (2025-02-07T16:45:40Z)
• Tensor-Programmable Quantum Circuits for Solving Differential Equations [0.0]
  We present a quantum solver for partial differential equations based on a flexible matrix product operator representation.<n>The capabilities of the framework are demonstrated for linear and non-linear partial differential equations.
  arXiv  Detail & Related papers  (2025-02-06T18:23:38Z)
• Quantum Algorithms for Nonlinear Dynamics: Revisiting Carleman Linearization with No Dissipative Conditions [0.7373617024876725]
  We explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Our analysis extends these findings by exploring error bounds beyond the traditional dissipative condition. We prove how this resonance condition leads to a linear convergence with respect to the truncation level $N$ in Carleman linearization.
  arXiv  Detail & Related papers  (2024-05-21T12:09:34Z)
• Liénard Type Nonlinear Oscillators and Quantum Solvability [0.0]
  Li'enard-type nonlinear oscillators with linear and nonlinear damping terms exhibit diverse dynamical behavior in both the classical and quantum regimes. The modified Emden equation categorized as Li'enard type-II exhibits isochronous oscillations at the classical level. The study on the quantum counterpart of the system provides a deeper understanding of the behavior in the quantum realm as a typical PT-symmetric system.
  arXiv  Detail & Related papers  (2024-05-02T11:26:52Z)
• Time complexity analysis of quantum algorithms via linear representations for nonlinear ordinary and partial differential equations [31.986350313948435]
  We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations. We compare the quantum linear systems algorithms based methods and the quantum simulation methods arising from different numerical approximations.
  arXiv  Detail & Related papers  (2022-09-18T05:50:23Z)
• Fractional Integrable Nonlinear Soliton Equations [0.0]
  We present a new class of integrable fractional nonlinear evolution equations describing dispersive transport in fractional media. These equations can be constructed from nonlinear integrable equations using a widely generalizable mathematical process. We show that these equations are shown to predict super-dispersive transport of non-dissipative solitons in fractional media.
  arXiv  Detail & Related papers  (2022-03-25T16:09:22Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Hessian Eigenspectra of More Realistic Nonlinear Models [73.31363313577941]
  We make a emphprecise characterization of the Hessian eigenspectra for a broad family of nonlinear models. Our analysis takes a step forward to identify the origin of many striking features observed in more complex machine learning models.
  arXiv  Detail & Related papers  (2021-03-02T06:59:52Z)
• Nonlinear Independent Component Analysis for Continuous-Time Signals [85.59763606620938]
  We study the classical problem of recovering a multidimensional source process from observations of mixtures of this process. We show that this recovery is possible for many popular models of processes (up to order and monotone scaling of their coordinates) if the mixture is given by a sufficiently differentiable, invertible function.
  arXiv  Detail & Related papers  (2021-02-04T20:28:44Z)
• Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms [74.17312533172291]
  We describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) We then explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation)
  arXiv  Detail & Related papers  (2020-12-12T00:01:10Z)
• Susceptibility of quasiclassical Brownian motion in harmonic nonlinear potentials [0.0]
  It is provided a recursion method to find its solutions based on functional equations in the Banach space. The ODE for the response function is a highly nonlinear damped non-autonomous Duffing equation.
  arXiv  Detail & Related papers  (2020-12-07T20:16:27Z)
• Dissipative flow equations [62.997667081978825]
  We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations. We first test our dissipative flow equations on a generic matrix and on a physical problem with a driven-dissipative single fermionic mode.
  arXiv  Detail & Related papers  (2020-07-23T14:47:17Z)
• On dissipative symplectic integration with applications to gradient-based optimization [77.34726150561087]
  We propose a geometric framework in which discretizations can be realized systematically. We show that a generalization of symplectic to nonconservative and in particular dissipative Hamiltonian systems is able to preserve rates of convergence up to a controlled error.
  arXiv  Detail & Related papers  (2020-04-15T00:36:49Z)

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.