Manley-Rowe relations for an arbitrary discrete system

Manley-Rowe relations are formulated for a discrete Hamiltonian system with an arbitrary number of resonances. Assuming that the resonances are defined as , where is an n×n integer matrix of rank r<n, and |ω〉≡T(ω₁,…,ωn) is the frequency vector, the projection of the action vector |J〉 on is an adiabatic invariant. Hence n−r independent integrals, from where the conventional Manley-Rowe relations for a single resonance follow as a particular case.     

Local effects in wind and wave fields in the Tyrrhenian sea

Summary A very sophisticated wave model has been applied to the western Mediterranean Sea. The results show the importance of local effects that had not been taken into account by the input atmospheric model. The need is stressed for the use of local models nested in the large-scale ones. Paper presented at the IV Congresso del Gruppo Nazionale per la Fisica dell'Atmosfera e dell'Oceano, June 22–24, 1987, Rome.     

Local commutativity for nonlocalisable fields

A definition of local commutativity for nonlocalisable field theory is given by means of a limiting procedure for the Wightman functions of the theory; it includes, as a special case, rational functions of the free field. Fields for which this limiting procedure is defined are shown to satisfy many of the desirable features of localisable fields, including the existence of a TCP operator,the clustet property, the existence of asymptotic limits, and the LSZ reduction formulas. A strengthening of the procedure allows forward scattering dispersion relations to be obtained; the effects of nonlocalisibility on rigorous high energy bounds is also considered.     

Quantum interference and Manley-Rowe relations in resonant four-wave frequency mixing in an optically thick Doppler-broadened medium

It is shown that under resonant interaction conditions certain notions in nonlinear optics which are based on the Manley-Rowe relations no longer hold because of the interference of elementary quantum-mechanical processes. This conclusion is illustrated by numerical examples corresponding to the experiments performed. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 12, 862–866 (25 June 1999)     

Local products for relativistic quantum fields

A definition of local functions of generalized free fields is suggested. Their concrete form is determined in a fairly general setting by analysing realizations of locality. A huge class of new models of relativistic quantum fields results in this way.Presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

Raster method for recording optical wave fields

We propose a new method for recording the wave field. The method is based on that the angular spectrum of the field is modulated using an amplitude mask. It is shown that the new method ensures high spatial and angular resolutions. An optical scheme for implementing the method and an algorithm for reconstructing the wave-field phase from the measurement data are developed. Computer simulation of the experiment for recording the wave field on the basis of the proposed method is performed.     

Uncertainty relations for information entropy in wave mechanics

New uncertainty relations in quantum mechanics are derived. They express restrictions imposed by quantum theory on probability distributions of canonically conjugate variables in terms of corresponding information entropies. The Heisenberg uncertainty relation follows from those inequalities and so does the Gross-Nelson inequality.     

Diffraction method for recording optical wave fields

We propose a method for recording an optical wave field that is based on diffraction of the optical wave field by two screens that are complementary to each other. We show that the new method ensures the measurement of the phase of the wave field with a high accuracy and spatial resolution. An optical scheme for implementing the diffraction method and an algorithm for reconstructing the phase of the wave field from the measurement data are developed. We perform a computer simulation of the experiment on recording the optical wave field based on the method proposed.     

Local relativistic invariant flows for quantum fields

For quantum fields with trigonometric interaction in arbitrary space dimension we construct a representation of the Lorentz group by automorphisms on a Banach space generated by the Weyl algebra.     

Partial wave relations from fixed-u dispersion relations

Partial wave relations are derived form fixed-u disperation relations for meson-baryon and meson-meson scattering. General expressions for the integral kernels are given and some problems pertaining to the application of the relations are discussed.     

Wigner function for highly convergent three-dimensional wave fields

The angle-impact Wigner function for highly convergent three-dimensional scalar wave fields is derived directly by use of the three-dimensional generalized optical transfer function rather than from a six-dimensional Wigner function. The angle-impact Wigner function is a real four-dimensional function from which the intensity at any point in space is readily determined.     

