Some exact models for nonspherical collapse.I

Evolution of incoherent matter distributions with cylindrical, pseudoplanar, and toroidal symmetries is considered. The system is described in terms of the scale factora (R, T) and the anisotropy factor (R, T) of the (x², x³ surfaces. A number of exact solutions is obtained under the assumptions=(a), =(R), and=(T) and their physical properties are breifly discussed. In particular, the solution with=(T) is noncollapsing and describes a matter distribution with unchanging density.     

Calculation of the dispersion of the third-order optical nonlinearity in C60 films

Using wave functions determined from ground-state local-density calculations, we have calculated the wave-dispersed free response of the optical nonlinear polarizability ⁽³⁾(–3;,,), for the C₆₀ molecule and ⁽³⁾(–3;,,) i.e. Third-Harmonic Generation (THG) for films using a sum-over-states approach. The influence of screening was determined by applying an external static electric field in separate selfconsistent calculations to evaluate induced dipole moments which was used to determine the static linear and nonlinear polarizabilities. The polarizabilities calculated in the static limit were used to determine an effective screening parameter which was, in turn, used together with an RPA approach to calculate screened wave-dispersed, third-order nonlinear optical properties such as ⁽³⁾(–3;,,) and ⁽³⁾(–3;,,). Comparing evaluated polarizabilities with experimental values we found that the non-resonant free polarizability compares well in absolute magnitude with experimental results. Inclusion of screening results in a polarizability about two orders of magnitude below the experimental values.Paper presented at the 129th WE-Heraeus-Seminar on Surface Studies by Nonlinear Laser Spectroscopies, Kassel, Germany, May 30 to June 1, 1994     

Ultrasound in spin glasses

The change of the sound velocity v(,T) and the damping of sound waves (,T) in spin glasses are calculated in the frame-work of an Ising model with a random distribution of exchange interactions. The calculation is based on linearized equations of motion for the spins and on an improved mean field approximation which includes the Onsager reaction field. Near to the freezing temperatureT _f and at high temperatures v(,T) and (,T) turn out to be approximately proportional to the real and the imaginary parts of the dynamical susceptibility. For the special case of infinite range interactions atT=T _f one has v(, T_f) ( )^1/2 and (, T_f) (/)^1/2 where is the relaxation time of independent spins. However, already slightly aboveT _f the frequency dependence of both quantities becomes rather small for RKKY spin glasses. At high temperatures both, v(,T) and (,T) vary asT ^–1.SFB 125 Aachen-Jülich-Köln     

Periodic Thermodynamics

This paper develops the thermodynamics of quantum Floquet systems, i.e., quantum systems driven by an arbitrarily strong periodic perturbation, which are in weak interaction with a heat bath. The physics differs in an essential way from that of undriven systems, because the usual energy conservation law, for interactions between the system and heat bath, is changed to +E=0, ±, ±2,... where is the driving frequency, is the difference of the so-called quasi-energies of the Floquet states and E the excitation energy of the bath. That is, a transition between two given physical Floquet states will be accompanied by bath transitions with many different energy changes, E=–+m, where m is an arbitrary integer. This results in a breakdown of detailed balance. There is a steady state in which the system has periodic fluctuations of period T=2/. The steady state density matrix is diagonal in the Floquet states, with all Floquet states having finite weights, even at zero temperature. Experimentally favorable conditions for studying periodic thermodynamics are briefly discussed.     

Derivation and solution of a low-friction Fokker-Planck equation for a bound Brownian particle

The low-friction region of an anharmonically bound Brownian particle is examined using systematic elimination procedures. We obtain an asymptotic expression for the spectrum of the Fokker-Planck operator. Asymptotic means both small anharmonicities and small friction constants compared to the oscillatory frequency . We conclude that Kramers' low-friction equation is generally valid only for 0<0.01 and has to be modified for 0.01 by including phase-dependent terms. From these the nonlinear part of the force field in connection with a finite temperature is shown to shorten the correlation time of the equilibrium velocity autocorrelation function and to renormalize the frequency of the corresponding spectral density.     

Spectral superbroadening of self-focused picosecond laser pulses in D2O

Intense picosecond light pulses of a mode-locked Nd: glass laser at _L =1054 nm (fundamental wavelength) and _SH =527 nm (second harmonic wavelength) are passed through a sample of D₂O under self-focusing conditions. Spectrally structured superbroadened, spatially bell-shaped emission in the forward direction is obtained. Primary generation processes are pump-pulse-degenerate stimulated parametric four-photon interaction (₁ + _{1 3} + ₄) and stimulated Raman scattering (_{1 R} + ), which occur concurrently (₁= _L or _SH angular pump frequency, #x03C9; _R first Stokes frequency, #x03C9; signal frequency, #x03C9;₃ signal frequency, #x03C9;₄ idler frequency). The parametric four-photon interaction occurs under collinear non-phase-matched conditions and under longitudinally phase-matched, transversally non-phase-matched (erenkov-like) conditions. Subsequent interaction processes are pump-pulse-nondegenerate four-photon interaction of the type ₁ + _{R 3} + ₄, coherent antiStokes Raman scattering (CARS, ₁ + ₁ – _{4 3}), inverse Raman scattering ( _A + ₁ + ), and cascading light up-conversion of the type ₁ + _(i) – _{R (i+1)}.     

