On dynamical tunneling and classical resonances

This work establishes a firm relationship between classical nonlinear resonances and the phenomenon of dynamical tunneling. It is shown that the classical phase space with its hierarchy of resonance islands completely characterizes dynamical tunneling and explicit forms of the dynamical barriers can be obtained only by identifying the key resonances. Relationship between the phase space viewpoint and the quantum mechanical superexchange approach is discussed in near-integrable and mixed regular-chaotic situations. For near-integrable systems with sufficient anharmonicity the effect of multiple resonances {\it i.e.,} resonance-assisted tunneling can be incorporated approximately. It is also argued that the, presumed, relation of avoided crossings to nonlinear resonances does not have to be invoked in order to understand dynamical tunneling. For molecules with low density of states the resonance-assisted mechanism is expected to be dominant.Comment: Completely rewritten and expanded version of a previous submission physics/0410033. 14 pages and 10 figure

Sequential measurement of conjugate variables as an alternative quantum state tomography

It is shown how it is possible to reconstruct the initial state of a one-dimensional system by measuring sequentially two conjugate variables. The procedure relies on the quasi-characteristic function, the Fourier-transform of the Wigner quasi-probability. The proper characteristic function obtained by Fourier-transforming the experimentally accessible joint probability of observing "position" then "momentum" (or vice versa) can be expressed as a product of the quasi-characteristic function of the two detectors and that, unknown, of the quantum system. This allows state reconstruction through the sequence: data collection, Fourier-transform, algebraic operation, inverse Fourier-transform. The strength of the measurement should be intermediate for the procedure to work.Comment: v2, 5 pages, no figures, substantial improvements in the presentation, thanks to an anonymous referee. v3, close to published versio

Symmetry of Quantum Phase Space in a Degenerate Hamiltonian System

Using Husimi function approach, we study the ``quantum phase space'' of a harmonic oscillator interacting with a plane monochromatic wave. We show that in the regime of weak chaos, the quantum system has the same symmetry as the classical system. Analytical results agree with the results of numerical calculations.Comment: 11 pages LaTex, including 2 Postscript figure

Quantum chaos in the mesoscopic device for the Josephson flux qubit

We show that the three-junction SQUID device designed for the Josephson flux qubit can be used to study quantum chaos when operated at high energies. In the parameter region where the system is classically chaotic we analyze the spectral statistics. The nearest neighbor distributions $P(s)$ are well fitted by the Berry Robnik theory employing as free parameters the pure classical measures of the chaotic and regular regions of phase space in the different energy regions. The phase space representation of the wave functions is obtained via the Husimi distributions and the localization of the states on classical structures is analyzed.Comment: Final version, to be published in Phys. Rev. B. References added, introduction and conclusions improve

Quantum versus Classical Dynamics in a driven barrier: the role of kinematic effects

We study the dynamics of the classical and quantum mechanical scattering of a wave packet from an oscillating barrier. Our main focus is on the dependence of the transmission coefficient on the initial energy of the wave packet for a wide range of oscillation frequencies. The behavior of the quantum transmission coefficient is affected by tunneling phenomena, resonances and kinematic effects emanating from the time dependence of the potential. We show that when kinematic effects dominate (mainly in intermediate frequencies), classical mechanics provides very good approximation of quantum results. Moreover, in the frequency region of optimal agreement between classical and quantum transmission coefficient, the transmission threshold, i.e. the energy above which the transmission coefficient becomes larger than a specific small threshold value, is found to exhibit a minimum. We also consider the form of the transmitted wave packet and we find that for low values of the frequency the incoming classical and quantum wave packet can be split into a train of well separated coherent pulses, a phenomenon which can admit purely classical kinematic interpretation

