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Demo at the End of the World: Apocalypse Media and the Limits of Techno-futurist Performance
Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
The celebrated tenfold-way of Altland-Zirnbauer symmetry classes discern any
quantum system by its pattern of non-spatial symmetries. It lays at the core of
the periodic table of topological insulators and superconductors which provided
a complete classification of weakly-interacting electrons' non-crystalline
topological phases for all symmetry classes. Over recent years, a plethora of
topological phenomena with diverse surface states has been discovered in
crystalline materials. In this paper, we obtain an exhaustive classification of
topologically distinct groundstates as well as topological phases with
anomalous surface states of crystalline topological insulators and
superconductors for key space-groups, layer-groups, and rod-groups. This is
done in a unified manner for the full tenfold-way of Altland-Zirnbauer
non-spatial symmetry classes. We establish a comprehensive paradigm that
harnesses the modern mathematical framework of equivariant spectra; it allows
us to obtain results applicable to generic topological classification problems.
In particular, this paradigm provides efficient computational tools that enable
an inherently unified treatment of the full tenfold-way.Comment: 22+26 pages, 6 figures, 16 table
Quantum chaos and the double-slit experiment
We report on the numerical simulation of the double-slit experiment, where
the initial wave-packet is bounded inside a billiard domain with perfectly
reflecting walls. If the shape of the billiard is such that the classical ray
dynamics is regular, we obtain interference fringes whose visibility can be
controlled by changing the parameters of the initial state. However, if we
modify the shape of the billiard thus rendering classical (ray) dynamics fully
chaotic, the interference fringes disappear and the intensity on the screen
becomes the (classical) sum of intensities for the two corresponding one-slit
experiments. Thus we show a clear and fundamental example in which transition
to chaotic motion in a deterministic classical system, in absence of any
external noise, leads to a profound modification in the quantum behaviour.Comment: 5 pages, 4 figure
Spin-polarized superconductivity: order parameter topology, current dissipation, and multiple-period Josephson effect
We discuss transport properties of fully spin-polarized triplet
superconductors, where only electrons of one spin component (along a certain
axis) are paired. Due to the structure of the order parameter space, wherein
phase and spin rotations are intertwined, a configuration where the
superconducting phase winds by in space is topologically equivalent to a
configuration with no phase winding. This opens the possibility of supercurrent
relaxation by a smooth deformation of the order parameter, where the order
parameter remains non-zero at any point in space throughout the entire process.
During the process, a spin texture is formed. We discuss the conditions for
such processes to occur and their physical consequences. In particular, we show
that when a voltage is applied, they lead to an unusual alternating-current
Josephson effect whose period is an integer multiple of the usual Josephson
period. These conclusions are substantiated in a simple time-dependent
Ginzburg-Landau model for the dynamics of the order parameter. One of the
potential applications of our analysis is for moir\'e systems, such as twisted
bilayer and double bilayer graphene, where superconductivity is found in the
vicinity of ferromagnetism.Comment: 12+7 pages, 6 figure
A comment on the relation between diffraction and entropy
Diffraction methods are used to detect atomic order in solids. While uniquely
ergodic systems with pure point diffraction have zero entropy, the relation
between diffraction and entropy is not as straightforward in general. In
particular, there exist families of homometric systems, which are systems
sharing the same diffraction, with varying entropy. We summarise the present
state of understanding by several characteristic examples.Comment: 7 page
Maximum entropy estimation of transition probabilities of reversible Markov chains
In this paper, we develop a general theory for the estimation of the
transition probabilities of reversible Markov chains using the maximum entropy
principle. A broad range of physical models can be studied within this
approach. We use one-dimensional classical spin systems to illustrate the
theoretical ideas. The examples studied in this paper are: the Ising model, the
Potts model and the Blume-Emery-Griffiths model
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