Related papers: Geometric Phases and Topological Effects

Liquid crystals have proven to provide a versatile experimental and theoretical platform for studying topological objects such as vortices, skyrmions, and hopfions. In parallel, in hard condensed matter physics, the concept of topological…

The search for new topological materials and states of matter is presently at the forefront of quantum materials research. One powerful approach to novel topological phases beyond the thermodynamic space is to combine different…

We stratify families of projective and very affine hypersurfaces according to their topological Euler characteristic. Our new algorithms compute all strata using algebro-geometric techniques. For very affine hypersurfaces, we investigate…

A salient feature of topological phases are surface states and many of the widely studied physical properties are directly tied to their existence. Although less explored, a variety of topological phases can however similarly be…

The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…

This book gives a geometry-first, hardware-aware route through quantum-information workflows, with one goal: connect states, circuits, and measurement to deterministic classical pipelines that make hybrid quantum systems run. Part 1…

Supersymmetry and Supersymmetric models are reviewed. Lecture given at the KOSEF-JSPS Winter School, Recent Developments in Particle and Nuclear Theory February 21- March 2, 1996,

This Resource Letter provides a guide to the literature on the geometric angles and phases in classical and quantum physics. Journal articles and books are cited for the following topics: anticipations of the geometric phase, foundational…

Lecture notes given at the summer school ``Applications of random matrices to physics", Les Houches, June 2004.

Here we present the results of the NSF-funded Workshop on Computational Topology, which met on June 11 and 12 in Miami Beach, Florida. This report identifies important problems involving both computation and topology.

This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from…

These are the substantially expanded notes of the lectures of JK at the summer school "Higher-Dimensional Geometry over Finite Fields" in G\"ottingen, June 2007. The first part gives an overview of the methods. The main new result is the…

A phase-field approach to the dynamics of liquid-solid interfaces that evolve due to precipitation and/or dissolution is presented. For the purpose of illustration and comparison with other methods, phase field simulations were carried out…

Hystory of topology is discussed uncluding the Golden Age Period (1950-1970), the Period of Decay (1970-1980) and the Period of Recovery in 80s and 90s based on the ideas borrowed from physics community. In the second part recent result of…

These are lecture notes from a series of three lectures given at the summer school "Geometric and Computational Spectral Theory" in Montreal in June 2015. The aim of the lecture was to explain the mathematical theory behind computations of…

Topological photonics and acoustics have recently garnered wide research interests for their topological ability to manipulate the light and sound at surfaces. Conventionally, the supercell technique is the standard approach to calculating…

We present a new phase-field model of solidification which allows efficient computations in the regime when interface kinetic effects dominate over capillary effects. The asymptotic analysis required to relate the parameters in the…

Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).

The ideas of mathematical topology play an important role in many aspects of modern physics - from phase transitions to field theory to nonlinear dynamics (Nakahara M (2003) in Geometry, Topology and Physics, ed Brewer DF (IOP Publishing…

Nucleation phenomena commonly observed in our every day life are of fundamental, technological and societal importance in many areas, but some of their most intimate mechanisms remain however to be unravelled. Crystal nucleation, the early…