Related papers: Quantum-classical hybrid dynamics: coupling mechan…
We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting…
Master equations in the Lindblad form describe evolution of open quantum systems that is completely positive and simultaneously has a semigroup property. We analyze a possibility to derive this type of master equations from an intrinsically…
Using the example of the harmonic oscillator, we illustrate the use of hybrid dynamical brackets in analyzing quantum-classical interaction. We only assume that a hybrid dynamical bracket exists, is bilinear, and reduces to the pure…
The dynamics of a quantum system coupled to a classical environment and subject to constraints that drive it out of equilibrium is described. The evolution of the system is governed by the quantum-classical Liouville equation. Rather than…
The dynamical equation of hybrid systems, being the combination of Schr\"odinger and Liouville equations, produces noncausal evolution when the initial state of interacting quantum and classical mechanical systems is as it is demanded in…
Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman-von Neumann theory, this paper addresses the long-standing problem of formulating a dynamical theory of classical-quantum coupling. The proposed model not only…
We discuss the Hamiltonian hybrid coupling between a classical and a quantum subsystem. If applicable to classical gravity coupled to quantized matter, this hybrid theory might realize a captivating `postquantum' alternative to full…
The conditions under which an open quantum mechanical system may be described by mixed quantum-classical dynamics are investigated. Decoherence is studied using influence functional methods in a model composite quantum system comprising two…
We characterize good clocks, which are naturally subject to fluctuations, in statistical terms. We also obtain the master equation that governs the evolution of quantum systems according to these clocks and find its general solution. This…
Quantum and classical systems can consistently be coupled via non-unitary time-irreversible mechanisms. In this paper we characterize which kind of corresponding dynamics converge in the stationary regime to a thermal hybrid state, that is,…
This paper extends the Madelung-Bohm formulation of quantum mechanics to describe the time-reversible interaction of classical and quantum systems. The symplectic geometry of the Madelung transform leads to identifying hybrid…
A quantum-classical limit of the canonical equilibrium time correlation function for a quantum system is derived. The quantum-classical limit for the dynamics is obtained for quantum systems comprising a subsystem of light particles in a…
By modeling the interaction of an open quantum system with its environment through a natural generalization of the classical concept of continuous time random walk, we derive and characterize a class of non-Markovian master equations whose…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
Non-Markovian effects in quantum evolution appear when the system is strongly coupled to the environment and interacts with it for long periods of time. To include memory effects in the master equations, one usually incorporates time-local…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
We consider a large number of two-level atoms interacting with the mode of a cavity in the rotating-wave approximation (Tavis-Cummings model). We apply the Holstein-Primakoff transformation to study the model in the limit of the number of…
We consider two limiting regimes, the large-spin and the mean-field limit, for the dynamical evolution of quantum spin systems. We prove that, in these limits, the time evolution of a class of quantum spin systems is determined by a…
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
A new approximate solution to the quantum-classical Liouville equation is derived starting from the formal solution of this equation in forward-backward form. The time evolution of a mixed quantum-classical system described by this equation…