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This is the problem of the 8th International Experimental Physics Olympiad (EPO8). The task of the EPO8 is to determine Planck constant ħh/2 using the given set-up with LED. If you have an idea how to do it, do it and send us the result; skip the reading of the detailed step by step instructions with increasing difficulties. We expect the participants to follow the suggested items – they are instructive for physics education in general. Only the reading of historical remarks given in the first section can be omitted during the Olympiad without loss of generality. Participants should try solving as much tasks as they can without paying attention to the age categories: give your best.

The polytropic (adiabatic) index for pure hydrogen plasma is analytically calculated as function of reciprocal temperature and degree of ionization. Additionally, the polytropic index is graphically represented as a function of temperature and density. It is concluded that the partially ionized hydrogen plasma cannot be exactly polytropic. The calculated deviations from the mono-atomic value 5/3 are measurable. The analytical result for pure hydrogen plasma is a test example how this approach can be extended for arbitrary gas cocktail., 5 pages, 4 figures, 32 refs

We describe a set-up for measurement of the absolute zero by Johnson-Nyquist thermal noise which can be performed within a week in every high-school or university. Necessary electronic components and technical guidelines for the construction of this noise thermometer are given. The operating temperature used is in the tea cup range from ice to boiling water and in this sense the set-up can be given in the hands of every high school and university physics student. The measurement requires a standard multi-meter with thermocouple and voltage probe and gives excellent for education purposes percent accuracy. The explanation is oriented to university level but due to the simplicity of the explanation motivated high-school students can follow the explanation derivation of the used formulas for determination of the absolute zero and the Boltzmann constant. As a by-product our set-up gives a new method for the determination of the spectral density of the voltage $e_\mathrm{N}$ and current noise $i_\mathrm{N}$ of operational amplifiers., 39 pages, 9 figs, 8 tables, 60 refs, 5 appendices. 2 new appendices contain: the EPO9 (9 Experimental-Physics Olympiad) problem with co-authors Aleksander P. Petkov, Leonora Velkoska and Riste Popeski-Dimovski; its solution by the EPO9 absolute champion Kristijan Shishkoski. EPO9.7z archive contains source and pdf files of the original problem given to the participants in English and Macedonian

The effective mass of a magnon in a neodymium magnet is evaluated using Bloch temperature dependence of spontaneous magnetization. We used the Hall effect magnetometer and thermo-couple thermometer for measuring of the temperature of the water in which the encapsulated commercial magnet is immersed. The experiment can be repeated in every school and methodological remarks for experimental data processing are given with great detail and attention. The purpose of the paper is to illustrate the simple relation between the quantum spectrum of magnons and the easily measured magnetic field of a permanent magnet., Second version manuscript - comparison with previous papers, 7 pages, 4 figures, 21 Refs

We describe electronic instruments for creation of effective Cooper pair spectroscopy. The suggested spectroscopy requires study of electric field effects on the surface of cleaved superconductors. The electronic instrument reacquires low noise amplifier with 10$^6$ amplitude amplification which we have formerly used for study of Johnson-Nyquist and Schottky noises. The nonspecific amplifier is followed by high-Q tunable resonance filter based on schematics of general impedance converter topology which is also and innovative device. The work of the device is based on the Manhattan equation of operational amplifier. After a final nonspecific amplification the total amplification can exceed 10$^9$ and in such a way sub-nano-volt signals can be reliably detected. In short the observation of new effects in condensed matter physics leads to creation of new generation of electronic equipment., 8 pages, 8 figures, 34 refs; manuscript for 21-st ISCMP in Varna 2020 conference proceedings

International audience; We present computer simulations of the work of an electronic device for generation of electric oscillation by negative differential conductivity of a superconductor supercooled below the critical temperature. The superconductor is cooled below its critical temperature in the normal state at a small constant electric voltage. To simulate the device, we use formerly derived explicit analytical expressions for the conductivity of nanostructured superconductors supercooled below the critical temperature in an electric field. Computer simulations reveal that the negative differential conductivity region of the current–voltage characteristic leads to excitation of electric oscillations. We simulate a circuit with distributed elements as a first step to obtain gigahertz frequency. This gives a hint that a hybrid device of nanostructured superconductors will work in terahertz frequencies. If the projected setup is successful, we consider the possibility for it to be put in a nanosatellite (such as a CubeSat). The study of layered high-T c superconductors and EM waves emitted from them in space vacuum would be an important task for future space technology.

