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Certain Feynman integrals are associated to Calabi-Yau geometries. We demonstrate how these integrals can be computed with the method of differential equations. The four-loop equal-mass banana integral is the simplest Feynman integral whose geometry is a nontrivial Calabi-Yau manifold. We show that its differential equation can be cast into an ϵ-factorized form. This allows us to obtain the solution to any desired order in the dimensional regularization parameter ϵ. The method generalizes to other Calabi-Yau Feynman integrals. Our calculation also shows that the four-loop banana integral is only minimally more complicated than the corresponding Feynman integrals at two or three loops.

We consider the one-dimensional (1D) topological superconductor that may form in a planar superconductor-metal-superconductor Josephson junction in which the metal is subjected to spin-orbit coupling and to an in-plane magnetic field. This 1D topological superconductor has been the subject of recent theoretical and experimental attention. We examine the effect of a perpendicular magnetic field and a supercurrent driven across the junction on the position and structure of the Majorana zero modes that are associated with the topological superconductor. In particular, we show that under certain conditions the Josephson vortices fractionalize to half-vortices, each carrying half of the superconducting flux quantum and a single Majorana zero mode. Furthermore, we show that the system allows for a current-controlled braiding of Majorana zero modes.

We show that carbon nanotubes (CNT) can be driven through a topological phase transition using either strain or a magnetic field. This can naturally lead to Jackiw-Rebbi soliton states carrying fractionalized charges, similar to those found in a domain wall in the Su-Schrieffer-Heeger model, in a setup with a spatially inhomogeneous strain and an axial field. Two types of fractionalized states can be formed at the interface between regions with different strain: a spin-charge separated state with integer charge and spin zero (or zero charge and spin ±ℏ/2), and a state with charge ±e/2 and spin ±ℏ/4. The latter state requires spin-orbit coupling in the CNT. We show that in our setup, the precise quantization of the fractionalized interface charges is a consequence of the symmetry of the CNT under a combination of a spatial rotation by π and time reversal.

We present thermodynamic studies of a new spin-1/2 antiferromagnet containing undistorted kagome lattices-barlowite Cu&#95;{4}(OH)&#95;{6}FBr. Magnetic susceptibility gives θ&#95;{CW}=-136  K, while long-range order does not happen until T&#95;{N}=15  K with a weak ferromagnetic moment μ<0.1μ&#95;{B}/Cu. A 60 T magnetic field induces a moment less than 0.5μ&#95;{B}/Cu at T=0.6  K. Specific-heat measurements have observed multiple phase transitions at T≪∣θ&#95;{CW}∣. The magnetic entropy of these transitions is merely 18% of k&#95;{B}ln2 per Cu spin. These observations suggest that nontrivial spin textures are realized in barlowite with magnetic frustration. Comparing with the leading spin-liquid candidate herbertsmithite, the superior interkagome environment of barlowite sheds light on new spin-liquid compounds with minimum disorder. The robust perfect geometry of the kagome lattice makes charge doping promising.

Using the Calogero model as an example, we show that the transport in interacting nondissipative electronic systems is essentially nonlinear and unstable. Nonlinear effects are due to the curvature of the electronic spectrum near the Fermi energy. As is typical for nonlinear systems, a propagating semiclassical wave packet develops a shock wave at a finite time. A wave packet collapses into oscillatory features which further evolve into regularly structured localized pulses carrying a fractionally quantized charge. The Calogero model can be used to describe fractional quantum Hall edge states. We discuss perspectives of observation of quantum shock waves and a direct measurement of the fractional charge in fractional quantum Hall edge states.

A semiclassical wave packet propagating in a dissipationless Fermi gas inevitably enters a "gradient catastrophe" regime, where an initially smooth front develops large gradients and undergoes a dramatic shock-wave phenomenon. The nonlinear effects in electronic transport are due to the curvature of the electronic spectrum at the Fermi surface. They can be probed by a sudden switching of a local potential. In equilibrium, this process produces a large number of particle-hole pairs, a phenomenon closely related to the orthogonality catastrophe. We study a generalization of this phenomenon to the nonequilibrium regime and show how the orthogonality catastrophe cures the gradient catastrophe, by providing a dispersive regularization mechanism.

The stochastic Loewner evolution is a recent tool in the study of two-dimensional critical systems. We extend this approach to the case of critical systems with continuous symmetries, such as SU(2) Wess-Zumino-Witten models, where domain walls carry an additional spin-1/2 degree of freedom.

We show that singularities developed in the Hele-Shaw problem have a structure identical to shock waves in dissipativeless dispersive media. We propose an experimental setup where the cell is permeable to a nonviscous fluid and study continuation of the flow through singularities. We show that a singular flow in this nontraditional cell is described by the Whitham equations identical to Gurevich-Pitaevski solution for a regularization of shock waves in Korteveg-de Vriez equation. This solution describes regularization of singularities through creation of disconnected bubbles.

Fractal geometry of critical curves appearing in 2D critical systems is characterized by their harmonic measure. For systems described by conformal field theories with central charge c < or = 1, scaling exponents of the harmonic measure have been computed by Duplantier [Phys. Rev. Lett. 84, 1363 (2000)10.1103/PhysRevLett.84.1363] by relating the problem to boundary two-dimensional gravity. We present a simple argument connecting the harmonic measure of critical curves to operators obtained by fusion of primary fields and compute characteristics of the fractal geometry by means of regular methods of conformal field theory. The method is not limited to theories with c < or = 1.

We point out that inflaton decays can be a copious source of stable or long-lived particles chi with mass exceeding the reheat temperature T(R) but less than half the inflaton mass. Once higher order processes are included, this statement is true for any chi particle with renormalizable (gauge or Yukawa) interactions. This contribution to the chi density often exceeds the contribution from thermal chi production, leading to significantly stronger constraints on model parameters than those resulting from thermal chi production alone, particularly in models containing stable charged particles.