Path integrals for classical-quantum dynamics

• URL: http://arxiv.org/abs/2301.04677v1
• Date: Wed, 11 Jan 2023 19:03:26 GMT
• Title: Path integrals for classical-quantum dynamics
• Authors: Jonathan Oppenheim and Zachary Weller-Davies
• Abstract summary: Consistent dynamics which couples classical and quantum degrees of freedom exists. We derive a general path integral representation for such dynamics in terms of a classical-quantum action. When the classical-quantum Hamiltonian is at most quadratic in the momenta we are able to derive a configuration space path integral.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations, we derive a general path integral representation for such dynamics in terms of a classical-quantum action, which includes the necessary and sufficient conditions for complete positivity and trace preservation. The path integral we study is a generalization of the Feynman path integral for quantum systems, and the stochastic path integral used to study classical stochastic processes, allowing for interaction between the classical and quantum systems. When the classical-quantum Hamiltonian is at most quadratic in the momenta we are able to derive a configuration space path integral, providing a map between master equations and covariant classical-quantum path integrals.

Related papers

• Markovian dynamics for a quantum/classical system and quantum trajectories [0.0]
  We develop a general approach to the dynamics of quantum/classical systems. An important feature is that, if the interaction allows for a flow of information from the quantum component to the classical one, necessarily the dynamics is dissipative.
  arXiv  Detail & Related papers  (2024-03-24T08:26:54Z)
• Covariant path integrals for quantum fields back-reacting on classical space-time [0.0]
  We introduce configuration space path integrals for quantum fields interacting with classical fields. We show that this can be done consistently by proving that the dynamics are completely positive directly. They generalize and combine the Feynman-Vernon path integral of open quantum systems and the path integral of classical dynamics.
  arXiv  Detail & Related papers  (2023-02-14T19:00:10Z)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• A healthier semi-classical dynamics [0.0]
  We study the back-reaction of quantum systems onto classical ones. 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)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• 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)
• The two classes of hybrid classical-quantum dynamics [0.0]
  Coupling between quantum and classical systems is consistent, provided the evolution is linear in the state space. We prove that if the dynamics is memoryless, there are two classes of these dynamics. We find the most general form of each class of classical-quantum master equation.
  arXiv  Detail & Related papers  (2022-03-02T19:00:01Z)
• 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)
• 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)
• Objective trajectories in hybrid classical-quantum dynamics [0.0]
  We introduce several toy models in which to study hybrid classical-quantum evolution. We present an unravelling approach to calculate the dynamics, and provide code to numerically simulate it.
  arXiv  Detail & Related papers  (2020-11-11T19:00:34Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)

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.