Explicit analytical expressions for conductivity of a superconducting film above and below critical temperature in an arbitrary electric field are derived in the frameworks of the time dependent Ginzburg-Landau theory. It is confirmed that slightly below critical temperature the differential conductivity of superconducting film can become negative for small enough values of electric field. This fact may cause generation of electromagnetic oscillations if the superconducting film is appropriately coupled of with a resonator. Their maximal frequency is proportional to the value of critical temperature of superconducting transition. The obtained results can stimulate the development of Terahertz generators on the basis of high temperature superconducting films., Comment: 5 pages, 3 figures

We predict a new effect in condensed matter surface magnetization of the vortex phase of a superconductor induced by electric field. The magnetized superconductor should be one of the plates of a plane capacitor on which a voltage has to be applied. Applying alternating voltage to the capacitor, electrostatic induction leads to oscillations of the magnetic moment which has to be measured by electromotive force inducted in a detector coil. The derived explicit formula for the magnetization contains the effective mass of Cooper pairs and a systematic investigation of the predicted magnetization will lead to a creation of an effective Cooper pair mass spectroscopy. For cleaved superconductors this effective mass is a property of the bulk material., 4 pages, 1 enhanced figure, changes in abstract, final journal version, to see discussions with referees delete %-sign before first \end{document}

A simple experiment for the electron charge qe measurement is described. The experimental set-up contains standard electronic equipment only and with 137$ budget can be built in every high-school lab all around the world. It is concluded that it is time such a practicum to be included in the regular high-school education. The achieved 13% accuracy is comparable to the best student university labs. The measurement is based on Schottky noise generated by a photodiode. Using the criterion dollar per accuracy for the electron charge qe measurement, this definitely is the world’s best educational experiment. An industrial replica can be easily sold across the globe.

We present a short review of the history and contemporary computer simulations of the work of a electronic device for generation of electric oscillation by negative differential conductivity of a supercooled below the critical temperature superconductor. The superconductor is cooled below its critical temperature at a small constant electric field and this applied external voltage keeps the superconductor in normal state. In order to simulate the device, we use the formerly derived explicit analytical expressions for the conductivity of nanostructured superconductors supercooled below the critical temperature in electric field. Numerical analysis intended to alleviate the development of a device reveal that the negative differential conductivity region of the current-voltage characteristic leads to excitation of electric oscillations. This gives a hint that a hybrid device of nanostructured superconductors will work in terahertz frequencies. The study of layered high-Tc superconductors and electromagnetic waves emitted from them in space vacuum would be an important task for the future space technology.

The time dependent master equation from the seminal article by Ragazzini, Randall and Russell [J. R. Ragazzini, R. H. Randall and F. A. Russell, "Analysis of Problems in Dynamics by Electronic Circuits", Proc. of the I.R.E., Vol. 35, pp. 444--452, (1947)] is recovered as necessary tool for the analysis of contemporary circuits with operational amplifiers. This equation gives the relation between time dependent the output voltage $U_0(t)$ and the difference between the input voltages ($U_{+}(t)$ and $U_{-}(t)$). The crossover frequency $f_0$ is represented the time constant $\tau_{_0}$ of this equation. The work of the master equation is illustrated by two typical examples: a) the stability criterion of the devices with negative impedance converters, which we consider as a new result b) the frequency dependence of the amplifiers with operational amplifiers given in the technical specifications without citations of time dependent equation. A simple circuit for determination of $f_0$ is suggested and the method is illustrated by determination of crossover frequency for the low-noise and high speed ADA4898 operational amplifier. It is concluded that for an exact calculation of the pass bandwidth of amplifiers with active filters the 70 years old master equation is a useful technique implicitly included in the contemporary software. The frequency dependent formulae for the amplification coefficient of inverting and non-inverting amplifiers are given for the case of non-zero conductivity between the inputs of the operational amplifiers., Comment: 14 pages, 9 figures, 3 appendices. arXiv admin note: text overlap with arXiv:1703.05224

We re-derive the Nyquist theorem and Callen-Welton fluctuation-dissipation theorem (FDT) as a consequence of detailed balance principle applied to a harmonic oscillator. The usage of electrical notions in the beginning makes the consideration understandable for every physicists. Perhaps it is the simplest derivation of these well-known theorems in statistical physics. The classical limit is understandable as a consequence of Waterston-Herapath equipartition theorem., 6 pages, 1 figure

