Related papers: Correspondence between classical and quantum reson…
When a regular classical system is perturbed, non-linear resonances appear as prescribed by the KAM and Poincar\`{e}-Birkhoff theorems. Manifestations of this classical phenomena to the morphologies of quantum wave functions are studied in…
The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to…
Coherent control of a quantum mechanical two-level system is at the heart of magnetic resonance imaging, quantum information processing, and quantum optics. Among the most prominent phenomena in quantum coherent control are Rabi…
The concept of duality reflects a link between two seemingly different physical objects. An example in quantum mechanics is a situation where the spectra (or their parts) of two Hamiltonians go into each other under a certain…
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…
Consider a bipartite quantum system with at least one of its two components being itself a composite system. By tracing over part of one (or both) of these two subsystems it is possible to obtain a reduced (separable) state that exhibits…
We study the resonances of a two-by-two semiclassical system of one dimensional Schr\"odinger operators, near an energy where the two potentials intersect transversally, one of them being bonding, and the other one anti-bonding. Under an…
We investigate the correlations of initially separable probability distributions in a globally pure bipartite system with two degrees of freedom for classical and quantum systems. A classical version of the quantum linear mutual information…
We study the transition between quantum and classical behavior of particles in a gravitational quantum well. We analyze how an increase in the particles mass turns the energy spectrum into a continuous one, from an experimental point of…
Quantum and classical systems evolving under the same formal Hamiltonian $H$ may dramatically differ after the Ehrenfest timescale $t_E \sim \log(\hbar^{-1})$, even as $\hbar \to 0$. Coupling the system to a Markovian environment results in…
The correspondence principle plays a fundamental role in quantum mechanics, which naturally leads us to inquire whether it is possible to find or determine close classical analogs of quantum states in phase space -- a common meeting point…
It is well known that a symmetric soliton in coupled nonlinear Schroedinger (NLS) equations with the cubic nonlinearity loses its stability with the increase of its energy, featuring a transition into an asymmetric soliton via a subcritical…
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g.,…
In this work, we investigate the semiclassical limit of a simple bosonic quantum many-body system exhibiting both integrable and chaotic behavior. A classical Hamiltonian is derived using coherent states. The transition from regularity to…
We systematically study several classical-quantum correspondence properties of the dissipative modified kicked rotator, a paradigmatic ratchet model. We explore the behavior of the asymptotic currents for finite $\hbar_{\rm eff}$ values in…
Previous studies have shown that noise can induce coherence resonance in some nonlinear dynamical systems close to a bifurcation of a periodic motion, such as in excitable systems. We demonstrate that coherence resonance can be observed in…
Radiative transfer calculations in strong (few $\times 10^{12}$ G) magnetic fields, observed in X-ray pulsars, require accurate resonant differential scattering cross sections. Such cross sections exist, but they are quite cumbersome. Here…
A unifying principle explaining the numerical bounds of quantum correlations remains elusive despite the efforts devoted to identifying it. Here we show that these bounds are indeed not exclusive to quantum theory: for any abstract…
The non-crossing rule for the energy levels of a parameter-dependent Hamiltonian is revisited and a flaw in a commonly accepted proof is revealed. Some aspects of avoided crossings are illustrated by means of simple models. One of them…
For relativistic energies the small angle classical cross section for scattering on a Coulomb potential agrees with the first Born approximation for quantum cross section for scalar particle only in the leading term. The disagreement in…