相关论文: A Simple Method for Computing Soliton Statistics
In this work we consider the well posed version of the Kaup-Broer-Kuperschmidt system in two dimensions. We numerically construct soliton type solutions and show that they are unstable both against dispersion and singularity formation.…
We use spin-coherent states as a time-dependent variational ansatz for a semiclassical description of a large family of Heisenberg models. In addition to common approaches we also evaluate the square variance of the Hamiltonian in terms of…
We consider a discrete-time non-Hamiltonian dynamics of a quantum system consisting of a finite sample locally coupled to several bi-infinite reservoirs of fermions with a translation symmetry. In this setup, we compute the asymptotic…
The possibility of generation and propagation of ultraslow bright optical solitons in asymmetric three-coupled quantum well systems is studied in this paper. These bright solitons owe their existence to Kerr and quintic nonlinearities which…
This paper is devoted to the study of solitary waves and solitons whose existence is related to the ratio energy/charge. These solitary waves are called hylomorphic. This class includes the Q-balls, which are spherically symmetric solutions…
We define an index of the fermionic signature operator on even-dimensional globally hyperbolic spin manifolds of finite lifetime. The invariance of the index under homotopies is studied. The definition is generalized to causal fermion…
We address the existence and properties of solitons in thermal media with periodic modulation of linear refractive index. Many kinds of solitons in such optical lattices, including symmetric and antisymmetric lattices, are found under…
An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory…
The gauge equivalent formulation of the Faddeev-Skyrme model is used for the study of the quantum theory. The rotational quantum excitations around the soliton solution of Hopf number unity are investigated by the method of collective…
Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices,…
Eisenstein series are real analytic functions which play a central role in spectral theory of the hyperbolic Laplacian. Kronecker limit formulas determine their connection to modular forms. The main result of this work is Theorem 7.2 in…
The Witten index for certain supersymmetric lattice models treated by de Boer, van Eerten, Fendley, and Schoutens, can be formulated as a topological invariant of simplicial complexes arising as independence complexes of graphs. We prove a…
We explore the space of solutions of the classical equations of motion in the Euclidean electroweak theory. We sketch a topological prescription that finds known solutions and indicates the existence of novel ones. All spatially-varying,…
This lecture note is intended to be a brief introduction to a recent development on the interplay between the ultradiscrete (or tropical) soliton systems and the combinatorial representation theory. We will concentrate on the simplest cases…
We record an observation about the Witten indices in two families of gauged linear sigma models: the U(2) model for linear sections of Grassmannians, and the U(1) model for quadric complete intersections. We describe how the Witten indices…
The scattering of fermions in the background field of a topological soliton of the modified $(2 + 1)$-dimensional $\mathbb{CP}^{1}$ model is studied here both analytically and numerically. Unlike the original $\mathbb{CP}^{1}$ model, the…
We consider static solutions of the sine-Gordon theory defined on a cylinder, which can be either periodic or quasi-periodic in space. They are described by the different modes of a simple pendulum moving in an inverted effective potential…
We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of…
A topological mechanism is a zero elastic-energy deformation of a mechanical structure that is robust against smooth changes in system parameters. Here, we map the nonlinear elasticity of a paradigmatic class of topological mechanisms onto…
We study invariants of bosonic and fermionic (Grassmann-valued) matrices under the adjoint action of $U(N)$, weighted by the fermion number. Such models naturally appear as the supersymmetric indices of supersymmetric gauge theories and are…