For the need of measurements focused in condensed matter physics and especially Bernoulli effect in superconductors we have developed an active resonator with dual operational amplifiers. A tunable high-Q resonator is performed in the schematics of the the General Impedance Converter (GIC). In the framework of frequency dependent open-loop gain of operational amplifiers, a general formula of the frequency dependence of the impedance of GIC is derived. The explicit formulas for the resonance frequency and Q-factor include as immanent parameter the crossover frequency of the operational amplifier. Voltage measurements of GIC with a lock-in amplifier perfectly agree with the derived formulas. A table reveals that electrometer operational amplifiers are the best choice to build the described resonator., a new formulae for the Q-factor expressed by resonance frequency, dominant frequency and cross-over frequency, a general guide with a table for selection of appropriate operational amplifiers, 9 new (30 total) references, Fig. 6 in appendix B corrected

The temperature dependence of rates of electron impact ionization and two electrons recombination are calculated using Wannier cross section of electron impact ionization of neutral hydrogen atom. Entropy production and power dissipation are derived for the case when the ionization degree deviates from its equilibrium value. This is the special case of the obtained general formula for entropy production accompanying chemical reactions. Damping rate of the sound waves is calculated and the conditions when ionization processes dominate are considered. A quasi-classical approximation for the heating mechanism of solar chromosphere is proposed. Several analogous phenomena for damping rates in liquids and crystals are shortly discussed, for example, deaf sound of a glass of beer or English salt solution. An explicit expression for the second or bulk (or volume) viscosity of hydrogen plasma is calculated from firsts principles. For the first time some second viscosity is calculated from first principles., Mandelstam-Leontovich theory applied to hydrogen plasma, 13 pages, 5 figs, 32 references

A new mechanisms for damping of slow magnetosonic waves (SMW) by pressure induced oscillations of the ionization degree is proposed. An explicit formula for the damping rate is quantitatively derived. Physical conditions where the new mechanism will dominate are briefly discussed. The ionization-recombination damping is frequency independent and has no hydrodynamic interpretation. Roughly speaking large area of partially ionized plasma are damper for basses of SMW while usual MHD mechanisms operate as a low pass filter. The derived damping rate is proportional to the square of the sine between the constant magnetic field and the wave-vector. Angular distribution of the spectral density of SMW and Alfv\'en waves (AW) created by turbulent regions and passing through large regions of partially ionized plasma is qualitatively considered. The calculated damping rate is expressed by the electron impact cross section of the hydrogen atom and in short all details of the proposed damping mechanisms are well studied., Comment: 6 pages, 1 figure

The sharp almost step like increase the temperature in the transition region (TR) between chromosphere and solar corona is well-known from decades; for first time we are giving a detailed magnetohydrodynamic (MHD) calculation of the height dependence of the temperature. The width of the transition region is evaluated by maximal value of the logarithmic derivative of the temperature. At fixed heating, only MHD can give such a narrow width and in such sense, even the qualitative agreement with the observational data, gives the final verdict what the heating mechanism of the solar corona is. Static profiles of the temperature and wind velocity are calculated for static frequency dependent spectral density of the incoming MHD waves; no time dependent computer simulations. At fixed spectral density of MHD waves, the MHD calculation predicts height dependence of the non-thermal broadening of spectral lines and its angular dependence. For illustration is used one dimensional approximation of completely ionized hydrogen plasma in weak magnetic field, but it is considered that the width of the TR is weakly dependent with respect of further elaboration. The analyzed MHD calculation is a numerical confirmation of the qualitative concept of self-induced opacity of the plasma with respect to MHD waves. The plasma viscosity strongly increases with the temperature. Heated by MHD waves, plasma increases the wave absorption and this positive feedback leads to further heating. The static temperature profile is a result of a self-consistent calculation of propagation of MHD wave through the static background of wind and temperature profile. The numerical method allows consideration of incoming MHD waves with an arbitrary spectral density. Further elaboration of the method are briefly discussed: influence of second viscosity in the chromospheric part of the TR, influence of the magnetic field on the coronal side of the TR and investigation of such type effects on the width of the TR.