Excited-state absorption and third-order optical nonlinearities in symmetric π-electron organic molecules

Excited-State Absorption (ESA), Two-Photon Absorption (TPA) and the third-order polarizability (;,, – ) have been investigated for a model dichloride derivative of a symmetrically substituted benzylidene analine (SBAC), using a multielectron configuration-interaction procedure. The calculations indicate that SBAC exhibits ESA across the visible region of the spectrum, but that it is not as extensive as for molecules such as the phthalocyanines. The magnitude of the third-order polarizability is dominated by resonance enhancement from a very strongA _g B _u one-photon absorption. The calculated off-resonance value for (;,, – ) suggests that SBAC is a potential candidate for ultrafast switching applications.     

Electromagnetic Modes in Schwarzschild Geometry in an Annular Region

The fundamental electromagnetic modes in a spherical annular cavity with perfectly conducting walls at r = a and r = b are calculated, in the presence of a weak Schwarzschild gravitational field. Explicit expressions are given for the case of a thin shell, (b - a)/a 1. The modified angular frequency for mode ,m can be written as = = ₀ \{ 1 - (GM/a)[2 - ( + 1)/(₀ a)²] where ₀ is the nongravitational frequency. This formula (being independent of m) holds for the magnetic as well as for the electric modes.     

Homogeneous and hypersurface-homogeneous shear-free perfect fluids in general relativity

Shear-free, general-relativistic perfect fluids are investigated in the case where they are either homogeneous or hypersurface-homogeneous (and, in particular, spatially homogeneous). It is assumed that the energy density and the presurep of the fluid are related by a barotropic equation of statep = p(), where +p 0. Under such circumstances, it follows that either the fluid's volume expansion rate or the fluid's vorticity (i.e., rotation) must vanish. In the homogeneous case, this leads to only two possibilities: either = = 0 (the Einstein static solution), or 0, = 0 (the Gödel solution). In the hypersurface-homogeneous case, the situation is more complicated: either = 0, 0 (as exemplified,inter alia, by the Friedmann-Robertson-Walker models), or 0, = 0 (which pertains, for example, in general stationary cylindrically symmetric fluids with rigid rotation, or = = 0 (as occurs for static spherically symmetric solutions). Each possibility is further subdivided in an invariant way, and related to the studies of other authors, thereby unifying and extending these earlier works.     

Experimental survey of the sticking problem in muon catalyzed dt fusion

The sticking process dt + n, which constitutes the most severe limit to the number of fusions which a muon can catalyze, is reviewed. Many attempts were made to determine by calculations and measurements the probability for initial sticking _s ⁰ (immediately after dt fusion) and for final sticking _s (after the came to rest). Previous results based on neutron disappearance rates and on the observation of -X-rays were controversial and also in some disagreement with theory. New data are reported from PSI on direct observation of final sticking, using a setup with the St. Petersburg ionization chamber. These data mark a significant improvement in reliability and may clarify questions concerning previous discrepancies. The new results is _s(0.56±0.04)%, lower than the theory prediction _s=(0.65±0.03)%, at medium density.     

Dynamic structure factor in a random diffusion model

Let {X _t:0} denote random walk in the random waiting time model, i.e., simple random walk with jump ratew ^–1(X _t), where {w(x):x^d} is an i.i.d. random field. We show that (under some mild conditions) theintermediate scattering function F(q,t)=E ₀ (q^d) is completely monotonic int (E ₀ denotes double expectation w.r.t. walk and field). We also show that thedynamic structure factor S(q, w)=2 ₀ cos(t)F(q, t) exists for 0 and is strictly positive. Ind=1, 2 it diverges as 1/||^1/2, resp. –ln(||), in the limit 0; ind3 its limit value is strictly larger than expected from hydrodynamics. This and further results support the conclusion that the hydrodynamic region is limited to smallq and small such that ||D |q|², whereD is the diffusion constant.     

Localization in general one dimensional random systems,I. Jacobi matrices

We consider random discrete Schrödinger operators in a strip with a potentialV (n, ) (n a label in and a finite label across the strip) andV an ergodic process. We prove thatH ₀+V has only point spectrum with probability one under two assumptions: (1) Theconditional distribution of {V (n,)} _n=0,1;all conditioned on {V } _n0,1;all has an absolutely continuous component with positive probability. (2) For a.e.E, no Lyaponov exponent is zero.Research partially supported by USNSF grant MCS-81-20833     

Two-photon resonance degenerate four-wave mixing in a three-level polar molecule (model calculations)

The third-order non-linear susceptibility, ⁽³⁾(; , , –), describing the phase conjugation by degenerate four-wave mixing (DFWM) is calculated for a three-level polar system under a two-photon resonance (TPR) condition. The part of the susceptibility expressed only by the transitional dipole moments and the part resulting from the permanent dipole moments are distinguished. The spectra of ⁽³⁾(; , , –), as well as the DFWM power-reflection and power-transmission spectra near to the TPR, are modelled for polar molecules. The effect of enhanced reflectivity of TPR-DFWM is obtained numerically.     

