Related papers: Classical and quantum resonances for hyperbolic su…
Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that…
In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in…
We define Pollicott-Ruelle resonances for geodesic flows on noncompact asymptotically hyperbolic negatively curved manifolds, as well as for more general open hyperbolic systems related to Axiom A flows. These resonances are the poles of…
The quantum resonances occurring with delta-kicked particles are studied with the help of a fictitious classical limit, establishing a direct correspondence between the nearly resonant quantum motion and the classical resonances of a…
A quantum mechanical version of a classical inverted pendulum is analyzed. The stabilization of the classical motion is reflected in the bounded evolution of the quantum mechanical operators in the Heisenberg picture. Interesting links with…
A rigorous (and simple) proof is given that there is a one-to-one correspondence between causal anti-deSitter covariant quantum field theories on anti-deSitter space and causal conformally covariant quantum field theories on its conformal…
A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…
In this note we explicitly compute the resonances on hyperbolic cones. These are hyperbolic manifolds with a conic singularity equipped with a warped product metric. The calculation is based on separation of variables and Kummer's…
Analysis of state reconstruction both classical and quantum mechanical on equal footing is outlined. The meaning of "mutual unbiased bases" (MUB) of Hilbert spaces is explained in detail. An alternative quantum state reconstruction, that…
The correspondence between classical spin models and quantum states has attracted much attention in recent years. However, it remains an open problem as to which specific spin model a given (well-known) quantum state maps to. In this…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
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…
Using Koopman's approach to classical dynamical systems we show that the classical damping may be interpreted as appearance of resonant states of the corresponding Koopman's operator. It turns out that simple classical damped systems give…
We present an analytical model for describing complex dynamics of a hybrid system consisting of interacting classical and quantum resonant structures. Classical structures in our model correspond to plasmonic nano-resonators of different…
A simple derivation of the classical solutions of a nonlinear model describing a harmonic oscillator on the sphere and the hyperbolic plane is presented in polar coordinates. These solutions are then related to those in cartesian…
On manifolds with an even Riemannian conformally compact Einstein metric, the resolvent of the Lichnerowicz Laplacian, acting on trace-free, divergence-free, symmetric 2-tensors is shown to have a meromorphic continuation to the complex…
We study topological phases in the hyperbolic plane using noncommutative geometry and T-duality, and show that fractional versions of the quantised indices for integer, spin and anomalous quantum Hall effects can result. Generalising models…
The coherence between quantum states with different particle numbers --- the Fock-space coherence --- qualitatively differs from the more common Hilbert-space coherence between states with equal particle numbers. For a quantum dot with…
We study the quantum-classical correspondence of an experimentally accessible system of interacting bosons in a tilted triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the…
A recently discovered classical-quantum correspondence (CQC) maps certain quantum problems to corresponding classical problems. We illustrate the CQC for a quantum scalar field in the gravitational background of a collapsing spherical…