The information entropy of quantum mechanical states

It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the latter is problematic from quantum information point of view. Consequently we introduce a new definition of entropy that reflects the inherent uncertainty of quantum mechanical states. We derive for it an explicit expression, and discuss some of its general properties. We distinguish between the minimum uncertainty entropy of pure states, and the excess statistical entropy of mixtures.Comment: 7 pages, 1 figur

Characterization of complex quantum dynamics with a scalable NMR information processor

We present experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor. The measurements were performed by implementing a scalable circuit in the model of deterministic quantum computation with only one quantum bit. The results show measurable differences between regular and complex behaviour and for complex dynamics are faithful to the expected theoretical decay rate. Moreover, we illustrate how the experimental method can be seen as an efficient way for either extracting coarse-grained information about the dynamics of a large system, or measuring the decoherence rate from engineered environments.Comment: 4pages, 3 figures, revtex4, updated with version closer to that publishe

Universal Quantum Signatures of Chaos in Ballistic Transport

The conductance of a ballistic quantum dot (having chaotic classical dynamics and being coupled by ballistic point contacts to two electron reservoirs) is computed on the single assumption that its scattering matrix is a member of Dyson's circular ensemble. General formulas are obtained for the mean and variance of transport properties in the orthogonal (beta=1), unitary (beta=2), and symplectic (beta=4) symmetry class. Applications include universal conductance fluctuations, weak localization, sub-Poissonian shot noise, and normal-metal-superconductor junctions. The complete distribution P(g) of the conductance g is computed for the case that the coupling to the reservoirs occurs via two quantum point contacts with a single transmitted channel. The result P(g)=g^(-1+beta/2) is qualitatively different in the three symmetry classes. ***Submitted to Europhysics Letters.****Comment: 4 pages, REVTeX-3.0, INLO-PUB-94032

Classical invariants and the quantization of chaotic systems

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 systems. In this respect, we demonstrate how a suitable dynamical analysis of chaotic quantum spectra unveils the fundamental role played by classical invariant areas related to the stable and unstable manifolds of short periodic orbits.Comment: 4 pages, 3 postscript figure

Universality of Decoherence

We consider environment induced decoherence of quantum superpositions to mixtures in the limit in which that process is much faster than any competing one generated by the Hamiltonian $H_{\rm sys}$ of the isolated system. While the golden rule then does not apply we can discard $H_{\rm sys}$. By allowing for simultaneous couplings to different reservoirs, we reveal decoherence as a universal short-time phenomenon independent of the character of the system as well as the bath and of the basis the superimposed states are taken from. We discuss consequences for the classical behavior of the macroworld and quantum measurement: For the decoherence of superpositions of macroscopically distinct states the system Hamiltonian is always negligible.Comment: 4 revtex pages, no figure

Pseudo-classical theory for fidelity of nearly resonant quantum rotors

Using a semiclassical ansatz we analytically predict for the fidelity of delta-kicked rotors the occurrence of revivals and the disappearance of intermediate revival peaks arising from the breaking of a symmetry in the initial conditions. A numerical verification of the predicted effects is given and experimental ramifications are discussed.Comment: Shortened and improved versio

Capture-zone scaling in island nucleation: phenomenological theory of an example of universal fluctuation behavior

In studies of island nucleation and growth, the distribution of capture zones, essentially proximity cells, can give more insight than island-size distributions. In contrast to the complicated expressions, ad hoc or derived from rate equations, usually used, we find the capture-zone distribution can be described by a simple expression generalizing the Wigner surmise from random matrix theory that accounts for the distribution of spacings in a host of fluctuation phenomena. Furthermore, its single adjustable parameter can be simply related to the critical nucleus of growth models and the substrate dimensionality. We compare with extensive published kinetic Monte Carlo data and limited experimental data. A phenomenological theory sheds light on the result.Comment: 5 pages, 4 figures, originally submitted to Phys. Rev. Lett. on Dec. 15, 2006; revised version v2 tightens and focuses the presentation, emphasizes the importance of universal features of fluctuations, corrects an error for d=1, replaces 2 of the figure

Scattering induced dynamical entanglement and the quantum-classical correspondence

The generation of entanglement produced by a local potential interaction in a bipartite system is investigated. The degree of entanglement is contrasted with the underlying classical dynamics for a Rydberg molecule (a charged particle colliding on a kicked top). Entanglement is seen to depend on the structure of classical phase-space rather than on the global dynamical regime. As a consequence regular classical dynamics can in certain circumstances be associated with higher entanglement generation than chaotic dynamics. In addition quantum effects also come into play: for example partial revivals, which are expected to persist in the semiclassical limit, affect the long time behaviour of the reduced linear entropy. These results suggest that entanglement may not be a pertinent universal signature of chaos.Comment: Published versio

Understanding the effect of seams on the aerodynamics of an association football

The aerodynamic properties of an association football were measured using a wind tunnel arrangement. A third scale model of a generic football (with seams) was used in addition to a 'mini-football'. As the wind speed was increased, the drag coefficient decreased from 0.5 to 0.2, suggesting a transition from laminar to turbulent behaviour in the boundary layer. For spinning footballs, the Magnus effect was observed and it was found that reverse Magnus effects were possible at low Reynolds numbers. Measurements on spinning smooth spheres found that laminar behaviour led to a high drag coefficient for a large range of Reynolds numbers, and Magnus effects were inconsistent, but generally showed reverse Magnus behaviour at high Reynolds number and spin parameter. Trajectory simulations of free kicks demonstrated that a football that is struck in the centre will follow a near straight trajectory, dipping slightly before reaching the goal, whereas a football that is struck off centre will bend before reaching the goal, but will have a significantly longer flight time. The curving kick simulation was repeated for a smooth ball, which resulted in a longer flight time, due to increased drag, and the ball curving in the opposite direction, due to reverse Magnus effects. The presence of seams was found to encourage turbulent behaviour, resulting in reduced drag and more predictable Magnus behaviour for a conventional football, compared with a smooth ball. © IMechE 2005

Overlap with the Separable State and Phase Transition in the Dicke Model: Zero and Finite Temperature

Overlap with the separable state is introduced in this paper for the purpose of characterizing the overall correlation in many-body systems. This definition has clear geometric and physical meaning, and moreover can be considered as the generalization of the concept-Anderson Orthogonality Catastrophe. As an exemplification, it is used to mark the phase transition in the Dicke model for zero and finite temperature. And our discussion shows that it can faithfully reflect the phase transition properties of this model whether for zero or finite temperature. Furthermore the overlap for ground state also indicates the appearance of multipartite entanglement in Dicke model.Comment: 11+ pages. Enlarged version including a formal proof for the method to find the maximal overlap. accepted by PRA