A simple experiment for the electron charge $q_e$ measurement is described. The experimental set-up contains standard electronic equipment only and can be built in every high-school lab all around the world with pocket money budget for several days. It is concluded that it is time such a practice to be included in the regular high-school education. The achieved 13\% accuracy is comparable to the best student university labs. The measurement is based on Schottky noise generated by a photodiode. Using the criterion dollar per accuracy for the electron charge $q_e$ measurement, this definitely is the world's best educational experiment. An industrial replica can be easily sold across the globe., Comment: 10 pages, 9 figures, 3 tables, last version corresponds to the published version in Eur. J. Phys, Eq. (15-17) have been corrected and minor typographical improvements have been made

A simple experimental setup for measuring the Planck’s constant which is using Landauer quantization of the conductance of touching golden wires is described. It is consisted of two golden wires with thickness of 500 µm and 1.5 cm length, and a fast operational amplifier. The setup costs less than $30 and it can be realized in every teaching laboratory in 10 days. The usage of oscilloscope is required.

A simple analytical formula for three-dimensional Fermi surface (3D FS) of \({\rm Tl}_2{\rm Ba}_2{\rm CuO}_{6+\delta}\) is derived in the framework of LCAO approximation spanned over Cu 4s, Cu 3d\(3d_{x^2 - y^2 }\), O 2px and O 2py states. This analytical result can be used for fitting of experimental data for 3D FS such as polar angle magnetoresistance oscillation. The model takes into account effective copper-copper hopping amplitude tss between Cu 4s orbitals from neighbouring \({\textrm{CuO}_2}\) layers. The acceptable correspondence with the experimental data gives a hint that the tss amplitude dominates in formation of coherent 3D FS, and other oxygen-oxygen and copper-oxygen amplitudes are rather negligible. For absolute determination of the hopping parameters a simple electronic experiment with a field effect transistor type microstructure is suggested. The thin superconductor layer is the source-drain channel of the layered structure where an AC current is applied.

Absorbtion of Alfven waves is considered to be the main mechanism of heating in the solar corona. It is concluded that the sharp increase of the plasma temperature by two orders of magnitude is related to a self-induced opacity with respect to Alfven waves. The maximal frequency for propagation of Alfven waves is determined by the strongly temperature dependent kinematic viscosity. In such a way the temperature jump is due to absorption of high frequency Alfven waves in a narrow layer above the solar surface. It is calculated that the power per unit area dissipated in this layer due to damping of Alfven waves blows up the plasma and gives birth to the solar wind. A model short wave-length (WKB) evaluation takes into account the 1/f^2 frequency dependance of the transversal magnetic field and velocity spectral densities. Such spectral densities agree with old magnetometric data taken by Voyager 1 and recent theoretical calculations in the framework of Langevin-Burgers MHD. The present theory predicts existence of intensive high frequency MHD Alfven waves in the cold layer beneath the corona. It is briefly discussed how this statement can be checked experimentally. It is demonstrated that the magnitude of the Alfven waves generating random noise and the solar wind velocity can be expressed only in terms of satellite experimental data. It is advocated that investigation of properties of the solar surface as a random driver by optical methods is an important task for future solar physics. Jets of accretion disks are speculated as a special case of the wind from magnetized turbulent plasma., Comment: 4 pages, no figures, minor corrections, final version for EPJD

A simple experimental setup for measuring the Planck's constant, using Landauer quantization of the conductance between touching gold wires, is described. It consists of two gold wires with thickness of 0.5 mm and 1.5 cm length, and an operational amplifier. The setup costs less than $30 and can be realized in every teaching laboratory in two weeks. The usage of oscilloscope is required., Comment: English text: 10 pages, 7 figures, Experimental setup description for teaching laboratory; Bulgarian translation: 10 pages, same 7 figures

In this paper, we report on the sharp peak observed in the third harmonic voltage response generated by a bias sinusoidal current applied to several strips patterned in a YBa2Cu3O 7 - δ thin film and in two La2-xSrxCuO4 thin films, when the temperature is close to the normal-superconductor transition. The lambda-shaped temperature dependence of the third harmonic signal on the current characteristics is studied. Several physical mechanisms of third harmonic generation are examined.

