Related papers: Quantum transfer operators and chaotic scattering
Quantum theory is used to model secondary financial markets. Contrary to stochastic descriptions, the formalism emphasizes the importance of trading in determining the value of a security. All possible realizations of investors holding…
The problem of time operator in quantum mechanics is revisited. The unsharp measurement model for quantum time based on the dynamical system-clock interaction, is studied. Our analysis shows that the problem of the quantum time operator…
We investigate a quantum algorithm which simulates efficiently the quantum kicked rotator model, a system which displays rich physical properties, and enables to study problems of quantum chaos, atomic physics and localization of electrons…
The idea that chaos could be a useful tool for analyze nonlinear systems considered in this paper and for the first time the two time scale property of singularly perturbed systems is analyzed on chaotic attractor. The general idea…
We study operator entanglement of the quantum chaotic evolutions. This study shows that properties of the operator entanglement production are qualitatively similar to the properties reported in literature about the pure state entanglement…
Chaotic cryptography describes the use of chaos theory (in particular physical dynamical systems working in chaotic regime as part of communication techniques and computation algorithms) to perform different cryptographic tasks in a…
Quantum walks on graphs are fundamental to quantum computing and have led to many interesting open problems in algebraic graph theory. This review article highlights three key classes of open problems in this domain; perfect state transfer,…
We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting…
We study the entanglement of unitary operators on $d_1\times d_2$ quantum systems. This quantity is closely related to the entangling power of the associated quantum evolutions. The entanglement of a class of unitary operators is quantified…
We introduce and study the classical and quantum mechanics of certain non hyperbolic maps on the unit square. These maps are modifications of the usual baker's map and their behaviour ranges from chaotic motion on the whole measure to chaos…
An analytically derived 'integral operator' approach is introduced to estimate the expectation value of a quantum operator for an evolving state weighted with an exponential function. This allows to compute quantities useful in Nuclear…
Except for the universe, all quantum systems are open, and according to quantum state diffusion theory, many systems localize to wave packets in the neighborhood of phase space points. This is due to decoherence from the interaction with…
We introduce Quantum Time-Frequency Analysis, which expands the approach of Quantum Harmonic Analysis to include modulations of operators in addition to translations. This is done by a projective representation of double-phase space, and we…
Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a…
Digital circuits based on residue number systems have been considered to produce a pseudo-random behavior. The present work is an initial step towards the complete implementation of those systems for similar applications using quantum…
Counter-intuitively, quantum mechanics enables quantum particles to propagate simultaneously among multiple space-time trajectories. Hence, a quantum information carrier can travel through different communication channels in a quantum…
Long periodic orbits constitute a serious drawback in Gutzwiller's theory of chaotic systems, and then it would be desirable that other classical invariants, not suffering from the same problem, could be used in the quantization of such…
We show on the example of the Arnold cat map that classical chaotic systems can be simulated with exponential efficiency on a quantum computer. Although classical computer errors grow exponentially with time, the quantum algorithm with…
Faster algorithms, novel cryptographic mechanisms, and alternative methods of communication become possible when the model underlying information and computation changes from a classical mechanical model to a quantum mechanical one. Quantum…
We discuss control of the quantum-transport properties of a mesoscopic device by connecting it in a coherent feedback loop with a quantum-mechanical controller. We work in a scattering approach and derive results for the combined scattering…