Radiative transport in a periodic structure with band crossings

• URL: http://arxiv.org/abs/2402.06828v2
• Date: Fri, 08 Nov 2024 02:58:00 GMT
• Title: Radiative transport in a periodic structure with band crossings
• Authors: Kunlun Qi, Li Wang, Alexander B. Watson,
• Abstract summary: We derive the semi-classical model for the Schr"odinger equation in arbitrary spatial dimensions. We consider both deterministic and random scenarios. As a specific application, we deduce the effective dynamics of a wave packet in graphene with randomness.
• Score: 47.82887393172228
• License:
• Abstract: We use the Wigner transformation and asymptotic analysis to systematically derive the semi-classical model for the Schr\"{o}dinger equation in arbitrary spatial dimensions, with any periodic structure. Our particular emphasis lies in addressing the \textit{diabatic} effect, i.e., the impact of Bloch band crossings. We consider both deterministic and random scenarios. In the former case, we derive a coupled Liouville system, revealing lower-order interactions among different Bloch bands. In the latter case, a coupled system of radiative transport equations emerges, with the scattering cross-section induced by the random inhomogeneities. As a specific application, we deduce the effective dynamics of a wave packet in graphene with randomness.

Related papers

• 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)
• Necessity of orthogonal basis vectors for the two-anyon problem in one-dimensional lattice [4.5808056387997516]
  We solve the finite difference equations for the two-anyon state in the one-dimensional lattice. Our findings are vital for quantum simulations of few-body physics with anyons in the lattice.
  arXiv  Detail & Related papers  (2024-05-13T01:42:26Z)
• Causal Modeling with Stationary Diffusions [89.94899196106223]
  We learn differential equations whose stationary densities model a system's behavior under interventions. We show that they generalize to unseen interventions on their variables, often better than classical approaches. Our inference method is based on a new theoretical result that expresses a stationarity condition on the diffusion's generator in a reproducing kernel Hilbert space.
  arXiv  Detail & Related papers  (2023-10-26T14:01:17Z)
• Differential scattering cross section of the non-Abelian Aharonov-Bohm effect in multiband systems [0.0]
  We develop a unified treatment of the non-Abelian Aharonov-Bohm (AB) effect in isotropic multiband systems. We present a complex contour integral representation of the scattering states for such systems. Using their form, we calculate the differential scattering cross section.
  arXiv  Detail & Related papers  (2023-06-23T11:30:06Z)
• Bloch Oscillations, Landau-Zener Transition, and Topological Phase Evolution in a Pendula Array [0.0]
  We study the dynamics of a one-dimensional array of pendula with a mild spatial gradient in their self-frequency. We map their dynamics to the topological Su-Schrieffer-Heeger model of charged quantum particles on a lattice with alternating hopping rates in an external electric field.
  arXiv  Detail & Related papers  (2023-05-30T20:01:52Z)
• Survey of the Hierarchical Equations of Motion in Tensor-Train format for non-Markovian quantum dynamics [0.0]
  This work is a survey about the hierarchical equations of motion and their implementation with the tensor-train format. We recall the link with the perturbative second order time convolution equations also known as the Bloch-Redfield equations. The main points of the tensor-train expansion are illustrated in an example with a qubit interacting with a bath described by a Lorentzian spectral density.
  arXiv  Detail & Related papers  (2023-03-08T14:21:43Z)
• Dynamical chaos in nonlinear Schr\"odinger models with subquadratic power nonlinearity [137.6408511310322]
  We deal with a class of nonlinear Schr"odinger lattices with random potential and subquadratic power nonlinearity. We show that the spreading process is subdiffusive and has complex microscopic organization. The limit of quadratic power nonlinearity is also discussed and shown to result in a delocalization border.
  arXiv  Detail & Related papers  (2023-01-20T16:45:36Z)
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect [68.8204255655161]
  We show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.
  arXiv  Detail & Related papers  (2021-12-08T11:41:38Z)
• Arbitrary length XX spin chains boundary-driven by non-Markovian environments [0.0]
  We provide a method of calculating the wavefunction of a XX spin chain coupled at both ends to non-Markovian reservoirs with arbitrary spectral density. The method is based on the appropriate handling of the time-dependent Schrodinger's equations of motion in Laplace space.
  arXiv  Detail & Related papers  (2021-11-15T16:01:46Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)

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.