High-temperature superconductors are nowadays found in great variety and hold technological promise. It is still an unsolved mystery that the critical temperature T_c of the basic cuprates is so high. The answer might well be hidden in a conventional corner of theoretical physics, overlooked in the recent hunt for exotic explanations of new effects in these materials. A forgotten intra-atomic s-d two-electron exchange in the Cu atom is found to provide a strong (~eV) electron pairing interaction. A Bardeen-Cooper-Schrieffer approach can explain the main experimental observations and predict the correct d_{x^2-y^2} symmetry of the gap., 4 pages, 3 figures, LaTeX2e

An experimental set-up for electrostatic measurement of , separate magnetostatic measurement of and determination of the speed of light according to Maxwell's theory with percent accuracy is described. No forces are measured with the experimental set-up, therefore there is no need for a scale, and the experiment cost of less than £20 is mainly due to the batteries used. Multiplied 137 times, this experimental set-up was given at the Fourth Open International Experimental Physics Olympiad (EPO4) and a dozen high school students performed successful experiments. The experimental set-up actually contains two different pendula for electric and magnetic measurements. In the magnetic experiment the pendulum is constituted by a magnetic coil attracted to a fixed one. In the electrostatic pendulum when the distance between the plates becomes shorter than a critical value the suspended plate catastrophically sticks to the fixed one, while in the magnetic pendulum the same occurs when the current in the coils becomes greater than a certain critical value. The basic idea of the methodology is to use the loss of stability as a tool for the determination of fundamental constants.

Four atom states Cu3 d x 2 − y 2 , Cu4 s , O a 2 p x are involved in a tight-binding model for the superconducting CuO 2 plane. The orthorhombic distortion is taken into account by the differences of Cu–O hopping amplitudes and single-site oxygen energies e a and e b of two oxygen positions in the elementary cell as well. An effective ‘oxygen’ Hamiltonian including only the electron amplitudes at the oxygen ions is derived. Simple expressions for the constant energy contours and the Fermi surface are obtained and they qualitatively describe the photoemission spectra. Extended saddle points near p = (π,0) and p = (0,π) are observed in qualitative agreement with the ARPES data. The van Hove singularities of the density of states (DOS) related to the extended saddle points are calculated by a Monte Carlo method. It is found that the splitting of the singularity of the DOS at the bottom of the conduction band is created by the energy difference e a − e b = 2δ.

A simple electronic experiment using a field-effect-transistor–type microstructure is suggested. The thin superconductor layer forms the source-drain channel of a layered structure across which an AC current is applied. It is found necessary to measure the second harmonic of the source-gate voltage, and the third harmonic of the source-drain voltage; these electronic measurements then give the logarithmic derivative of the density of states, which is an important consideration when fitting parameters of the band structure.

Double electron exchange between Cu4s and O2pσ orbitals is analyzed as mechanism which creates traditional cooper pairing in layered cuprates. The conductivity band is obtained in the oversimplified model which considers only hopping between O2pσ orbitals, and the amplitude of the Cu4s-O2pσ hybridization is accounted as perturbation. The proposed toy model possesses most of the distinguishable features of the experimental data: angle dependence of the superconducting gap, the shape of the Fermi surface, dispersion law for conductivity band and the electron spectrum of the superconducting phase. The influence of the Cu3dx2−y2 orbital, electron doping and disorder for transition to s-type superconducting gap is briefly discussed.

The superconductivity of the conducting CuO2plane of the layered cuprates is considered in the framework of a two-dimensional (2D) tight-binding model which contains O2pσand Cu3dx2 − y2states. Besides the standard LCAO amplitudes the correlated hopping between O2pσand Cu3dx2 − y2orbitals is also considered. The fact that the conduction band is mainly oxygen like and that the one electron hopping between next nearest neighbours (NNN) oxygen ions is relatively smaller then the nearest neighbours (NN) hopping between NN Cu and O ions is taken into account. The equations for the superconducting gap are derived. It is shown that such a choice of the orbitals leads to as-type superconducting gap, which is in qualitative agreement with data for strongly irradiated samples. It is briefly discussed that the addition to the Emery model of the Cu4sorbital could lead to ad-type gap in agreement with the π-shift of the Josephson effect and location of Δ(p) zeroes by recent ARPES data.

Above the critical temperature T c the fluctuations of the superconducting order parameter Ψ are described within the framework of time-dependent Ginzburt–Landua theory using Langevin's approach of stochastic differential equations. The excess Aslamazov–Larkin conductivity is derived as an improtant test example for the case of non interacting fluctuations. It is shown at what conditions the kinetic arguments can be successively derived. A fluctuation Hall conductivity σ xy (fl) and Nernst coefficient ν xy (fl) are calculated for the case of weak magnetic field. The comparison with the BCS will result by Varlamov and Livanov [A. A. Varlamov and D. V. Livanov, Phys. Lett. A 157, 519 (1991)] gives the final determination of all the coefficients of the phenomenological TDGL theory.

