What makes a crystal supersolid?

For nearly half a century the supersolid phase of matter has remained mysterious, not only eluding experimental observation, but also generating a great deal of controversy among theorists. The recent discovery of what is interpreted as a non-classical moment of inertia at low temperature in solid ⁴He [E. Kim and M.H.W. Chan, Nature 427 225 (2004a); E. Kim and M.H.W. Chan, Science 305 1941 (2004b); E. Kim and M.H.W. Chan, Phys. Rev. Lett. 97 115302 (2006); A.C. Clark and M.H.W. Chan, J. Low Temp. Phys. 138 853 (2005)] has elicited much excitement as a possible first observation of a supersolid phase. In the two years following the discovery, however, more puzzles than answers have been provided to the fundamental issue of whether the supersolid phase exists, in helium or any other naturally occurring condensed matter system. Presently, there is no established theoretical framework to understand the body of experimental data on ⁴He. Different microscopic mechanisms that have been suggested to underlie superfluidity in a perfect quantum crystal do not seem viable for ⁴He, for which a wealth of experimental and theoretical evidence points to an insulating crystalline ground state. This perspective addresses some of the outstanding problems with the interpretation of recent experimental observations of the apparent superfluid response in ⁴He (seen now by several groups, e.g. A.S. Rittner and J.D. Reppy 2006; M. Kondo, S. Takada, Y. Shibayama and K. Shirahama, Proceedings of QFS2006, Kyoto, Submitted to J. Low Temp. Phys.; A. Penzyev, Y. Yasuta and M. Kubota, Proceedings of QFS2006, Kyoto, Submitted to J. Low Temp. Phys., cond-mat/0702632.) and discusses various scenarios alternative to the homogeneous supersolid phase, such as superfluidity induced by extended defects of the crystalline structure, including grain boundaries, dislocations and anisotropic stresses. Can a metastable superfluid ‘glassy’ phase exist, and can it be relevant to some of the experimental observations? One of the most interesting and unsolved fundamental questions is what interatomic potentials, given the freedom to design one, can support an ideal supersolid phase in continuous space, and can they be found in Nature.     

What makes a theory physically “complete”?

Three claims about what makes a theory physically complete are (1) Shimony's assertion that a complete theory says all there is to say about nature; (2) EPR's requirement that a complete theory describe all elements of reality; and (3) Ballentine and Jarrett's claim that a predictively complete theory must obey a condition used in Bell deviations. After introducing statistical completeness as a partial formalization of (1), we explore the logical and motivational relationships connecting these completeness conditions. We find that statistical completeness motivates but does not imply Jarrett's completeness condition, because Jarrett's condition encodes further intuitions about locality and causality. We also dispute Ballentine and Jarrett's claim that EPR-completeness implies Jarrett's completeness condition.     

What makes a phase transition? Analysis of the random satisfiability problem

In the last 30 years it was found that many combinatorial systems undergo phase transitions. One of the most important examples of these can be found among the random k-satisfiability problems (often referred to as k-SAT), asking whether there exists an assignment of Boolean values satisfying a Boolean formula composed of clauses with k random variables each. The random 3-SAT problem is reported to show various phase transitions at different critical values of the ratio of the number of clauses to the number of variables. The most famous of these occurs when the probability of finding a satisfiable instance suddenly drops from 1 to 0. This transition is associated with a rise in the hardness of the problem, but until now the correlation between any of the proposed phase transitions and the hardness is not totally clear. In this paper we will first show numerically that the number of solutions universally follows a lognormal distribution, thereby explaining the puzzling question of why the number of solutions is still exponential at the critical point. Moreover we provide evidence that the hardness of the closely related problem of counting the total number of solutions does not show any phase transition-like behavior. This raises the question of whether the probability of finding a satisfiable instance is really an order parameter of a phase transition or whether it is more likely to just show a simple sharp threshold phenomenon. More generally, this paper aims at starting a discussion where a simple sharp threshold phenomenon turns into a genuine phase transition.     

What is a photon?

Certain properties of photons viewed as quanta (particles of an electromagnetic field) are discussed. Specifically, the nature of localization (size) of photons along and across the direction of wave propagation is examined.     

Can elemental bismuth be a liquid crystal?

