Linear dynamics of quantum-classical hybrids

Abstract

A formulation of quantum-classical hybrid dynamics is presented, which concerns the direct coupling of classical and quantum mechanical degrees of freedom. It is of interest for applications in quantum mechanical approximation schemes and may be relevant for the foundations of quantum mechanics, in particular, when it comes to experiments exploring the quantum-classical border. The present linear theory differs from the nonlinear ensemble theory of Hall and Reginatto, but shares with it to fullfill all consistency requirements discussed in the literature, while earlier attempts failed in this respect. Our work is based on the representation of quantum mechanics in the framework of classical analytical mechanics by A. Heslot, showing that notions of states in phase space, observables, Poisson brackets, and related canonical transformations can be naturally extended to quantum mechanics. This is suitably generalized for quantum-classical hybrids here.

Replaced by final revtex version; references updated, section V.E. added

References in corpus (10)

• Gravitation and quantummechanical localization of macroobjects
• Consistent classical and quantum mixed dynamics
• Does quantum mechanics tell an atomistic spacetime?
• Four questions for quantum-classical hybrid theory
• Quantum-classical interactions and measurement: a consistent description using statistical ensembles on configuration space
• General linear dynamics - quantum, classical or hybrid
• Interacting classical and quantum particles
• A path integral for classical dynamics, entanglement, and Jaynes-Cummings model at the quantum-classical divide
• Does wave function collapse cause gravity?
• Loss of entanglement in quantum mechanics due to the use of realistic measuring rods

Cited by in corpus (76)

• Time-retarded damping and magnetic inertia in the Landau-Lifshitz-Gilbert equation self-consistently coupled to electronic time-dependent nonequilibrium Green functions
• On two recent proposals for witnessing nonclassical gravity
• Hybrid classical-quantum formulations ask for hybrid notions
• Action principle for cellular automata and the linearity of quantum mechanics
• Hybrid Quantum-Classical Master Equations
• Statistical moments for classical and quantum dynamics: formalism and generalized uncertainty relations
• Spin dynamics and relaxation in the classical-spin Kondo-impurity model beyond the Landau-Lifschitz-Gilbert equation
• The Entropic Dynamics approach to Quantum Mechanics
• Anomalous spin precession under a geometrical torque
• Classical and Quantum-Mechanical Axioms with the Higher Time Derivative Formalism
• Statistical ensembles in Hamiltonian formulation of hybrid quantum-classical systems
• Classical and quantum behavior of the harmonic and the quartic oscillators
• Any consistent coupling between classical gravity and quantum matter is fundamentally irreversible
• Four questions for quantum-classical hybrid theory
• Relaxation of a classical spin coupled to a strongly correlated electron system
• Discrete mechanics, time machines and hybrid systems
• De Donder-Weyl Hamiltonian formulation and precanonical quantization of vielbein gravity
• Quantum-classical hybrid dynamics - a summary
• Proliferation of observables and measurement in quantum-classical hybrids
• Semi-classical approximations based on Bohmian mechanics
• Inertia effects in the real-time dynamics of a quantum spin coupled to a Fermi sea
• Canonical bracket in quantum-classical hybrid systems
• An exact mapping between the states of arbitrary N-level quantum systems and the positions of classical coupled oscillators
• Entropy and canonical ensemble of hybrid quantum classical systems
• Classicality of a quantum oscillator
• When can localized spins interacting with conduction electrons in ferro- or antiferromagnets be described classically via the Landau-Lifshitz equation: Transition from quantum many-body entangled to quantum-classical nonequilibrium states
• Hamiltonian formulation of nonequilibrium quantum dynamics: geometric structure of the BBGKY hierarchy
• Nonlocal signaling in the configuration space model of quantum-classical interactions
• Accessing long timescales in the relaxation dynamics of spins coupled to a conduction-electron system using absorbing boundary conditions
• Mirror-induced decoherence in hybrid quantum-classical theory
• A holographic map of action onto entropy
• Entanglement dynamics in a quantum-classical hybrid of two q-bits and one oscillator
• Long-time relaxation dynamics of a spin coupled to a Chern insulator
• Classical-quantum limits
• Classicalization of Quantum Variables and Quantum-Classical Hybrids
• Vindication of entanglement-based witnesses of non-classicality in hybrid systems
• Derivation of quantum theory with superselection rules
• Optical squeezing for an optomechanical system without quantising the mechanical motion
• Quantum F_un: the q=1 Limit of Galois Field Quantum Mechanics, Projective Geometry, and the Field with One Element
• Hybrid quantum-classical simulation of quantum speed limits in open quantum systems
• Classical evolution in quantum systems
• The linearity of quantum mechanics from the perspective of Hamiltonian cellular automata
• About the computation of finite temperatureensemble averages of hybrid quantum-classicalsystems with Molecular Dynamics
• Emergent Non-Abelian Gauge Theory in Coupled Spin-Electron Dynamics
• Ontological states and dynamics of discrete (pre-)quantum systems
• Dynamics of spin relaxation in nonequilibrium magnetic nanojunctions
• Phase space quantum-classical hybrid model
• Density-Functional theory, finite-temperature classical maps, and their implications for foundational studies of quantum systems
• Quantum-Classical Dynamical Brackets
• Nonequilibrium dynamics in a spin valve with noncollinear magnetization
• Ehrenfest principle and unitary dynamics of quantum-classical systems with general potential interaction
• Emergence from irreversibility
• Internal environment: What is it like to be a Schrodinger cat?
• Are quantum spins but small perturbations of ontological Ising spins?
• Minkowski Spacetime and QED from Ontology of Time
• Phase space hybrid theory of quantum measurement with nonlinear and stochastic dynamics
• Orbits of hybrid systems as qualitative indicators of quantum dynamics
• Qubit exchange interactions from permutations of classical bits
• Emergent quantum mechanics as a classical, irreversible thermodynamics
• The Entropic Dynamics of Spin
• Controlling the real-time dynamics of a spin coupled to the helical edge states of the Kane-Mele model
• Are Quantum-Classical Hybrids compatible with Ontological Cellular Automata?
• Generalised complex geometry in thermodynamical fluctuation theory
• Microscopic theory of spin friction and dissipative spin dynamics
• Prerelaxation in quantum, classical, and quantum-classical two-impurity models
• Poisson bracket operator
• Cloning in nonlinear Hamiltonian quantum and hybrid mechanics
• Measurement of a quantum system with a classical apparatus using ensembles on configuration space
• Geometrical torque on magnetic moments coupled to a correlated antiferromagnet
• Quantum-classical comparison: arrival times and statistics
• Quantum Mechanics in symmetry language
• Hydrogen atom as a quantum-classical hybrid system
• An illustration of canonical quantum-classical dynamics
• Beyond Born-Oppenheimer Green's function theories: absolute and relational
• Hilbert bodies as quantum-classical continua
• Comment on "Vindication of entanglement-based witnesses of non-classicality in hybrid systems"