Markovian master equations for quantum-classical hybrid systems

• URL: http://arxiv.org/abs/2310.02006v2
• Date: Fri, 17 Nov 2023 17:24:20 GMT
• Title: Markovian master equations for quantum-classical hybrid systems
• Authors: Alberto Barchielli
• Abstract summary: In the Markovian case, the problem is formalized by the notion of hybrid dynamical semigroup. A classical component can be observed without perturbing the system. Information on the quantum component can be extracted, thanks to the quantum-classical interaction.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: The problem of constructing a consistent quantum-classical hybrid dynamics is afforded in the case of a quantum component in a separable Hilbert space and a continuous, finite-dimensional classical component. In the Markovian case, the problem is formalized by the notion of hybrid dynamical semigroup. A classical component can be observed without perturbing the system and information on the quantum component can be extracted, thanks to the quantum-classical interaction. This point is formalized by showing how to introduce positive operator valued measures and operations compatible with the hybrid dynamical semigroup; in this way the notion of hybrid dynamics is connected to quantum measurements in continuous time. Then, the case of the most general quasi-free generator is presented and the various quantum-classical interaction terms are discussed. To bee quasi-free means to send, in the Heisenberg description, hybrid Weyl operators into multiples of Weyl operators; the results on the structure of quasi-free semigroups were proved in the article arXiv:2307.02611. Even in the pure quantum case, a quasi-free semigroup is not restricted to have only a Gaussian structure, but also jump-type terms are allowed. An important result is that, to have interactions producing a flow of information from the quantum component to the classical one, suitable dissipative terms must be present in the generator. Finally, some possibilities are discussed to go beyond the quasi-free case.

Related papers

• Quantum-classical correspondence of non-Hermitian spin-orbit coupled bosonic junction [4.934387267206206]
  We show that near the symmetry-breaking phase transition point, the correspondence between classical (mean-field) and quantum dynamics is more likely to break down. In both the mean-field and many-particle models, the SOC effects can greatly promote the synchronous periodic oscillations between the spin-up and spin-down components.
  arXiv  Detail & Related papers  (2024-10-17T02:58:17Z)
• 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)
• Generalized Gleason and Kraus Theorems for hybrid classical-quantum probabilities [0.0]
  We propose axioms for hybrid classical-quantum probability measures that readily generalize the usual ones for classical and quantum probability measures. We formulate a requirement for the transformations of hybrid probability measures analogous to the complete positive assumption for quantum operations. Explicit expressions for these transformations are derived when the classical and quantum subsystems are non-interacting, the classical subsystem is discrete, or the Hilbert space of the quantum subsystem is finite-dimensional.
  arXiv  Detail & Related papers  (2024-08-20T14:13:44Z)
• 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)
• Analytical approximations for generalized quantum Rabi models [7.708919339137053]
  The quantum Rabi model serves as the simplest non-integrable yet solvable model describing the interaction between a two-level system and a single mode of a bosonic field. We show that the energy spectrum of the generalized quantum Rabi model can be analytically determined by a bi-confluent Fuchsian equation.
  arXiv  Detail & Related papers  (2024-01-11T01:42:17Z)
• Hybrid classical-quantum systems in terms of moments [0.0]
  We describe the dynamics of hybrid systems with mixed classical and quantum degrees of freedom. In particular, a closed formula for the Poisson brackets between any two moments for an arbitrary number of degrees of freedom is presented.
  arXiv  Detail & Related papers  (2023-12-21T15:36:40Z)
• Hybrid quantum-classical systems: Quasi-free Markovian dynamics [0.0]
  In the case of a quantum-classical hybrid system, the problem of characterizing the most general dynamical semigroup is solved under the restriction of being quasi-free. We show how to extract multi-time probabilities and how to connect them to the quantum notions of positive operator valued measure and instrument. A concrete example is given, showing how a classical component can input noise into a quantum one and how the classical system can extract information on the behaviour of the quantum one.
  arXiv  Detail & Related papers  (2023-07-05T19:26:09Z)
• 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)
• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain [21.24186888129542]
  We study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. Special emphasis is devoted to the simplest types of solutions, describing precessional motion and elliptic magnetisation waves.
  arXiv  Detail & Related papers  (2020-10-14T16:46:11Z)
• Quantum and semi-classical aspects of confined systems with variable mass [0.3149883354098941]
  We explore the quantization of classical models with position-dependent mass terms constrained to a bounded interval in the canonical position. For a non-separable function $Pi(q,p)$, a purely quantum minimal-coupling term arises in the form of a vector potential for both the quantum and semi-classical models.
  arXiv  Detail & Related papers  (2020-05-28T18:50:24Z)
• 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.