Related papers: Wave Functions of the Toda Chain with Boundary Int…

We study boundary reflection matrix for the quantum field theory defined on a half line using Feynman's perturbation theory. The boundary reflection matrix can be extracted directly from the two-point correlation function. This enables us…

Controlling single-particle wave functions in single semiconductor quantum dots is in demand to implement solid-state quantum information processing and spintronics. Normally, particle wave functions can be tuned transversely by an…

For each one of the Lie algebras $\mathfrak{gl}_{n}$ and $\widetilde {\mathfrak{gl}}_{n}$, we constructed a family of integrable generalizations of the Toda chains characterized by two integers $m_{+}$ and $m_{-}$. The Lax matrices and the…

We propose a time-domain boundary integral method to model linear wave propagation with refractive, focusing, and Doppler effects arising from medium heterogeneities and moving obstacles. In contrast to existing techniques, our method…

Exact reflection and transmission coefficients for supersymmetric shape-invariant potentials barriers are calculated by an analytical continuation of the asymptotic wave functions obtained via the introduction of new generalized ladder…

Standard practice attempts to remove coordinate influence in physics through the use of invariant equations. Trans-coordinate physics proceeds differently by not introducing space-time coordinates in the first place. Differentials taken…

In earlier papers on the loop variable approach to gauge invariant interactions in string theory, a ``wave functional'' with some specific properties was invoked. It had the purpose of converting the generalized momenta to space time…

Non-relativistic quantum particles bounded to a curve in R^2 by attractive contact $\delta$-interaction are considered. The interval between the energy of the transversal bound state and zero is shown to belong to the absolutely continuous…

We construct a certain reduction of the 2D Toda hierarchy and obtain a tau-symmetric Hamiltonian integrable hierarchy. This reduced integrable hierarchy controls the linear Hodge integrals in the way that one part of its flows yields the…

We establish a new geometric wave function that combined with a variational principle efficiently describes a system of bosons interacting in a one-dimensional trap. By means of a a combination of the exact wave function solution for…

This work comes as the second part in a series of investigations into the dynamics of rotating waves as solutions to lattice dynamical systems. Such nonlinear waves as solutions to mathematical equations are of great interest throughout the…

Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…

The Ising quantum chain with a peculiar twisted boundary condition is considered. This boundary condition, first introduced in the framework of the spin-1/2 XXZ Heisenberg quantum chain, is related to the duality transformation, which…

A problem of diffraction by an elongated body of revolution is studied. The incident wave falls along the axis. The wavelength is small comparatively to the dimensions of the body. The parabolic equation of the diffraction theory is used to…

For a general two-body bound state in quantum mechanics, both in the stable and decaying cases, we establish a way to extract its two-body wave function in momentum space from the scattering amplitude of the constituent two particles. For…

The squared eigenfunction symmetry for the Toda lattice hierarchy is explicitly constructed in the form of the Kronecker product of the vector eigenfunction and the vector adjoint eigenfunction, which can be viewed as the generating…

We study multifractal properties of wave functions for a one-parameter family of quantum maps displaying the whole range of spectral statistics intermediate between integrable and chaotic statistics. We perform extensive numerical…

The energy spectrum and corresponding wave functions of two bosonic particles confined in a spherically symmetric shell trap and interacting via a three-dimensional zero-range potential are computed. Confinement-induced resonances,…

In this paper we consider the Toda lattice $(\mathbf{p}(t);\mathbf{q}(t))$ at thermal equilibrium, meaning that its variables $(p_j)$ and $(e^{q_j-q_{j+1}})$ are independent Gaussian and Gamma random variables, respectively. We show under…

We consider gravitational wave production by bubble collisions during a cosmological first-order phase transition. In the literature, such spectra have been estimated by simulating the bubble dynamics, under so-called thin-wall and envelope…