Dendrites and measures with discrete spectrum

We are interested in dendrites for which all invariant measures of zero-entropy mappings have discrete spectrum, and we prove that this holds when the closure of the endpoint set of the dendrites is countable. This solves an open question which has been around for awhile, and almost completes the characterization of dendrites with this property.

Loosely Bernoulli odometer-based systems whose corresponding circular systems are not loosely Bernoulli

Foreman and Weiss [Measure preserving diffeomorphisms of the torus are unclassifiable. Preprint, 2020, arXiv:1705.04414] obtained an anti-classification result for smooth ergodic diffeomorphisms, up to measure isomorphism, by using a functor $\mathcal {F}$ (see [Foreman and Weiss, From odometers to circular systems: a global structure theorem. J. Mod. Dyn.15 (2019), 345–423]) mapping odometer-based systems, $\mathcal {OB}$ , to circular systems, $\mathcal {CB}$ . This functor transfers the classification problem from $\mathcal {OB}$ to $\mathcal {CB}$ , and it preserves weakly mixing extensions, compact extensions, factor maps, the rank-one property, and certain types of isomorphisms. Thus it is natural to ask whether $\mathcal {F}$ preserves other dynamical properties. We show that $\mathcal {F}$ does not preserve the loosely Bernoulli property by providing positive and zero-entropy examples of loosely Bernoulli odometer-based systems whose corresponding circular systems are not loosely Bernoulli. We also construct a loosely Bernoulli circular system whose corresponding odometer-based system has zero entropy and is not loosely Bernoulli.

Discovery and characterization of five new eclipsing AM CVn systems

AM CVn systems are ultra-compact, hydrogen-depleted and helium-rich, accreting binaries with degenerate or semi-degenerate donors. We report the discovery of five new eclipsing AM CVn systems with orbital periods of 61.5, 55.5, 53.3, 37.4, and 35.4 minutes. These systems were discovered by searching for deep eclipses in the Zwicky Transient Facility (ZTF) lightcurves of white dwarfs selected using Gaia parallaxes. We obtained phase-resolved spectroscopy to confirm that all systems are AM CVn binaries, and we obtained high-speed photometry to confirm the eclipse and characterize the systems. The spectra show double-peaked He-lines but also show metals, including K and Zn, elements that have never been detected in AM CVn systems before. By modelling the high-speed photometry, we measured the mass and radius of the donor star, potentially constraining the evolutionary channel that formed these AM CVn systems. We determined that the average mass of the accreting white dwarf is ≈0.8 M⊙, and that the white dwarfs in long-period systems are hotter than predicted by recently updated theoretical models. The donors have a high entropy and are a factor of ≈ 2 more massive compared to zero-entropy donors at the same orbital period. The large donor radius is most consistent with He-star progenitors, although the observed spectral features seem to contradict this. The discovery of 5 new eclipsing AM CVn systems is consistent with the known observed AM CVn space density and estimated ZTF recovery efficiency.

Smooth, mixing transformations with loosely Bernoulli Cartesian square

A zero-entropy system is said to be loosely Bernoulli if it can be induced from an irrational rotation of the circle. We provide a criterion for zero-entropy systems to be loosely Bernoulli that is compatible with mixing. Using this criterion, we show the existence of smooth mixing zero-entropy loosely Bernoulli transformations whose Cartesian square is loosely Bernoulli.

From black hole to white hole via the intermediate static state

We discuss the macroscopic quantum tunneling from the black hole to the white hole of the same mass. Previous calculations in [G. E. Volovik, Universe 6, 133 (2020)] demonstrated that the probability of the tunneling is [Formula: see text], where [Formula: see text] is the entropy of the Schwarzschild black hole. This in particular suggests that the entropy of the white hole is with minus sign the entropy of the black hole, [Formula: see text]. Here, we use a different way of calculations. We consider three different types of the hole objects: black hole, white hole and the fully static intermediate state. The probability of tunneling transitions between these three states is found using singularities in the coordinate transformations between these objects. The black and white holes are described by the Painleve–Gullstrand coordinates with opposite shift vectors, while the intermediate state is described by the static Schwarzschild coordinates. The singularities in the coordinate transformations lead to the imaginary part in the action, which determines the tunneling exponent. For the white hole the same negative entropy is obtained, while the intermediate state — the fully static hole — has zero entropy. This procedure is extended to the Reissner–Nordström black hole and to its white and static partners, and also to the entropy and temperature of the de Sitter Universe.

Meissner Effect: History of Development and Novel Aspects

The discovery of the Meissner (Meissner–Ochsenfeld) effect in 1933 was an incontestable turning point in the history of superconductivity. First, it demonstrated that superconductivity is an unknown before equilibrium state of matter, thus allowing to use the power of thermodynamics for its study. This provided a justification for the two-fluid model of Gorter and Casimir, a seminal thermodynamic theory founded on a postulate of zero entropy of the superconducting (S) component of conduction electrons. Second, the Meissner effect demonstrated that, apart from zero electric resistivity, the S phase is also characterized by zero magnetic induction. The latter property is used as a basic postulate in the theory of F. and H. London, which underlies the understanding of electromagnetic properties of superconductors. Here the experimental and theoretical aspects of the Meissner effect are reviewed. The reader will see that, in spite of almost nine decades age, the London theory still contains questions, the answers to which can lead to a revision of the standard picture of the Meissner state (MS) and, if so, of other equilibrium superconducting states. An attempt is made to take a fresh look at electrodynamics of the MS and try to work out with the issues associated with this the most important state of all superconductors. It is shown that the concept of Cooper's pairing along with the Bohr–Sommerfeld quantization condition allows one to construct a semi-classical theoretical model consistently addressing properties of the MS and beyond, including non-equilibrium properties of superconductors caused by the total current. As follows from the model, the three “big zeros” of superconductivity (zero resistance, zero induction and zero entropy) have equal weight and grow from a single root: quantization of the angular momentum of paired electrons. The model predicts some yet unknown effects. If confirmed, they can help in studies of microscopic properties of all superconductors. Preliminary experimental results suggesting the need to revise the standard picture of the MS are presented.

Analytic critical points of charged Rényi entropies from hyperbolic black holes

We analytically study phase transitions of holographic charged Rényi entropies in two gravitational systems dual to the $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory at finite density and zero temperature. The first system is the Reissner-Nordström-AdS5 black hole, which has finite entropy at zero temperature. The second system is a charged dilatonic black hole in AdS5, which has zero entropy at zero temperature. Hyperbolic black holes are employed to calculate the Rényi entropies with the entangling surface being a sphere. We perturb each system by a charged scalar field, and look for a zero mode signaling the instability of the extremal hyperbolic black hole. Zero modes as well as the leading order of the full retarded Green’s function are analytically solved for both systems, in contrast to previous studies in which only the IR (near horizon) instability was analytically treated.