Finite-sample deviations and convergence in the statistics of Bohmian trajectory ensembles

• URL: http://arxiv.org/abs/2511.06217v1
• Date: Sun, 09 Nov 2025 04:02:35 GMT
• Title: Finite-sample deviations and convergence in the statistics of Bohmian trajectory ensembles
• Authors: Bingyu Cui, Yanting Cao,
• Abstract summary: We analyze finite-sample statistics of Bohmian trajectories for single spinless and spin-1/2 particles.<n>We show that in regular flows sample means and/or variances over modest $N$ are consistent with Born-rule moments.<n>For the spin-1/2 particle, both convective and Pauli currents conserve $|psi|2$, but they are associated with different velocity fields.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We analyze finite-sample statistics of Bohmian trajectories for single spinless and spin-1/2 particles. Equivariance ensures agreement with $|\psi|^2$ in the quantum equilibrium limit, yet experiments and simulations necessarily use finite ensembles. We show that in regular flows (e.g., wavepackets or low-mode superpositions of eigenstates of harmonic oscillators) sample means and/or variances over modest $N$ are consistent with Born-rule moments. In contrast, degenerate superpositions of 3D oscillators with nodal barriers and chaotic Bohmian dynamics exhibit sensitive dependence on initial conditions and complex flow partitioning, which can yield noticeable finite-sample deviations in the mean and variance. For the spin-1/2 particle, both convective and Pauli currents conserve $|\psi|^2$, but they are associated with different velocity fields and thus might yield different finite-sample trajectory statistics. These findings calibrate the interpretation of trajectory-based uncertainty and provide practical guidance for numerical Bohmian simulations of spin and transport, without challenging the equivalence to orthodox quantum mechanics in the quantum equilibrium ensemble.

Related papers

• Symmetry-protected topology and deconfined solitons in a multi-link $\mathbb{Z}_2$ gauge theory [45.88028371034407]
  We study a $mathbbZ$ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell.<n>We show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability.<n>By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization.
  arXiv  Detail & Related papers  (2026-03-02T22:59:25Z)
• Variance Decomposition in Bohmian Mechanics with Weak Actual Value Field and Quantum Potential [0.8460698440162889]
  We introduce a trajectory-based decomposition of quantum variances within Bohmian mechanics.<n>We prove that the standard quantum variance splits into two non-negative terms: the ensemble variance of weak actual value and a quantum termarising from phase-amplitude coupling.
  arXiv  Detail & Related papers  (2025-12-31T06:38:34Z)
• Freeness Reined in by a Single Qubit [36.94429692322632]
  We find that, even in this setting, the correlation functions predicted by free probability theory receive corrections of order $O(1)$.<n>We trace their origin to non-uniformly distributed stationary quantum states, which we characterize analytically and confirm numerically.
  arXiv  Detail & Related papers  (2025-12-15T19:00:09Z)
• Average-case quantum complexity from glassiness [45.57609001239456]
  Glassiness -- a phenomenon in physics characterized by a rough free-energy landscape -- implies hardness for stable classical algorithms.<n>We prove that the standard notion of quantum glassiness based on replica symmetry breaking obstructs stable quantum algorithms for Gibbs sampling.
  arXiv  Detail & Related papers  (2025-10-09T17:37:33Z)
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation.<n>We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue.<n>We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)
• Driving a Quantum Phase Transition at Arbitrary Rate: Exact solution of the Transverse-Field Ising model [0.0]
  We study the crossing of the quantum phase transition in the transverse-field Ising model after the magnetic field at an arbitrary rate.<n>We analyze the defect density, the complete kink number distribution, and its cumulants upon completion of a linearized quench.
  arXiv  Detail & Related papers  (2025-01-16T19:03:37Z)
• Semiclassical Quantum Trajectories in the Monitored Lipkin-Meshkov-Glick Model [41.94295877935867]
  We investigate the dynamics of the Lipkin-Meshkov-Glick model, composed of $N$ all-to-all interacting spins $1/2$, under a weak external monitoring. We derive a set of semiclassical equations describing the evolution of the expectation values of global spin observables, which become exact in the thermodynamic limit. The transition is not affected by post-selection issues, as it is already visible at the level of ensemble averages.
  arXiv  Detail & Related papers  (2024-07-29T18:00:00Z)
• Information and majorization theory for fermionic phase-space distributions [0.0]
  We analyze the uncertainty of fermionic phase-space distributions using the theory of supernumbers.<n>Although fermionic phase-space distributions are Grassmann-valued, the corresponding uncertainty measures are expressed as Berezin integrals.
  arXiv  Detail & Related papers  (2024-01-16T17:42:38Z)
• Robust spectral $\pi$ pairing in the random-field Floquet quantum Ising model [44.84660857803376]
  We study level pairings in the many-body spectrum of the random-field Floquet quantum Ising model. The robustness of $pi$ pairings against longitudinal disorder may be useful for quantum information processing.
  arXiv  Detail & Related papers  (2024-01-09T20:37:48Z)
• Theory of free fermions dynamics under partial post-selected monitoring [49.1574468325115]
  We derive a partial post-selected Schrdinger"o equation based on a microscopic description of continuous weak measurement. We show that the passage to the monitored universality occurs abruptly at finite partial post-selection. Our approach establishes a way to study MiPTs for arbitrary subsets of quantum trajectories.
  arXiv  Detail & Related papers  (2023-12-21T16:53:42Z)
• Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons [2.9491988705158843]
  We characterize the geometry of quantum states associated with different values of $kappa$, i.e., different quantum statistics. We characterize this decay using quantum speed limits on the flow of $kappa$, illustrate our results with a model of hard-core anyons, and discuss possible experiments in quantum simulation.
  arXiv  Detail & Related papers  (2022-10-19T17:59:59Z)
• Statistical mechanics of one-dimensional quantum droplets [0.0]
  We study the dynamical relaxation process of modulationally unstable one-dimensional quantum droplets. We find that the instability leads to the spontaneous formation of quantum droplets featuring multiple collisions.
  arXiv  Detail & Related papers  (2021-02-25T15:30:30Z)
• Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions [0.0]
  A wave function exposed to measurements undergoes pure state dynamics. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions. A key finding is that this field theory decouples into one set of degrees of freedom that heats up indefinitely.
  arXiv  Detail & Related papers  (2021-02-16T19:00:00Z)
• Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations [77.34726150561087]
  The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
  arXiv  Detail & Related papers  (2020-07-20T18:00:02Z)

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.