A dynamic programming interpretation of quantum mechanics

• URL: http://arxiv.org/abs/2401.04085v1
• Date: Mon, 8 Jan 2024 18:43:40 GMT
• Title: A dynamic programming interpretation of quantum mechanics
• Authors: Adam Brownstein
• Abstract summary: We introduce a transformation of the quantum phase $S'=S+frachbar2logrho$, which converts the deterministic equations of quantum mechanics into the Lagrangian reference frame of particles. We show that the quantum potential can be removed from the transformed quantum Hamilton-Jacobi equations if they are solved as Hamilton-Jacobi-Bellman equations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a transformation of the quantum phase $S'=S+\frac{\hbar}{2}\log\rho$, which converts the deterministic equations of quantum mechanics into the Lagrangian reference frame of stochastic particles. We show that the quantum potential can be removed from the transformed quantum Hamilton-Jacobi equations if they are solved as stochastic Hamilton-Jacobi-Bellman equations. The system of equations provide a local description of quantum mechanics, which is enabled by the inherently retrocausal nature of stochastic Hamilton-Jacobi-Bellman equations. We also investigate the stochastic transformation of the classical system, where is it shown that quantum mechanics with the quantum potential reduced by a factor of $\frac{1}{2}$ has a classical representation, which may have interesting implications. Finally, we discuss the notion of a subsystem correspondence principle, which constrains the ontology of the total quantum system.

Related papers

• Self-consistency, relativism and many-particle system [0.0]
  Interrelation between concepts of self-consistency, relativism and many-particle systems is considered. Paper shows that quantum systems with a time independent function of quasi-density probability in phase space are not capable to emit electromagnetic radiation.
  arXiv  Detail & Related papers  (2024-04-21T08:38:40Z)
• Equivalence Principle for Quantum Mechanics in the Heisenberg Picture [0.0]
  We present an exact quantum observable analog of the weak equivalence principle for a relativistic' quantum particle. The quantum geodesic equations are obtained from Heisenberg equations of motion as an exact analog of a fully covariant classical Hamiltonian evolution picture.
  arXiv  Detail & Related papers  (2023-09-05T06:39:01Z)
• Classical stochastic representation of quantum mechanics [0.0]
  We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. The probabilistic character of quantum mechanics is devised by treating the wave function as a variable.
  arXiv  Detail & Related papers  (2023-07-31T21:02:43Z)
• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• Dispersion chain of quantum mechanics equations [0.0]
  The paper considers the construction of a new chain of equations of quantum mechanics of high kinematical values. The proposed approach can be applied to consideration of classical and quantum systems with radiation.
  arXiv  Detail & Related papers  (2022-09-28T12:58:19Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Lyapunov equation in open quantum systems and non-Hermitian physics [0.0]
  The continuous-time differential Lyapunov equation is widely used in linear optimal control theory. In quantum physics, it is known to appear in Markovian descriptions of linear (quadratic Hamiltonian, linear equations of motion) open quantum systems. We establish the Lyapunov equation as a fundamental and efficient formalism for linear open quantum systems.
  arXiv  Detail & Related papers  (2022-01-03T14:40:07Z)
• From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
  We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation. We describe quantum decays in a 2-level system as coherent and continuous processes.
  arXiv  Detail & Related papers  (2021-07-29T18:27:38Z)
• 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)
• 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)
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond [46.39654665163597]
  We report on experimental tests of topological defect formation via the one-dimensional transverse-field Ising model. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system.
  arXiv  Detail & Related papers  (2020-01-31T02:55:35Z)

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.