Solution to a class of multistate Landau-Zener model beyond integrability conditions

• URL: http://arxiv.org/abs/2306.09023v2
• Date: Tue, 25 Jun 2024 04:01:08 GMT
• Title: Solution to a class of multistate Landau-Zener model beyond integrability conditions
• Authors: Rongyu Hu, Fuxiang Li, Chen Sun,
• Abstract summary: We study a class of multistate Landau-Zener model which cannot be solved by integrability conditions or other standard techniques. We find nearly exact analytical expressions of all its transition probabilities for specific parameter choices. We show that this model can describe a Su-Schrieffer-Heeger chain with couplings changing linearly in time.
• Score: 5.390814126989423
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study a class of multistate Landau-Zener model which cannot be solved by integrability conditions or other standard techniques. By analyzing analytical constraints on its scattering matrix and performing fitting to results from numerical simulations of the Schr\"{o}dinger equation, we find nearly exact analytical expressions of all its transition probabilities for specific parameter choices. We also determine the transition probabilities up to leading orders of series expansions in terms of the inverse sweep rate (namely, in the diabatic limit) for general parameter choices. We further show that this model can describe a Su-Schrieffer-Heeger chain with couplings changing linearly in time. Our work presents a new route, i.e., analytical constraint plus fitting, to analyze those multistate Landau-Zener models which are beyond the applicability of conventional solving methods.

Related papers

• Perturbative approach to time-dependent quantum systems and applications to one-crossing multistate Landau-Zener models [6.058734838997002]
  We study a class of time-dependent quantum systems with constant off-diagonal couplings and diabatic energies being odd functions of time. Applying this approach to a general multistate Landau-Zener (MLZ) model, we derive analytical formulas of all its transition up to $4$th order in the couplings.
  arXiv  Detail & Related papers  (2024-07-09T13:05:35Z)
• Bethe ansatz solutions and hidden $sl(2)$ algebraic structure for a class of quasi-exactly solvable systems [0.638421840998693]
  We revisit a class of models for which the odd solutions were largely missed previously in the literature. We present a systematic and unified treatment for the odd and even sectors of these models. We also make progress in the analysis of solutions to the Bethe ansatz equations in the spaces of model parameters.
  arXiv  Detail & Related papers  (2023-09-21T02:04:44Z)
• Predicting Ordinary Differential Equations with Transformers [65.07437364102931]
  We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. Our method is efficiently scalable: after one-time pretraining on a large set of ODEs, we can infer the governing law of a new observed solution in a few forward passes of the model.
  arXiv  Detail & Related papers  (2023-07-24T08:46:12Z)
• Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers [90.45898746733397]
  We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. We show that one step along the probability flow ODE can be expressed as two steps: 1) a restoration step that runs ascent on the conditional log-likelihood at some infinitesimally previous time, and 2) a degradation step that runs the forward process using noise pointing back towards the current gradient.
  arXiv  Detail & Related papers  (2023-03-06T18:59:19Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• A Variational Inference Approach to Inverse Problems with Gamma Hyperpriors [60.489902135153415]
  This paper introduces a variational iterative alternating scheme for hierarchical inverse problems with gamma hyperpriors. The proposed variational inference approach yields accurate reconstruction, provides meaningful uncertainty quantification, and is easy to implement.
  arXiv  Detail & Related papers  (2021-11-26T06:33:29Z)
• Rational Approximations of Quasi-Periodic Problems via Projected Green's Functions [0.0]
  We introduce the projected Green's function technique to study quasi-periodic systems. The technique is flexible and can be used to extract both analytic and numerical results.
  arXiv  Detail & Related papers  (2021-09-28T18:00:00Z)
• Nonadiabatic transitions in Landau-Zener grids: integrability and semiclassical theory [0.0]
  We show that the general model of a linearly time-dependent crossing of two energy bands is integrable. We apply this property to four-state Landau-Zener (LZ) models.
  arXiv  Detail & Related papers  (2021-01-11T19:59:31Z)
• Probabilistic Circuits for Variational Inference in Discrete Graphical Models [101.28528515775842]
  Inference in discrete graphical models with variational methods is difficult. Many sampling-based methods have been proposed for estimating Evidence Lower Bound (ELBO) We propose a new approach that leverages the tractability of probabilistic circuit models, such as Sum Product Networks (SPN) We show that selective-SPNs are suitable as an expressive variational distribution, and prove that when the log-density of the target model is aweighted the corresponding ELBO can be computed analytically.
  arXiv  Detail & Related papers  (2020-10-22T05:04:38Z)
• Estimation of Switched Markov Polynomial NARX models [75.91002178647165]
  We identify a class of models for hybrid dynamical systems characterized by nonlinear autoregressive (NARX) components. The proposed approach is demonstrated on a SMNARX problem composed by three nonlinear sub-models with specific regressors.
  arXiv  Detail & Related papers  (2020-09-29T15:00:47Z)
• Neural Controlled Differential Equations for Irregular Time Series [17.338923885534197]
  An ordinary differential equation is determined by its initial condition, and there is no mechanism for adjusting the trajectory based on subsequent observations. Here we demonstrate how this may be resolved through the well-understood mathematics of emphcontrolled differential equations We show that our model achieves state-of-the-art performance against similar (ODE or RNN based) models in empirical studies on a range of datasets.
  arXiv  Detail & Related papers  (2020-05-18T17:52:21Z)

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.