Related papers: Gauged linear sigma model in geometric phase. II. …
We examine various properties of double field theory and the doubled string sigma model in the context of geometric quantisation. In particular we look at T-duality as the symplectic transformation related to an alternative choice of…
We construct Gromov-Witten invariants of general symplectic manifolds.
The ordering dynamics of the Higgs field is studied, using techniques inspired by the study of phase ordering in condensed matter physics, as a first step to understanding the evolution of cosmic structure through the formation of…
We present a brief introduction to quantum sheaf cohomology, a generalization of quantum cohomology based on the physics of the (0,2) nonlinear sigma model.
We calculate the geometric phase for an open system (spin-boson model) which interacts with an environment (ohmic or nonohmic) at arbitrary temperature. However there have been many assumptions about the time scale at which the geometric…
We develop a quasisymmetric analogue of the theory of Schubert cycles, building off of our previous work on a quasisymmetric analogue of Schubert polynomials and divided differences. Our constructions result in a natural geometric…
The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by…
We describe a class of (2,2) superconformal field theories obtained by fibering a Landau-Ginzburg orbifold CFT over a compact Kaehler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model, our…
In this paper we will discuss gauged linear sigma model descriptions of toric stacks. Toric stacks have a simple description in terms of (symplectic, GIT) ${\bf C}^{\times}$ quotients of homogeneous coordinates, in exactly the same form as…
Based on a simple example, it is explained how the homological analysis may be applied for modeling of the electric circuits. The homological branch, mesh and nodal analyses are presented. Geometrical interpretations are given.
The big phase space, the geometric setting for the study of quantum cohomology with gravitational descendents, is a complex manifold and consists of an infinite number of copies of the small phase space. The aim of this paper is to define a…
This thesis considers one and two dimensional supersymmetric nonlinear sigma models. First there is a discussion of the geometries of one and two dimensional sigma models, with rigid supersymmetry. For the one-dimensional case, the…
We propose a new way to generate an observable geometric phase by means of a completely incoherent phenomenon. We show how to imprint a geometric phase to a system by "adiabatically" manipulating the environment with which it interacts. As…
A topologically equivalent tight binding model is proposed to study the quantum phase transitions of dimer chain driven by an imaginary ac field. I demonstrate how the partner Hamiltonian is constructed by a similarity transformation to…
Although the geometric phase for one-mode squeezed state had been studied in detail, the counterpart for two-mode squeezed state is vacant. It is be evaluated explicitly in this paper. Furthermore, the total phase factor is in an elegent…
We discuss and review in this chapter the developing field of research of quantum simulation of gauge theories with ultracold atoms.
The different quantum phases appearing in strongly correlated systems as well as their transitions are closely related to the entanglement shared between their constituents. In 1D systems, it is well established that the entanglement…
The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of…
In a prevous paper (Phys. Rev. Lett. 96, 150403 (2006)) we have proposed a new way to generate an observable geometric phase on a quantum system by means of a completely incoherent phenomenon. The basic idea was to force the ground state of…
We show how to simulate U(1) gauge fields coupled to three-dimensional quantum gravity and then examine the phase diagram of this system. Quenched mean field theory suggests that a transition separates confined and deconfined phases (for…