Quantum Paradoxes and the Quantum-Classical Transition under Unitary Measurement Dynamics with Random Hamiltonians

• URL: http://arxiv.org/abs/2601.17976v1
• Date: Sun, 25 Jan 2026 20:13:07 GMT
• Title: Quantum Paradoxes and the Quantum-Classical Transition under Unitary Measurement Dynamics with Random Hamiltonians
• Authors: Alexey A. Kryukov,
• Abstract summary: We develop a framework for quantum measurement based on but unitary evolution in projective state space.<n>We show that, in this setting, measurement, state reduction, and the quantum-classical transition emerge from unitary dynamics alone.<n>The framework provides a unified dynamical account of measurement and classicality compatible with the structure of quantum mechanics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a dynamical framework for quantum measurement based on stochastic but unitary evolution in projective state space. Random Hamiltonians drawn from the Gaussian Unitary Ensemble generate stochastic unitary dynamics of the quantum state, while equivalence classes reflecting finite detector resolution define classical observables as well as classical configuration-space and phase-space submanifolds. When the evolution is constrained to the phase-space submanifold, free Schrödinger dynamics reduces to Newtonian motion, while stochastic motion constrained to the classical configuration-space submanifold yields ordinary Brownian motion in classical space. Transition probabilities under the stochastic dynamics satisfy the Born rule, whereas the constrained classical evolution produces the normal probability distributions characteristic of classical measurements. We show that, in this setting, measurement, state reduction, and the quantum-classical transition emerge from unitary dynamics alone, without invoking nonunitary collapse or additional postulates. Entanglement and EPR correlations arise geometrically from the evolution of joint states in composite state space, preserving locality in spacetime. The framework provides a unified dynamical account of measurement and classicality compatible with the structure of quantum mechanics.

Related papers

• Classical vs quantum dynamics and the onset of chaos in a macrospin system [3.3924804264271757]
  We study a periodically driven macrospin system with anisotropic long-range interactions and collective dissipation.<n>We map out chaotic, quasiperiodic, and periodic phases via bifurcation diagrams, MLEs, and spectra of evolved observables.
  arXiv  Detail & Related papers  (2025-12-31T19:00:01Z)
• Emergence of cosmic structure from Planckian discreteness [47.03992469282679]
  In the standard paradigm the inhomogeneities observed in the CMB arise from quantum fluctuations of an initially homogeneous and isotropic vacuum state.<n>We propose an alternative paradigm in which such inhomogeneities are present from the very beginning.<n>Specifically, inhomogeneities in the quantum state at the Planck scale propagate into semiclassical inhomogeneities on CMB scales.
  arXiv  Detail & Related papers  (2025-06-18T12:33:31Z)
• Quantum and Semi-Classical Signatures of Dissipative Chaos in the Steady State [0.40498500266986387]
  We investigate the quantum-classical correspondence in open quantum many-body systems using the SU(3) Bose-Hubbard trimer as a minimal model.<n>We show that classical dynamical behavior, as quantified by the sign of the Lyapunov exponent, governs the level statistics of the steady-state density matrix.
  arXiv  Detail & Related papers  (2025-06-17T20:21:06Z)
• Theory of the correlated quantum Zeno effect in a monitored qubit dimer [41.94295877935867]
  We show how the competition between two measurement processes give rise to two distinct Quantum Zeno (QZ) regimes.<n>We develop a theory based on a Gutzwiller ansatz for the wavefunction that is able to capture the structure of the Hilbert phase diagram.<n>We show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.
  arXiv  Detail & Related papers  (2025-03-28T19:44:48Z)
• A healthier semi-classical dynamics [0.0]
  We study the back-reaction of quantum systems onto classical ones.<n>We take the starting point that semi-classical physics should be described at all times by a point in classical phase space and a quantum state in Hilbert space.
  arXiv  Detail & Related papers  (2022-08-24T18:04:14Z)
• Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
  Quantization smears the gravitational singularity avoiding its localization in the configuration space. Results suggest that the generic singularity of general relativity can be avoided at quantum level.
  arXiv  Detail & Related papers  (2022-04-24T13:32:45Z)
• Random matrices: Application to quantum paradoxes [0.0]
  Recently, a geometric embedding of the classical space and classical phase space of an n-particle system was constructed and shown to be physically meaningful. Namely, the Newtonian dynamics of the particles was recovered from the Schroedinger dynamics by constraining the state of the system to the classical phase space submanifold of the space of states. A series of theorems related to the embedding and the Schroedinger evolution with a random Hamiltonian was proven and shown to be applicable to the process of measurement in classical and quantum mechanics.
  arXiv  Detail & Related papers  (2022-04-08T20:26:03Z)
• 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)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Quantum chaos in the spin coherent state representation [0.0]
  We use spin coherent states to compare classical and quantum evolution of a simple paradigmatic, discrete-time quantum dynamical system. In the paper, we presented a different way by comparing evolution of appropriately defined moments of classical and quantum distributions.
  arXiv  Detail & Related papers  (2020-10-27T15:04:40Z)
• 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.