Related papers: One-Dimensional String Theory with Vortices as Ups…
Quasi-one-dimensional (Q1D) systems, i.e., three- and two-dimensional (3D/2D) arrays composed of weakly coupled one-dimensional lattices of interacting quantum particles, exhibit rich and fascinating physics. They are studied across various…
Partitions of unity in ${\mathbf R}^d$ formed by (matrix) scales of a fixed function appear in many parts of harmonic analysis, e.g., wavelet analysis and the analysis of Triebel-Lizorkin spaces. We give a simple characterization of the…
We show, by using a correlated Jastrow wave function and a mapping onto a classical model, that the two-dimensional Mott transition in a simple half-filled one-band model can be unconventional and very similar to the binding-unbinding…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
We investigate half-vortex sheets and domain-wall trains of rotating two-component Bose-Einstein condensates in spin-dependent optical lattices. The two-component condensates undergo phase separation in the form of stripes arranged…
This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…
We investigate theoretically globally nonuniform configurations of quantized-flux vortices in clean superconductors trapped by an external force field that induces a nonuniform vortex density profile. Using an extensive series of numerical…
The formalism of matrix product states is used to perform a numerical study of 1+1 dimensional QED -- also known as the (massive) Schwinger model -- in the presence of an external static `quark' and `antiquark'. We obtain a detailed picture…
In two-dimensional (2D) inviscid incompressible flow, low background vorticity distribution accelerates intense vortices (clumps) to merge each other and to array in the symmetric pattern which is called ``vortex crystals''; they are…
This paper fires the opening salvo in the systematic construction of the lattice-continuum correspondence, a precise dictionary that describes the emergence of continuum quantum theories from finite, nonperturbatively defined models…
We investigate the properties of the QCD string in the Euclidean SU(N) pure gauge theory when the space-time dimensions transverse to it are periodic. From the point of view of an effective string theory, the string tension $\sigma$ and the…
A mathematical lattice, called the von Neumann lattice, is a subset of coherent states and exists periodically in the phase space. It is unlike solids or Abrikosov lattices that are observable in physical systems. Abrikosov lattices are…
We investigate unoriented strings and superstrings in two dimensions and their dual matrix quantum mechanics. Most of the models we study have a tachyon tadpole coming from the RP^2 worldsheet which needs to be cancelled by a…
We review the topic of quantized vortices in multicomponent Bose-Einstein condensates of dilute atomic gases, with an emphasis on that in two-component condensates. First, we review the fundamental structure, stability and dynamics of a…
Applying the machinery of random matrix theory and Toeplitz determinants we study the level $k$, $U(N)$ Chern-Simons theory coupled with fundamental matter on $S^2\times S^1$ at finite temperature $T$. This theory admits a discrete matrix…
We study the vortex lines that are a feature of many random or disordered three-dimensional systems. These show universal statistical properties on long length scales, and geometrical phase transitions analogous to percolation transitions…
The mean field like gauge invariant variational method formulated recently, is applied to a topologically massive QED in 3 dimensions. We find that the theory has a phase transition in the Chern Simons coefficient $n$. The phase transition…
All the models of elementary particles and their interactions derived from String Theory involve a compact six-dimensional internal space. Its volume and shape should be fixed or stabilized, since otherwise massless scalar fields (moduli)…
We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the…
We study an effective field theory of a vortex lattice in a two-dimensional neutral rotating superfluid. Utilizing particle-vortex dualities, we explore its formulation in terms of a $U(1)$ gauge theory coupled to elasticity, that at low…