On some one-dimensional quantum-mechanical models with a delta-potential interaction

• URL: http://arxiv.org/abs/2306.09371v1
• Date: Wed, 14 Jun 2023 18:33:08 GMT
• Title: On some one-dimensional quantum-mechanical models with a delta-potential interaction
• Authors: Francisco M. Fern\'andez
• Abstract summary: We discuss a systematic construction of dimensionless quantum-mechanical equations. We choose some simple one-dimensional models proposed recently for the study of localized states in inhomogeneous media.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We discuss a systematic construction of dimensionless quantum-mechanical equations. The process reduces the number of independent model parameters to a minimum and, at the same time, provides the natural units of length, energy, etc. in a clear, straightforward way. We compare this systematic procedure with the widely adopted one that consists of setting $\hbar=1$. As illustrative examples, we choose some simple one-dimensional models proposed recently for the study of localized states in inhomogeneous media.

Related papers

• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment. We find sufficient conditions under which dynamical decoupling works for such systems. Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces a novel family of deep dynamical models designed to represent continuous-time sequence data. We train the model using maximum likelihood estimation with Markov chain Monte Carlo. Experiments on oscillating systems, videos and real-world state sequences (MuJoCo) illustrate that ODEs with the learnable energy-based prior outperform existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• 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)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• A brief journey through collision models for multipartite open quantum dynamics [0.0]
  We review the main collision models for the dynamics of multipartite open quantum systems. We show how they may be simulated on a quantum computer.
  arXiv  Detail & Related papers  (2022-09-30T13:59:24Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• 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)
• Duality in quantum transport models [0.0]
  We develop the duality approach', that has been extensively studied for classical models of transport. We show that any dynamic process of this kind with generic baths may be mapped onto one with equilibrium baths.
  arXiv  Detail & Related papers  (2020-08-08T08:48:15Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)
• Certified variational quantum algorithms for eigenstate preparation [0.0]
  We develop a means to certify the termination of variational algorithms. We demonstrate our approach by applying it to three models: the transverse field Ising model, the model of one-dimensional spinless fermions with competing interactions, and the Schwinger model of quantum electrodynamics.
  arXiv  Detail & Related papers  (2020-06-23T18:00:00Z)
• Gaussian Process States: A data-driven representation of quantum many-body physics [59.7232780552418]
  We present a novel, non-parametric form for compactly representing entangled many-body quantum states. The state is found to be highly compact, systematically improvable and efficient to sample. It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
  arXiv  Detail & Related papers  (2020-02-27T15:54:44Z)

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.