Non-Hermitian Realization of Quantum Dynamics on Embedded Manifolds

• URL: http://arxiv.org/abs/2510.11845v1
• Date: Mon, 13 Oct 2025 18:55:16 GMT
• Title: Non-Hermitian Realization of Quantum Dynamics on Embedded Manifolds
• Authors: Samuel Alperin,
• Abstract summary: We show that the Floquet Hamiltonian of a quantum particle driven by a general time-periodic imaginary potential is exactly equivalent at stroboscopic times.<n>We illustrate the construction for a sinusoidal drive and for the torus of revolution, and outline how the framework can guide experimental design of curved-space quantum dynamics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that the Floquet Hamiltonian of a quantum particle driven by a general time-periodic imaginary potential is exactly equivalent, at stroboscopic times, to the Hamiltonian of a free particle constrained to a curved Riemannian manifold with fixed embedding. We illustrate the construction for a sinusoidal drive and for the torus of revolution, and outline how the framework can guide experimental design of curved-space quantum dynamics. Our results unify non-Hermitian Floquet physics with spectral geometry and provide a general recipe for engineering quantum dynamics on embedded manifolds.

Related papers

• Observing quantum many-body dynamics in emergent curved spacetime using programmable quantum processors [0.0]
  We digitally simulate quantum many-body dynamics in emergent curved backgrounds using 80 superconducting qubits on IBM Heron processors.<n>We observe curved light-cone propagation, horizon-induced freezing in the local magnetization, and position-dependent oscillation frequencies set by the engineered spatial deformation.
  arXiv  Detail & Related papers  (2026-02-17T11:55:30Z)
• Programmable Exploration of Magnetic States in Lieb-Kagome Interpolated Lattices [44.99833362998488]
  A quantum annealer is used to simulate magnetic interactions in molecular qubit lattices inspired by experimentally realizable systems.<n>The annealer provides access to observables such as the static structure factor and magnetization over a wide parameter space.<n>This framework defines a modular and scalable paradigm for probing the limits of engineered quantum matter across chemistry, condensed matter, and quantum information science.
  arXiv  Detail & Related papers  (2025-07-24T21:47:54Z)
• Site-resolved magnon and triplon dynamics on a programmable quantum dot spin ladder [1.451379135950017]
  We use an array of germanium quantum dots to simulate the dynamics of single-spin excitations (magnons) and two-spin excitations (triplons)<n>Using these techniques, we can reconstruct quantum walk plots for both magnons and triplons, and for various configurations of Heisenberg exchange couplings.
  arXiv  Detail & Related papers  (2025-06-10T10:22:43Z)
• Integral quantization based on the Heisenberg-Weyl group [39.58317527488534]
  We develop a framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime.<n>The proposed scheme is based on coherent states generated by the action of the Heisenberg-Weyl group.<n>A direct application of our model, including a computation of transition amplitudes between states characterized by fixed positions and momenta, is postponed to a forthcoming article.
  arXiv  Detail & Related papers  (2024-10-31T14:36:38Z)
• Emergent Fracton Hydrodynamics of Ultracold Atoms in Partially Filled Landau Levels [41.94295877935867]
  We establish key signatures of fractional quantum Hall systems in their non-equilibrium quantum dynamics.<n>We show that in the lowest Landau level the system generically relaxes subdiffusively.<n>We discuss the prospect of rotating quantum gases as well as ultracold atoms in optical lattices for observing this unconventional relaxation dynamics.
  arXiv  Detail & Related papers  (2024-10-09T18:00:02Z)
• Simulating a quasiparticle on a quantum device [0.0]
  We propose a variational approach to explore quasiparticle excitations in interacting quantum many-body systems.<n>We benchmark the proposed algorithm via numerical simulations performed on the one-dimension transverse field Ising chain.<n>We show that the localized quasiparticle states constructed with VQE contain accessible information on the full band of quasiparticles.
  arXiv  Detail & Related papers  (2024-09-13T05:39:13Z)
• A Floquet-Rydberg quantum simulator for confinement in $\mathbb{Z}_2$ gauge theories [44.99833362998488]
  Recent advances in the field of quantum technologies have opened up the road for the realization of small-scale quantum simulators. We present a scalable Floquet scheme for the quantum simulation of the real-time dynamics in a $mathbbZ$ LGT. We show that an observation of gauge-invariant confinement dynamics in the Floquet-Rydberg setup is at reach of current experimental techniques.
  arXiv  Detail & Related papers  (2023-11-28T13:01:24Z)
• Coupled Hydrodynamics in Dipole-Conserving Quantum Systems [0.0]
  We investigate the coupled dynamics of charge and energy in interacting lattice models with dipole conservation. We numerically verify its applicability to the late-time dynamics of a specific bosonic quantum system. We discuss the relation of our results to experiments in ultracold atom quantum simulators.
  arXiv  Detail & Related papers  (2022-01-21T19:00:01Z)
• Visualizing spinon Fermi surfaces with time-dependent spectroscopy [62.997667081978825]
  We propose applying time-dependent photo-emission spectroscopy, an established tool in solid state systems, in cold atom quantum simulators. We show in exact diagonalization simulations of the one-dimensional $t-J$ model that the spinons start to populate previously unoccupied states in an effective band structure. The dependence of the spectral function on the time after the pump pulse reveals collective interactions among spinons.
  arXiv  Detail & Related papers  (2021-05-27T18:00:02Z)
• 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)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Microscopic biasing of discrete-time quantum trajectories [0.0]
  We consider a discrete-time quantum dynamics, where the open system collides sequentially with qubit probes which are then measured. We show that the desired biasing is achieved by suitably modifying the Kraus operators describing the discrete open dynamics. The above extends the theory of biased quantum trajectories from Lindblad-like dynamics to sequences of arbitrary dynamical maps.
  arXiv  Detail & Related papers  (2020-07-30T18:00:02Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)

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.