Variance Decomposition in Bohmian Mechanics with Weak Actual Value Field and Quantum Potential

• URL: http://arxiv.org/abs/2512.24664v1
• Date: Wed, 31 Dec 2025 06:38:34 GMT
• Title: Variance Decomposition in Bohmian Mechanics with Weak Actual Value Field and Quantum Potential
• Authors: Weixiang Ye,
• Abstract summary: 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.
• Score: 0.8460698440162889
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a trajectory-based decomposition of quantum variances within Bohmian mechanics. By extending the weak actual value to a field on configuration space, we prove, under strong regularity conditions for stationary bound states, 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. For momentum, linking variance-level fluctuations to the average quantum potential. The decomposition fails to provide a physical interpretation for spin, reinforcing the Bohmian tenet that only position is fundamental. The work provides a formal tool for analyzing quantum fluctuations and clarifies the interpretative limits of such a trajectory-based approach.

Related papers

• Tight any-shot quantum decoupling [23.729027844524893]
  We prove a novel one-shot decoupling theorem formulated in terms of quantum entropy relative distance.<n>We show that this bound is ensemble-tight in quantum relative entropy distance.
  arXiv  Detail & Related papers  (2026-02-19T15:01:26Z)
• Error exponents of quantum state discrimination with composite correlated hypotheses [40.82628972269358]
  We study the error exponents in quantum hypothesis testing between two sets of quantum states.<n>We introduce and compare two natural extensions of the quantum Hoeffding divergence and anti-divergence to sets of quantum states.
  arXiv  Detail & Related papers  (2025-08-18T13:04:06Z)
• Topological control of quantum speed limits [55.2480439325792]
  We show that even if the quantum state is completely dispersionless, QFI in this state remains momentum-resolved.<n>We find bounds on quantum speed limit which scales as $sqrt|C|$ in a (dispersionless) topological phase.
  arXiv  Detail & Related papers  (2025-07-21T18:00:07Z)
• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• Quantum simulation of bubble nucleation across a quantum phase transition [31.874825130479174]
  We use a trapped-ion quantum simulator to observe the real-time dynamics of bubble nucleation'' induced by quantum fluctuations.<n>Results demonstrate the power of quantum simulators to probe out-of-equilibrium many-body physics.
  arXiv  Detail & Related papers  (2025-05-14T17:57:25Z)
• Quantum Gravity Without Metric Quantization: From Hidden Variables to Hidden Spacetime Curvatures [0.0]
  Bohmian mechanics offers a deterministic alternative to conventional quantum theory through well-defined particle trajectories.<n>We develop a covariant extension of Bohmian mechanics in curved spacetime that removes the need for metric quantization.<n>This new approach has far-reaching implications for the role of determinism and potential observational signatures of quantum non-equilibrium in cosmology.
  arXiv  Detail & Related papers  (2025-02-12T14:03:54Z)
• Attractive-repulsive interaction in coupled quantum oscillators [14.37149160708975]
  We find an interesting symmetry-breaking transition from quantum limit cycle oscillation to quantum inhomogeneous steady state. This transition is contrary to the previously known symmetry-breaking transition from quantum homogeneous to inhomogeneous steady state. Remarkably, we find the generation of entanglement associated with the symmetry-breaking transition that has no analogue in the classical domain.
  arXiv  Detail & Related papers  (2024-08-23T10:45:19Z)
• The generalized uncertainty principle within the ordinary framework of quantum mechanics [0.0]
  A proper deformation of the underlying coordinate and momentum commutation relations in quantum mechanics accounts for the influence of gravity on small scales. Introducing the squared momentum term results in a generalized uncertainty principle, which limits the minimum uncertainty in particle position to the Planck length. It is shown that the deformed algebra of position and momentum operators can be incorporated into the framework of ordinary quantum mechanics.
  arXiv  Detail & Related papers  (2024-07-12T09:37:51Z)
• Exact finite-time correlation functions for multi-terminal setups: Connecting theoretical frameworks for quantum transport and thermodynamics [11.061707876645764]
  Transport in open quantum systems can be explored through various theoretical frameworks, including the quantum master equation, scattering matrix, and Heisenberg equation of motion. Existing literature treats these approaches independently, lacking a unified perspective. Our work addresses this gap by clarifying the role and status of these approaches using a minimal single-level quantum dot model in a two-terminal setup.
  arXiv  Detail & Related papers  (2023-12-22T21:09:18Z)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• Spin operator, Bell nonlocality and Tsirelson bound in quantum-gravity induced minimal-length quantum mechanics [0.0]
  We show that the spin operator acquires a momentum-dependent contribution in quantum mechanics equipped with a minimal length. Among other consequences, this modification induces a form of quantum nonlocality stronger than the one arising in ordinary quantum mechanics.
  arXiv  Detail & Related papers  (2022-07-21T11:22:33Z)
• Exact-WKB analysis for SUSY and quantum deformed potentials: Quantum mechanics with Grassmann fields and Wess-Zumino terms [0.0]
  Quantum deformed potentials arise naturally in quantum mechanical systems of one bosonic coordinate coupled to $N_f$ Grassmann valued fermionic coordinates. Using exact WKB, we derive exact quantization condition and its median resummation. For quantum deformed triple-well potential, we demonstrate the P-NP relation, by computing period integrals and Mellin transform.
  arXiv  Detail & Related papers  (2021-11-10T20:35:38Z)
• Stability of quantum eigenstates and kinetics of wave function collapse in a fluctuating environment [0.0]
  The work analyzes the stability of the quantum eigenstates when they are submitted to fluctuations. In the limit of sufficiently slow kinetics, the quantum eigenstates show to remain stationary configurations. The work shows that the final stationary eigenstate depends by the initial configuration of the superposition of states.
  arXiv  Detail & Related papers  (2020-11-25T10:41:53Z)
• Detecting dynamical quantum phase transition via out-of-time-order correlations in a solid-state quantum simulator [12.059058714600607]
  We develop and experimentally demonstrate that out-of-time-order correlators can be used to detect nonoequilibrium phase transitions in the transverse field Ising model. Further applications of this protocol could enable studies other of exotic phenomena such as many body localization, and tests of the holographic duality between quantum and gravitational systems.
  arXiv  Detail & Related papers  (2020-01-17T14:28:42Z)

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.