Generalized phase-space description of non-linear Hamiltonian systems and the Harper-like dynamics

• URL: http://arxiv.org/abs/2202.12036v2
• Date: Fri, 18 Mar 2022 11:47:44 GMT
• Title: Generalized phase-space description of non-linear Hamiltonian systems and the Harper-like dynamics
• Authors: Alex E. Bernardini and Orfeu Bertolami
• Abstract summary: Phase-space features of the Wigner flow for generic one-dimensional systems with a Hamiltonian are analytically obtained. A framework can be extended to any quantum system described by Hamiltonians in the form of $HW(q,,p) = K(p) + V(q)$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Phase-space features of the Wigner flow for generic one-dimensional systems with a Hamiltonian, $H^{W}(q,\,p)$, constrained by the $\partial ^2 H^{W} / \partial q \partial p = 0$ condition are analytically obtained in terms of Wigner functions and Wigner currents. Liouvillian and stationary profiles are identified for thermodynamic (TD) and Gaussian quantum ensembles to account for exact corrections due to quantum modifications over a classical phase-space pattern. General results are then specialized to the Harper Hamiltonian system which, besides working as a feasible test platform for the framework here introduced, admits a statistical description in terms of TD and Gaussian ensembles, where the Wigner flow properties are all obtained through analytical tools. Quantum fluctuations over the classical regime are therefore quantified through probability and information fluxes whenever the classical Hamiltonian background is provided. Besides allowing for a broad range of theoretical applications, our results suggest that such a generalized Wigner approach works as a probe for quantumness and classicality of Harper-like systems, in a framework which can be extended to any quantum system described by Hamiltonians in the form of $H^{W}(q,\,p) = K(p) + V(q)$.

Related papers

• Quantum State Transfer in Interacting, Multiple-Excitation Systems [41.94295877935867]
  Quantum state transfer (QST) describes the coherent passage of quantum information from one node to another. We describe Monte Carlo techniques which enable the discovery of a Hamiltonian that gives high-fidelity QST. The resulting Jaynes-Cummings-Hubbard and periodic Anderson models can, in principle, be engineered in appropriate hardware to give efficient QST.
  arXiv  Detail & Related papers  (2024-05-10T23:46:35Z)
• Quantum tomography of helicity states for general scattering processes [65.268245109828]
  Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics. We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
  arXiv  Detail & Related papers  (2023-10-16T21:23:42Z)
• Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer [27.84599956781646]
  We study the operation of a quantum-classical time-series algorithm on a present-day quantum computer. Specifically, we measure the Loschmidt amplitude for the Fermi-Hubbard model on a $16$-site ladder geometry (32 orbitals) on the Quantinuum H2-1 trapped-ion device. We numerically analyze the influence of noise on the full operation of the quantum-classical algorithm by measuring expectation values of local observables at finite energies.
  arXiv  Detail & Related papers  (2023-09-19T11:59:36Z)
• Distorted stability pattern and chaotic features for quantized prey-predator-like dynamics [0.0]
  Non-equilibrium and instability features of prey-predator-like systems are investigated in the framework of the Weyl-Wigner quantum mechanics. From the non-Liouvillian pattern driven by the associated Wigner currents, hyperbolic equilibrium and stability parameters are shown to be affected by quantum distortions.
  arXiv  Detail & Related papers  (2023-03-16T19:55:36Z)
• Guidable Local Hamiltonian Problems with Implications to Heuristic Ansätze State Preparation and the Quantum PCP Conjecture [0.0]
  We study 'Merlinized' versions of the recently defined Guided Local Hamiltonian problem. These problems do not have a guiding state provided as a part of the input, but merely come with the promise that one exists. We show that guidable local Hamiltonian problems for both classes of guiding states are $mathsfQCMA$-complete in the inverse-polynomial precision setting.
  arXiv  Detail & Related papers  (2023-02-22T19:00:00Z)
• Non-commutative phase-space Lotka-Volterra dynamics: the quantum analogue [0.0]
  The Lotka-Volterra (LV) dynamics is investigated in the framework of the Weyl-Wigner (WW) quantum mechanics (QM) The WW framework provides the ground for identifying how classical and quantum evolution coexist at different scales. The generality of the framework developed here extends the boundaries of the understanding of quantum-like effects on competitive microscopical bio-systems.
  arXiv  Detail & Related papers  (2022-06-14T11:23:04Z)
• Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans\"atze [13.651587339535961]
  We develop a framework for convolutional quantum circuits with SU$(d)$symmetry. We prove Harrow's statement on equivalence between $nameSU(d)$ and $S_n$ irrep bases.
  arXiv  Detail & Related papers  (2021-12-14T18:03:43Z)
• Eigenvalues and Eigenstates of Quantum Rabi Model [0.0]
  We present an approach to the exact diagonalization of the quantum Rabi Hamiltonian. It is shown that the obtained eigenstates can be represented in the basis of the eigenstates of the Jaynes-Cummings Hamiltonian.
  arXiv  Detail & Related papers  (2021-04-26T17:45:41Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Variational quantum eigensolvers for sparse Hamiltonians [0.0]
  Hybrid quantum-classical variational algorithms such as the variational quantum eigensolver (VQE) are promising applications for noisy, intermediate-scale quantum computers. We extend VQE to general sparse Hamiltonians.
  arXiv  Detail & Related papers  (2020-12-13T22:36:51Z)
• Hamiltonian operator approximation for energy measurement and ground state preparation [23.87373187143897]
  We show how to approximate the Hamiltonian operator as a sum of propagators using a differential representation. The proposed approach, named Hamiltonian operator approximation (HOA), is designed to benefit analog quantum simulators.
  arXiv  Detail & Related papers  (2020-09-07T18:11:00Z)

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.