Related papers: An illustration of canonical quantum-classical dyn…
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 consider one-dimensional classical time-dependent Hamiltonian systems with quasi-periodic orbits. It is well-known that such systems possess an adiabatic invariant which coincides with the action variable of the Hamiltonian formalism. We…
Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values…
In this paper, we analyze classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open or closed-loop feedback evolution of a control…
Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schroedinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter…
Assuming that the Hamiltonian of a canonical field theory can be written in the form N H + N^i H_i, and using as the only input the actual choice of the canonical variables, we derive: (i) The algebra satisfied by H and H_i, (ii) any…
We present a detailed study of the dynamics of correlations in non-Markovian environments, applying the hierarchy equations approach. This theoretical treatment is able to take the system-bath interaction into consideration carefully. It is…
In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be…
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…
Mixed quantum-classical spin systems have been proposed in spin chain theory and, more recently, in magnon spintronics. However, current models of quantum-classical dynamics beyond mean-field approximations typically suffer from…
We discuss the roles of the macroscopic limit and of different system-environment interactions in the quantum-classical transition for a chaotic system. We consider the kicked harmonic oscillator subject to reservoirs that correspond in the…
One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics. Here, we tackle the supervised…
How well can quantum computers simulate classical dynamical systems? There is increasing effort in developing quantum algorithms to efficiently simulate dynamics beyond Hamiltonian simulation, but so far exact resource estimates are not…
We study dynamical systems which admit action-angle variables at leading order which are subject to nearly resonant perturbations. If the frequencies characterizing the unperturbed system are not in resonance, the long-term dynamical…
For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for…
We introduce a hybrid classical-quantum algorithm to compute dynamical correlation functions and excitation spectra in many-body quantum systems, with a focus on molecular systems. The method combines classical preparation of a perturbed…
We describe an $p$-mechanical (see funct-an/9405002 and quant-ph/9610016) brackets which generate quantum (commutator) and classic (Poisson) brackets in corresponding representations of the Heisenberg group. We \emph{do not} use any kind of…
We review our results on a mathematical dynamical theory for observables for open many-body quantum nonlinear bosonic systems for a very general class of Hamiltonians. We show that non-quadratic (nonlinear) terms in a Hamiltonian provide a…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
The dynamics of systems composed of a classical sector plus a quantum sector is studied. We show that, even in the simplest cases, (i) the existence of a consistent canonical description for such mixed systems is incompatible with very…