Intertwining relations and Darboux transformations for the wave equations

Using the intertwining operator technique we construct Darboux transformations for the wave equation with position-dependent effective mass and with linearly energy-dependent potentials. The formally adjoint generators of supersymmetry and two formally self-adjoint superpartner Hamiltonians are constructed and they close a quadratic pseudo-superalgebra. The Darboux transformations are constructed in differential and integral forms and an interrelation is established between them. The approach is applied to generation of isospectral potentials with additional or removal bound states or construction of new partner potentials without changing the spectrum, i.e. fully isospectral potentials. The method is illustrated by some concrete examples. The influence of distance between levels on the form of potentials is investigated. In particular, asymmetric double well potentials are generated.     

Filter performance parameters for vectorial high-aperture wave fields

Performance parameters have been presented that can be used to compare the focusing performance of different optical systems, including the effect of pupil filters. These were originally given for the paraxial case and recently extended to the high-aperture scalar regime. We generalize these parameters to the full vectorial case for an aplanatic optical system illuminated by a plane-polarized wave. The behavior of different optical systems is compared.     

Friedmann universes containing wave fields

In this paper the Friedmann universes containing(i) a massless real scalar field,(ii) a massive real scalar field,(iii) electromagnetic fields,(iv) the combined massive complex scalar and electromagnetic fields are investigated. In(i) the field has to be either purely spatial or else purely temporal and the latter case is completely solved. Similarly in(ii) the purely time-dependent case has been reduced to a single fourth order ordinary differential equation. In this case graphs of the numerical solutions have been exhibited. In(iii) as expected, no non-trivial solution exists. In(iv) all possible cases are studied. In case the complex wave function is a product of two non-constant functions, i.e. ψ=ξ(r)τ(t), there exists no solution. In the subcase gx(r)=ξ^*(r)=constant, ¦τ(t)¦=constant the problem is completely solved. In the subcase ξ(r)=ξ^*(r)=constant and ¦τ(t)¦ is non-constant, the system of equations boil down to the same fourth order ordinary differential equation as mentioned before. In the last two sub-cases, the time-dependent wave field carries electric charge density which, strangely enough, is decoupled from the electromagnetic fields.     

Parabolic nondiffracting optical wave fields

We demonstrate the existence of parabolic beams that constitute the last member of the family of fundamental nondiffracting wave fields and determine their associated angular spectrum. Their transverse structure is described by parabolic cylinder functions, and contrary to Bessel or Mathieu beams their eigenvalue spectrum is continuous. Any nondiffracting beam can be constructed as a superposition of parabolic beams, since they form a complete orthogonal set of solutions of the Helmholtz equation. A novel class of traveling parabolic waves is also introduced for the first time.     

Phase-modulus relations in cyclic wave functions

We derive reciprocal integral relations between phases and amplitude moduli for a class of wave functions that are cyclically varying in time. The relations imply that changes of a certain kind (e.g. not arising from the dynamic phase) obligate changes in the other. Numerical results indicate the approximate validity of the relationships for arbitrarily (non-cyclically) varying states in the adiabatic (slowly changing) limit.     

Local and global Markoff fields

We discuss the relation between local and global Markoff property for processes and (generalized) random fields, both in the case of discrete and continuous ”time parameters“. In particular, we give a short account of our proof of the global Markoff property for the Euclidean Sine-Gordon fields in two dimensions. We also give an account of our proof of the uniqueness of the solutions of the DLR equations in this case (extremality of the Gibbs state, implying in particular uniqueness of the phase). We also discuss more generally the relation between the uniqueness and global Markoff properties, and discuss some consequences of the global Markoff property. Finally, we indicate shortly how the global Markoff property is proven (by ourselves together with G. Olsen) in the case of lattice systems.     

Scanning Michelson interferometer for imaging surface acoustic wave fields

A scanning homodyne Michelson interferometer is constructed for two-dimensional imaging of high-frequency surface acoustic wave (SAW) fields in SAW devices. The interferometer possesses a sensitivity of ~10(-5)nm/ radicalHz , and it is capable of directly measuring SAW's with frequencies ranging from 0.5 MHz up to 1 GHz. The fast scheme used for locating the optimum operation point of the interferometer facilitates high measuring speeds, up to 50,000 points/h. The measured field image has a lateral resolution of better than 1 mu;m . The fully optical noninvasive scanning system can be applied to SAW device development and research, providing information on acoustic wave distribution that cannot be obtained by merely electrical measurements.