Simple analytical expressions for the electron band dispersion ϵpare obtained within the framework of a tight-binding model. Formulae for the Fermi surfacepz = pz(px,py;EF) are derived as well. Opσstates of the perovskite anion andsstate of small cation Bi6sare taken into account. The hopping amplitude between next-nearest neighbours is considered as a small parameter of the theory and an effective oxygen Hamiltonian is derived. Band dispersions and density of states are graphically presented. Isoenergy surfaces of cubic bismuthates for the particular caseEF/wcd = 0.38 (wcdis the band width) are shown and discussed as well. The adopted model can be used as a realistic one-electron part of the tight-binding models of superconducting perovskites.

A simple tight-binding model for the conduction band of Sr2Ru04 is presented. The Ru4de and 02pπ orbitals of RuU2 conduction plane are taken into account. In momentum representation the LCAO Hamiltonian has a block structure, containing hopping amplitudes between the in-plane orbitals Oa2py, Ob2px, Ru4dxy, and those vertical to RuO2 plane — Ru4dyz, Ru4dzx, Oa2pz and Ob2pz. This simple structure allows an analytical derivation of electron band dispersions e(px,Py) and constant energy contours e(px,py) = const. The energy surfaces e(px,Py) (numerically calculated) are also related to angle-resolved photoemission spectra. Based on the analytical results a fitting philosophy for both the available experimental data and ab initio calculations is discussed. The tight-binding parameters calculated within the adopted model are found to be in acceptable agreement with the first principles calculations.

The creation of contactless Cooper-pair mass spectroscopy based on the Bernoulli-Venturi effect in thin superconducting films is suggested. The preparation of layered metal-insulator-superconductor-type heterostructures and standard electronics are necessary for the realization of the method. Two electrodes are patterned from the metallic layer: a circle and concentric-ring electrode. The currents in the superconducting film are induced by a drive coil concentric to the electrodes. The Bernoulli potential of the charged Cooper-pair superfluid creates a measurable electric polarization of gate electrodes of this plane-capacitor device. The current-induced contact-potential difference is limited by the Ginzburg-Landau potential [minus][ital a][sub GL]([ital T])= 1/2[h bar][ital e][sup *][ital H][sub [ital c]2]([ital T])/[ital m][sup *][ital c]=[h bar][sup 2]/2[ital m][sup *][xi][sup 2]([ital T]). The additional charge of the polarized circular electrode has the same sign as the free charge carriers of the superconductor.

Polarized neutron reflectometry (PNR) provides evidence that nonlocal electrodynamics governs the magnetic field penetration in an extreme low-k superconductor. The sample is an indium film with a large elastic mean free path (11 mkm) deposited on a silicon oxide wafer. It is shown that PNR can resolve the difference between the reflected neutron spin asymmetries predicted by the local and nonlocal theories of superconductivity. The experimental data support the nonlocal theory, which predicts a nonmonotonic decay of the magnetic field., 5 pages, 4 figures, LaTex, corrected typos and figures

On the basis of a simple tight-binding model for the band structure of superconducting perovskites we address some open questions related to the Fermi level location in Ba 1 − x K x BiO 3 invoked by the ACAR study of this material. The latter reports a roughly cubic Fermi surface centered around the Γ point of the Brillouin zone. Two basically different alternatives explaining the observed shape and location are discussed. They reflect, respectively, the two possible effects of potassium doping of BaBiO 3 : the smaller positive valency of K 1+ (compared to Ba 2+ ) creates (1) a hole in the upper metallic Bi6 s band, or (2) a hole in the narrow O2 p σ bands, as in the case of hole doping of layered cuprates. The corresponding ACAR spectra are calculated and compared to the experiment. The importance of ACAR spectra of halogen-containing layered cuprates is analyzed as well. A comparison of such spectra with those related to cubic materials should help elucidate the nature, in general, of conductivity in perovskites.

We predict that below T_c a regime of negative differential conductivity (NDC) can be reached. The superconductor should be supercooled to T, Comment: 7 pages