Holography: an interpretation from the phase-space point of view

The formation of holograms is interpreted as the consequence of the bilinearity of the ambiguity function. Reconstruction can then be regarded as the manipulation of the ambiguity function. Specifically, we show that in the case of in-line holography, the reconstruction can be regarded as phase tomography. In this way we provide a unified picture for the formulation of both noninterferometric and interferometric phase-retrieval techniques.     

Nonrelativistic phase-space and octonions

The octonion algebra seems to constitute the natural underlying algebra of nonrelativistic phase-space. A correspondence between the imaginary unit of quantum mechanics and the seventh imaginary unit of octonion algebra is proposed. Conjectures as to the possible physical meaning of some particular transformations from the automorphism group of octonions are presented.     

Thermal heat reservoirs via Gauss' principle of least constraint; Dissipation,chaos, and phase-space dimensionality loss in one-dimensional chains

We use Gauss' principle of least constraint to impose different kinetic temperatures on the two halves of a periodic one-dimensional chain. The thermodynamic result is heat flow, as predicted by the Second Law of Thermodynamics. The statistical-mechanical result can be either a phase-space limit cycle or a strange attractor, depending on the chain length and the size of the temperature difference. We document the sensitivity of the Lyapunov spectrum and the underlying phase-space topology by varying the chain length and the size of the kinetic-temperature difference.     

Impenetrable barriers in phase-space.

Dynamical systems theory is used to construct a general phase-space version of transition state theory. Special multidimensional separatrices are found which act as impenetrable barriers in phase-space between reacting and nonreacting trajectories. The elusive momentum-dependent transition state between reactants and products is thereby characterized. A practical algorithm is presented and applied to a strongly coupled Hamiltonian.     

Diagrammatic methods in phase-space regularization

Using the scalar prototype and gauge theory as the simplest possible examples, diagrammatic methods are developed for the recently proposed phasespace form of continuum regularization. A number of one-loop and all-order applications are given, including general diagrammatic discussions of the no-growth theorem and the uniqueness of the phase-space stochastic calculus. The approach also generates an alternate derivation of the equivalence of the large-β phase-space regularization to the more conventional coordinate-space regularization.     

Universal pion freeze-out phase-space density

Results on the pion phase-space density at freeze-out in sulphur-nucleus, Pb–Pb and π–p collisions at the CERN SPS are presented. All heavy-ion reactions are consistent with the thermal Bose–Einstein distribution f=[exp(E/T)−1]⁻¹ at T∼ 120 MeV, modified for radial expansion. π–p data are also consistent with f, but at T∼ 180 MeV and without radial flow.     

Quantum-mechanical operators and phase-space operators

By means of the Weyl transform we propose to associate phase-spaceoperators, and not functions with the dynamical operators of quantum-mechanics. This way one achieves a consistent and one-to-one mapping of the quantum-mechanical operator calculus unto a phase-space operator calculus in which only variables associated with the canonical variables of position and momenta appear. Contrary to the usual Weyl transform technique, here no composition law is needed for the Weyl transforms. As a consequence the calculus involving Weyl transforms is greatly simplified, which we demonstrate at two examples.     

Foundations of phase-space quantum mechanics

In the present paper a general concept of a phase-space representation of the ordinary Hilbert-space quantum theory is formulated, and then, by using some elementary facts of functional analysis, several equivalent forms of that concept are analyzed. Several important physical examples are presented in Section 3 of the paper.Supported by the NSERC research grant No. A5206.On leave of absence from the Theoretical Physics Institute, University of Gdansk, Gdansk, Poland.     

Autoresonant phase-space holes in plasmas

Electron phase-space holes are formed and controlled in a plasma by adiabatic nonlinear phase locking (autoresonance) with a chirped frequency driving wave. The process has a threshold on the driving amplitude and involves dragging a void region in phase space into the bulk of the distribution via persistent Cherenkov-type resonance.     

Microlocal analysis and phase-space decompositions

A general class of phase-space decompositions f(x)=a(x,p) dp of functions f defined in ⁿ is presented. In the latter, a(x,p) depends on values of the Fourier transform F of f in a region around p whose width tends to zero as |x| increases and it decays exponentially, for each p, in all directions in x-space outside the microsupport at p of F, with a rate of exponential fall-off linked to analyticity properties of F in local tubes (in complex space) around p. A possible application in quantum-field theory is mentioned.     

Optimal observables and phase-space ambiguities

Optimal observables are known to lead to minimal statistical errors on parameters for a given normalised event distribution of a physics reaction. Thereby all statistical correlations are taken into account. Therefore, on the one hand they are a useful tool to extract values on a set of parameters from measured data. On the other hand one can calculate the minimal constraints on these parameters achievable by any data-analysis method for the specific reaction. In case the final states can be reconstructed without ambiguities optimal observables have a particularly simple form. We give explicit formulae for the optimal observables for generic reactions in case of ambiguities in the reconstruction of the final state and for general parameterisation of the final-state phase space.Received: 12 January 2005, Published online: 7 March 2005     

On marginalization of phase-space distribution functions

We discuss marginalization procedures based on integration of quantum phase-space distribution functions over a family of phase-space manifolds. We show that under some conditions the resulting marginals are always nonnegative.     

Revealing nonclassicality via s-ordered phase-space distribution

Nonclassical states play a crucial role in both theoretical and experimental investigations of quantum optics, and there is a wide interest in characterization and quantification of nonclassicality. By exploiting the freedom of the parameter s in the s-ordered phase-space distribution introduced by Cahill and Glauber [Phys. Rev. 177, 1882(1969)], we develop a method to reveal and quantify optical nonclassicality via the divided difference of the s-ordered phase-space distribution. Our approach y...     

Amplitude phase-space model for quantum mechanics

We show that there is a close relationship between quantum mechanics and ordinary probability theory. The main difference is that in quantum mechanics the probability is computed in terms of an amplitude function, while in probability theory a probability distribution is used. Applying this idea, we then construct an amplitude model for quantum mechanics on phase space. In this model, states are represented by amplitude functions and observables are represented by functions on phase space. If we now postulate a conjugation condition, the model provides the same predictions as conventional quantum mechanics. In particular, we obtain the usual quantum marginal probabilities, conditional probabilities and expectations. The commutation relations and uncertainty principle also follow. Moreover Schrödinger's equation is shown to be an averaged version of Hamilton's equation in classical mechanics.     

The Wigner phase-space description of collision processes

This year marks the 50th anniversary of the birth of the celebrated Wigner distribution function. Many advances made in various areas of science during the 50 year period can be attributed to the physical insights that the Wigner distribution function provides when applied to specific problems. In this paper the usefulness of the Wigner distribution function in collision theory is described.     

Dynamics and instability of electron phase-space tubes

Two-dimensional simulations of beam-driven turbulence in the auroral ionosphere have shown the formation and instability of phase-space tubes. These tubes are a generalization of electron phase-space holes in a one-dimensional plasma. In a strongly magnetized plasma, such tubes vibrate at frequencies below the bounce frequency of the trapping potential. A theory for these vibrations yields quantitative agreement with kinetic simulations. Furthermore, the theory predicts that the vibrations can become unstable when resonantly coupled to electrostatic whistlers-also in agreement with simulations.