A number of anomalies have been reported in molten Bi, including a first-order liquid-liquid transition at 1010 K and ambient pressure, which is irreversible at cooling rates of several degrees per minute. An interpretation of these effects as due to long-range bond-orientational order is suggested. Significant evidence for directionality in liquid Bi, albeit only at temperatures close to melting, is available in experiments made circa 1930. Further experimentation is called for.     

What makes the T_c of FeSe/SrTiO_3 so high?

This paper reviews some of the recent progresses in the study of high temperature superconductivity in the interface between a single unit cell Fe Se and SrTiO3. It offers the author's personal view of why Tc is high and how to further increase it.     

What is a complex graph?

Many papers published in recent years show that real-world graphs G(n,m) (n nodes, m edges) are more or less “complex” in the sense that different topological features deviate from random graphs. Here we narrow the definition of graph complexity and argue that a complex graph contains many different subgraphs. We present different measures that quantify this complexity, for instance C_1e, the relative number of non-isomorphic one-edge-deleted subgraphs (i.e. DECK size). However, because these different subgraph measures are computationally demanding, we also study simpler complexity measures focussing on slightly different aspects of graph complexity. We consider heuristically defined “product measures”, the products of two quantities which are zero in the extreme cases of a path and clique, and “entropy measures” quantifying the diversity of different topological features. The previously defined network/graph complexity measures Medium Articulation and Offdiagonal complexity (OdC) belong to these two classes. We study OdC measures in some detail and compare it with our new measures. For all measures, the most complex graph has a medium number of edges, between the edge numbers of the minimum and the maximum connected graph . Interestingly, for some measures this number scales exactly with the geometric mean of the extremes: . All graph complexity measures are characterized with the help of different example graphs. For all measures the corresponding time complexity is given.Finally, we discuss the complexity of 33 real-world graphs of different biological, social and economic systems with the six computationally most simple measures (including OdC). The complexities of the real graphs are compared with average complexities of two different random graph versions: complete random graphs (just fixed n,m) and rewired graphs with fixed node degrees.     

What is in a pebble shape?

We propose to characterize the shapes of flat pebbles in terms of the statistical distribution of curvatures measured along the pebble contour. This is demonstrated for the erosion of clay pebbles in a controlled laboratory apparatus. Photographs at various stages of erosion are analyzed, and compared with two models. We find that the curvature distribution complements the usual measurement of aspect ratio, and connects naturally to erosion processes that are typically faster at protruding regions of high curvature.     

What is a mean gravitational field?

The equations of General Relativity are non-linear. This makes their averaging non-trivial. The notion of mean gravitational field is defined and it is proven that this field obeys the equations of General Relativity if the unaveraged field does. The workings of the averaging procedure on Maxwells field and on perfect fluids in curved space-times are also discussed. It is found that Maxwells equations are still verified by the averaged quantities but that the equation of state for other kinds of matter generally changes upon average. In particular, it is proven that the separation between matter and gravitational field is not scale-independent. The same result can be interpreted by introducing a stress-energy tensor for a mean-vacuum. Possible applications to cosmology are discussed. Finally, the work presented in this article also suggests that the signature of the metric might be scale-dependent too.Received: 16 October 2003, Published online: 15 March 2004PACS: 04.20.Cv Fundamental problems and general formalism 04.40.Nr Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields - 95.35. + d Dark matter (stellar, interstellar, galactic, and cosmological)     

How reproducible are dynamic heterogeneities in a supercooled liquid?

The particle dynamics in a liquid exhibits a transient spatial distribution of dynamic heterogeneities. The relationship between this kinetic structure and the underlying particle configuration remains an outstanding problem. In this Letter, we present a general simulation technique for identifying the features of the dynamic heterogeneity which arise due to a specific configuration, as distinct from the random spatial variation due to the intermittent particle dynamics.     

Electro- and photo-controllable spatial filter based on?a?liquid crystal film with a photoconductive layer

This work presents an electro- and photo-controllable spatial filter that is based on a liquid crystal (LC) film with a photoconductive layer. The controllable spatial filter can be formed because of the controllability of the photoelectro-induced screen effect of the space charge in the LC cell. An applied dc voltage or incident pumped intensity can be controlled to enable different spatial distributions of the diffraction pattern of the target object to be selected for filtering by the LC cell, such that various reconstructed images can be obtained. A simulation using Fourier analysis is developed, and its results agree closely with experimental results. Additionally, the LC spatial filter has the extra advantage of controllable low or high filtering functions: they are controlled by switching the configuration between normally black and normally white modes.     

