László Deák

Neutron and X-ray reflectometry are widely used for investigating thin multilayer structures. Numerical modeling of such systems is commonly performed using the Parratt formalism or the method of characteristic (transfer) matrices. The conventional Parratt method was originally formulated for isotropic media, whereas the transfer-matrix approach can treat anisotropic (magnetic) systems but is prone to numerical instabilities, particularly for multilayers with a large number of periods, where the total thickness becomes large under grazing-incidence conditions. In this work, a generalized Parratt formalism applicable to anisotropic layered systems is derived. Explicit expressions are obtained for both reflectivity and transmissivity. A simulation and data-analysis program implementing the new formalism has been developed and used to perform numerical studies of representative multilayer structures. Direct comparisons with transfer-matrix calculations demonstrate the improved numerical stability of the generalized Parratt approach. A mathematical analysis clarifies the origin of the instabilities inherent in the transfer-matrix formulation. The treatment of rough interfaces is also discussed, and several commonly used approximations are compared.

Symmetry transformations are defined by operators in quantum mechanics that preserve the modulus of the scalar product between Hilbert space vectors. According to Wigner’s theorem, any such transformation is represented by either a unitary linear operator or an antiunitary (isometric conjugate-linear) operator. Although antiunitary symmetries—most notably time reversal and charge conjugation—are encountered less frequently than unitary ones, they are fundamental to the description of non-conservative and reversible systems. The most frequently treated antiunitary operators are the involutive ones, called conjugations. Any antiunitary operator can be written as a product of a conjugation and a unitary operator. Considering general scattering problems defined by a scattering potential and separating conjugation from the symmetry operator, one can find the role of complex symmetric (in other words self-transpose) unitary operators in physical problems. This approach provides a robust framework for analyzing the role of non-Hermitian symmetries in wave scattering and dissipative dynamics. To demonstrate the practical applicability of these theoretical concepts, we analyze the case of polarized neutron reflectometry (PNR). We show that the scattering potential in PNR, comprising nuclear and magnetic terms, can satisfy the condition of being unitarily equivalent to its transpose, thereby guaranteeing reciprocity under specific orientations of the magnetic field.

Egy kísérleti kavitációs berendezés tervezésével, létrehozásával és kisüzemi alkalmazásával a szennyezett vizek egyik lehetséges tisztítási módját vizsgáltuk. A kísérleti berendezés mobil kivitelű, és alkalmas különböző szennyezettségű vizek tisztítására. Bemutatjuk a kavitáció hatását különböző mikroszkopikus méretű élőlényekre. Először egy hígított zöldalgatenyészetet vizsgáltunk, megállapítottuk, hogy 16–32 perces kavitáció több mint 10–20%-kalcsökkenti a klorofillkoncentrációt és az ép sejtek arányát. Biológiailag bontható szennyvízzel kevert algás halastóvízben, kavitáció hatására a cianobaktériumok, ostoros algák mennyisége 40–80%-kalcsökkent, a zöldalgáknál minimális volt a csökkenés. Ezeknél a méréseknél síkszelepes, nagynyomású kavitációgenerátort alkalmaztunk. Bizonyítottuk,hogy a hajók ballasztvize és a szennyvizek mikrobiótája mennyiségének csökkentésére a kavitációs vízkezelés ígéretes megoldásnak tekinthető, de figyelemmel kell lenni arra, hogy csak elpusztul a mikrobióta, de nem tűnik el a vízből.

Reciprocity is when wave or quantum scattering satisfies a symmetry property, connecting a scattering process with the reversed one. While reciprocity involves the interchange of source and detector, it is fundamentally different from rotational invariance, and is a generalization of time reversal invariance, occurring in absorptive media as well. Due to its presence at diverse areas of physics, it admits a wide variety of applications. For polarization dependent scatterings, reciprocity is often violated, but violation in the phase of the scattering amplitude is much harder to experimentally observe than violation in magnitude. Enabled by the advantageous properties of nuclear resonance scattering of synchrotron radiation, we have measured maximal, i.e., 180-degree, reciprocity violation in the phase. For accessing phase information, we introduced a new version of stroboscopic detection. The scattering setting was devised based on a generalized reciprocity theorem that opens the way to construct new types of reciprocity related devices.

The reciprocity principle is that, when an emitted wave gets scattered on an object, the scattering transition amplitude does not change if we interchange the source and the detector - in other words, if incoming waves are interchanged with appropriate outgoing ones. Reciprocity is sometimes confused with time reversal invariance, or with invariance under the rotation that interchanges the location of the source and the location of the detector. Actually, reciprocity covers the former as a special case, and is fundamentally different from - but can be usefully combined with - the latter. Reciprocity can be proved as a theorem in many situations and is found violated in other cases. The paper presents a general treatment of reciprocity, discusses important examples, shows applications in the field of photon (M\"ossbauer) scattering, and establishes a fruitful connection with a recently developing area of mathematics.

The theory of heterodyne/stroboscopic detection of nuclear resonance scattering is developed, starting from the total scattering matrix as a product of the matrix of the reference sample and the sample under study. This general approach holds for all dynamical scattering channels. In the forward channel, which has been discussed in detail in the literature, the electronic scattering manifests itself only in an energy-independent diminution of the scattered intensity. In all other channels, complex resonance line shapes of the heterodyne/stroboscopic spectra are encountered, as a result of the interference of electronic and nuclear scattering. The grazing-incidence case will be evaluated and described in detail. Experimental data of classical X-ray reflectivity and their stroboscopically detected resonant counterpart spectra on the [^natFe/⁵⁷Fe]₁₀isotope periodic multilayer and antiferromagnetic [⁵⁷Fe/Cr]₂₀superlattice are fitted simultaneously.