Related papers: Classicalization of Quantum Variables and Quantum-…
A filtering problem for a class of quantum systems disturbed by a classical stochastic process is investigated in this paper. The classical disturbance process, which is assumed to be described by a linear stochastic differential equation,…
This article provides an accessible illustration of the measurement approach to the study of the quantum-classical transition suitable for beginning graduate students. As an example, we apply it to a quantum system with a general quadratic…
The classical dynamical system possessing a quantum spectrum of energy and "quantum" behavior is suggested and investigated. The proposed model can be considered as a dynamical variant of the old quantum theory for harmonic oscillator in…
A recent development of the studies on classical and quasi-classical properties of supersymmetric quantum mechanics in Witten's version is reviewed. First, classical mechanics of a supersymmetric system is considered. Solutions of the…
Variational techniques have long been at the heart of atomic, solid-state, and many-body physics. They have recently extended to quantum and classical machine learning, providing a basis for representing quantum states via neural networks.…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
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,…
A mathematically consistent procedure for coupling quasiclassical and quantum variables through coupled Hamilton-Heisenberg equations of motion is derived from a variational principle. During evolution, the quasiclassical variables become…
Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…
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. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…
A hybrid formalism is proposed for interacting classical and quantum sytems. This formalism is mathematically consistent and reduces to standard classical and quantum mechanics in the case of no interaction. However, in the presence of…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…
A long-standing challenge in mixed quantum-classical trajectory simulations is the treatment of entanglement between the classical and quantal degrees of freedom. We present a novel approach which describes the emergence of entangled states…
We derive a model of quantum-classical hybrids for a simplified model of quantum electrodynamics in the framework of the stochastic variational method. In this model, charged particle trajectories are affected by the interaction with…
A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality…
We study continuous variable systems, in which quantum and classical degrees of freedom are combined and treated on the same footing. Thus all systems, including the inputs or outputs to a channel, may be quantum-classical hybrids. This…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…