Can surfactant be present at pinch-off of a liquid filament?

Surfactants lower surface tension and are used to facilitate breakup and spreading. How much surfactant remains where a filament of initial radius R breaks is set by the ratio of convection, which sweeps surfactant away, to diffusion, which replenishes it, or Peclet number Pe proportional, variantR. Thus, as is well known, surfactant concentration Gamma-->0 when a macroscale filament breaks. Here theory and simulation are used to investigate pinch-off of microscopic filaments. At breakup, Gamma is shown to be nonzero but uniform on a filament of negligible Pe. Since R must be finite, the zero-Pe limit is transitory and yields to a final regime. Two such regimes with distinct dynamics characterized by different scaling exponents are reported.     

Thermal modes of a plug flow reactor with a liquid–liquid heterogeneous system

The thermal modes of a flow plug reactor with an exothermic chemical reaction are numerically simulated. A heterogeneous reaction system consisting of two immiscible liquids is studied: one of the liquids (dispersed phase) in the form of droplets is distributed in the other (dispersion phase). The characteristics of the thermal modes of the reactor at various values of two governing parameters, the Damköhler number and the rate of extraction of the dissolved substance from the dispersed phase into the dispersion phase is examined. Two modes of chemical reaction in the reactor are demonstrated to be possible: low-temperature and high-temperature. Critical criteria of thermal ignition are formulated. The dependence of the structure of the thermal wave on the governing parameters is investigated.     

Quantum mechanics in a two-dimensional spacetime: What is a wavefunction?

Conventional quantum mechanics specifies the mathematical properties of wavefunctions and relates them to physical experiments by invoking the Born postulate. There is no known direct connection between wavefunctions and any external physical object. However, in the case of a two-dimensional spacetime there is a completely classical context for wavefunctions where the connection with an external reality is transparent and unambiguous. By examining this case, we show how a classical stochastic process assembles a Dirac wavefunction based solely on the detailed counting of reversible paths. A direct comparison of how a related process assembles a Probability Density Function reveals both how and why PDFs and wavefunctions differ, including the ubiquitous implication of complex numbers for the latter. The appearance of wavefunctions in a context that is free of the complexities of quantum mechanics suggests the study of such models may shed some light on interpretive issues.     

What Would Be Outcome of a Big Crunch?

I suggest the existence of a still undiscovered interaction: repulsion between matter and antimatter. The simplest and the most elegant candidate for such a force is gravitational repulsion between matter and antimatter. I argue that such a force may give birth to a new Universe; by transforming an eventual Big Crunch of our Universe, to an event similar to Big Bang. In fact, when a collapsing Universe is reduced to a supermassive black hole of a small size, a very strong field of the conjectured force may create particle-antiparticle pairs from the surrounding quantum vacuum. The amount of antimatter created from the physical vacuum is equal to the decrease of mass of “black hole Universe” and violently repelled from it. When the size of the black hole is sufficiently small, the creation of antimatter may become so huge and fast, that matter of our Universe may disappear in a fraction of the Planck time. So fast transformation of matter to antimatter may look like a Big Bang with initial size about 30 orders of magnitude greater than the Planck length, questioning the need for inflation. In addition, a Big Crunch, of a Universe dominated by matter, leads to a new Universe dominated by antimatter, and vice versa; without need to invoke CP violation as explanation of matter-antimatter asymmetry. Simply, our present day Universe is dominated by matter, because the previous Universe was dominated by antimatter.     

What aligns liquid crystals on solid substrates? The role of surface roughness anisotropy

The mechanism responsible for liquid crystal (LC) alignment on mechanically buffed or UV exposed polymer films is poorly understood. A comprehensive study of LC alignment on variously prepared substrates unequivocally shows that the anisotropy in the surface roughness of the substrate completely determines the direction of LC alignment. In all the cases studied, including those where an anchoring transition occurs with temperature, the LC director (re)aligns in the directions of low roughness.