Final dt stickingω s using the “survived moun method”

A new direct measurement of the final dt sticking probability _s using a special data analysis called the survived muon method is presented. The data were obtained at PSI using a high pressure ionization chamber with H/D/T gas mixtures. The method can provide information on final sticking dt +n independent of theoretical models of stripping and initial sticking. It was found: _s=(0.57±0.07±0.02)%. The experiment and the analysis method are discussed in detail.     

Some exact models for nonspherical collapse. III

The gravitational nonradiative collapse of dust configurations in the presence of electromagnetic field is analyzed in terms of exact dynamical solutions for a wide range of spacetime symmetries: cylindrical, pseudoplanar, toroidal, and also spherical, planar, and pseudospherical [when the anisotropy factor of the (x ²,x ³) surfaces,(R, T), is replaced by a massless scalar field]. The condition that the collapse is nonradiative leaves three possibilities for the coordinate dependence of(R,T) (i)=(a),a (R, T) being the scale factor of the (x ²,x ³) surfaces, (ii)=(T), and (iii)=(R). Almost all (in the meaning indicated in the text) solutions for charged dust with=(a) and for dust in the external electromagnetic field with=(T) and=(R) have been obtained and discussed. A wideranging discussion concerning the topics of papers I–III is given. Special attention is paid to the question of horizon existence and formation and also the perspective of extension of the techniques developed onto the more realistic case of axial symmetry.     

Singular behavior of the density of states and the Lyapunov coefficient in binary random harmonic chains

We study the integrated density of statesH( ²) of a chain of harmonic oscillators with a binary random distribution of the masses. We show in particular that there is a dense set of values of the squared frequency for which the differenceH( ²+)-H( ²) has a singularity of the type ¦¦², multiplied by a periodic function of ln ¦¦, where the exponent and the period depend continuously on ². In the region where < 1/2,H is not differentiate on a dense set of points. The same type of singularities is also present in the Lyapunov coefficient.     

Localization effects and dispersion of the dielectric response function in one-dimensional metals

We report the results of calculations and analysis concerning the dependence of the dielectric response function(, q) on frequency and wave numberq in one-dimensional conductors. The localization of electron states leads to unusually complicated dependences of(, q) on andq in low-frequency and long-wavelength regions, while the spatial and time dispersions become closely interwoven with each other. The effect of geometric resonance is discussed. It appears as quasiharmonical oscillations of complex susceptibility as function of andq, owing to the hopping nature of electron conductivity in a nonuniform electromagnetic field.     

Double phase-matched cascaded fifth harmonic generation in single nonlinear medium by focussed laser beam

Generation of a fifth harmonic by the cascading of two phase-matched third-order processes in a single centrosymmetric nonlinear medium with a focused fundamental beam is investigated theoretically. With the help of analytical and numerical investigations the optimized conditions for maximum conversion into the fifth harmonic are found. In general the optimal position of focusing depends on the values of the mismatches k₁ and k₂ for both steps of the third order cascading (++=3; 3++=5). It is shown that for best efficiency this method of fifth harmonic generation requires specially chosen k_1,opt and k_2,opt and focusing in the center of the nonlinear media. If the phase matching parameters are fixed and they deviate from the optimal values, then the optimal strength of focusing and position of the focus spot should be calculated according to the analysis presented here. PACS 42.65.-k; 42.65.Ky; 42.79.Nv     

Cubic nonlinear tensor of a ferromagnet

The nonlinear properties of a ferromagnet are studied. Many-time retarded Green's functions are used to obtain an expression for the cubic nonlinearity tensor with allowance for spatial dispersion of a uniaxial ferromagnet. The components due to the dipole-dipole interaction of the spins and also due to the anisotropy energy are found. A comparative analysis is made of the different components of the cubic nonlinearity tensor in both the nonresonance case and for various resonances, in particular when ₀, 3 2w₀, 2 ₀, 3 ₀ for the case in tripling of the frequency. Here, is the frequency of the incident wave and ₀ is the frequency of uniform precession. It is shown that in the non-resonance case the largest components are those that are nonvanishing when no allowance is made for spatial dispersion; in the resonance cases the largest components are those due to the dipole-dipole interaction of the ferromagnetism spins.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 53–58, December, 1973.     

A Note on the Time Development of Quantum Lattice Systems

The time development of quantum lattice systems is studied without any restrictions on the growth condition of the potential . A thermodynamic limit of quantum Gibbs state, a *-algebra and an automorphism group _t for which is a KMS state are constructed.