Understanding highly excited states via parametric variations

Highly excited vibrational states of an isolated molecule encode the vibrational energy flow pathways in the molecule. Recent studies have had spectacular success in understanding the nature of the excited states mainly due to the extensive studies of the classical phase space structures and their bifurcations. Such detailed classical-quantum correspondence studies are presently limited to two or quasi two dimensional systems. One of the main reasons for such a constraint has to do with the problem of visualization of relevant objects like surface of sections and Wigner or Husimi distributions associated with an eigenstate. This neccesiates various alternative techniques which are more algebraic than geometric in nature. In this work we introduce one such method based on parametric variation of the eigenvalues of a Hamiltonian. It is shown that the level velocities are correlated with the phase space nature of the corresponding eigenstates. A semiclassical expression for the level velocities of a single resonance Hamiltonian is derived which provides theoretical support for the correlation. We use the level velocities to dynamically assign the highly excited states of a model spectroscopic Hamiltonian in the mixed phase space regime. The effect of bifurcations on the level velocities is briefly discussed using a recently proposed spectroscopic Hamiltonian for the HCP molecule.Comment: 12 pages, 9 figures, submitted to J. Chem. Phy

Husimi coordinates of multipartite separable states

A parametrization of multipartite separable states in a finite-dimensional Hilbert space is suggested. It is proved to be a diffeomorphism between the set of zero-trace operators and the interior of the set of separable density operators. The result is applicable to any tensor product decomposition of the state space. An analytical criterion for separability of density operators is established in terms of the boundedness of a sequence of operators.Comment: 19 pages, 1 figure, LaTe

Determination of Compton profiles at solid surfaces from first-principles calculations

Projected momentum distributions of electrons, i.e. Compton profiles above the topmost atomic layer have recently become experimentally accessible by kinetic electron emission in grazing-incidence scattering of atoms at atomically flat single crystal metal surfaces. Sub-threshold emission by slow projectiles was shown to be sensitive to high-momentum components of the local Compton profile near the surface. We present a method to extract momentum distribution, Compton profiles, and Wigner and Husimi phase space distributions from ab-initio density-functional calculations of electronic structure. An application for such distributions to scattering experiments is discussed.Comment: 13 pages, 5 figures, submitted to PR

Fisher information, Wehrl entropy, and Landau Diamagnetism

Using information theoretic quantities like the Wehrl entropy and Fisher's information measure we study the thermodynamics of the problem leading to Landau's diamagnetism, namely, a free spinless electron in a uniform magnetic field. It is shown that such a problem can be "translated" into that of the thermal harmonic oscillator. We discover a new Fisher-uncertainty relation, derived via the Cramer-Rao inequality, that involves phase space localization and energy fluctuations.Comment: no figures. Physical Review B (2005) in pres

Quantum and Fisher Information from the Husimi and Related Distributions

The two principal/immediate influences -- which we seek to interrelate here -- upon the undertaking of this study are papers of Zyczkowski and Slomczy\'nski (J. Phys. A 34, 6689 [2001]) and of Petz and Sudar (J. Math. Phys. 37, 2262 [1996]). In the former work, a metric (the Monge one, specifically) over generalized Husimi distributions was employed to define a distance between two arbitrary density matrices. In the Petz-Sudar work (completing a program of Chentsov), the quantum analogue of the (classically unique) Fisher information (montone) metric of a probability simplex was extended to define an uncountable infinitude of Riemannian (also monotone) metrics on the set of positive definite density matrices. We pose here the questions of what is the specific/unique Fisher information metric for the (classically-defined) Husimi distributions and how does it relate to the infinitude of (quantum) metrics over the density matrices of Petz and Sudar? We find a highly proximate (small relative entropy) relationship between the probability distribution (the quantum Jeffreys' prior) that yields quantum universal data compression, and that which (following Clarke and Barron) gives its classical counterpart. We also investigate the Fisher information metrics corresponding to the escort Husimi, positive-P and certain Gaussian probability distributions, as well as, in some sense, the discrete Wigner pseudoprobability. The comparative noninformativity of prior probability distributions -- recently studied by Srednicki (Phys. Rev. A 71, 052107 [2005]) -- formed by normalizing the volume elements of the various information metrics, is also discussed in our context.Comment: 27 pages, 10 figures, slight revisions, to appear in J. Math. Phy