Related papers: Bound State Energies using Phase Integral Analysis
We consider the problem of recovering of initial data in the IBVP for the wave-type equation in the half-space by the solution restricted to the boundary. The singular value decomposition of this problem is concerned: the asymptotics of…
We illustrate how dynamical transitions in nonlinear semiclassical models can be recognized as phase transitions in the corresponding -- inherently linear -- quantum model, where, in a Statistical Mechanics framework, the thermodynamic…
We consider a modified Boltzmann equation which contains, together with the collision operator, an additional drift term that is characterized by a matrix A. Furthermore, we consider a Maxwell gas, where the collision kernel has an angular…
The dynamical behaviour of many-body systems is often richer than what can be anticipated from their static properties. Here we show that in closed quantum systems this becomes evident by considering time-integrated observables as order…
The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. This is because the phase-field…
The singularities that arise in elliptic boundary value problems are treated locally by a singular function boundary integral method. This method extracts the leading singular coefficients from a series expansion that describes the local…
The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\"odinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U(1). For initial states close to…
We study a Penrose-Fife phase transition model coupled with homogeneous Neumann boundary conditions. Improving previous results, we show that the initial value problem for this model admits a unique solution under weak conditions on the…
We investigate the qualitative properties of a critical Hartree equation defined on punctured domains. Our study has two main objectives: analyzing the asymptotic behavior near isolated singularities and establishing radial symmetry of…
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…
A multiscale approach was adopted for the calculation of confined states in self-assembled semiconductor quantum dots (QDs). While results close to experimental data have been obtained with a combination of atomistic strain and…
Asymptotic behavior of energy of a harmonic map defined on an asymptotically hyperbolic manifold is considered. Using the growth of energy, we show that a harmonic map defined on some asymptotically hyperbolic manifolds has to be constant…
In this paper, we establish the asymptotic stability of the steady-state for a 1-D stochastic Euler-Poisson equations with Ohmic contact boundary conditions forced by the Wiener process. We utilize Banach's fixed point theorem and the a…
A preceding paper demonstrated that explicit asymptotic methods generally work much better for extremely stiff reaction networks than has previously been shown in the literature. There we showed that for systems well removed from…
Analytical complexity of quantum wavefunction whose argument is extended into the complex plane provides an important information about the potentiality of manifesting complex quantum dynamics such as time-irreversibility, dissipation and…
We study the Stokes phenomenon via hyperfunctions for the solutions of the 1-dimensional complex heat equation under the condition that the Cauchy data are holomorphic on $\mathbb{C}$ but a finitely many singular or branching points with…
There are two well-known approaches to studying nonperturbative aspects of quantum mechanical systems: Saddle point analysis of the partition functions in Euclidean path integral formulation and the exact-WKB analysis based on the wave…
We study the non-selfadjoint Dirac system on the line having an non-integrable regular singularity in an interior point with additional matching conditions at the singular point. Special fundamental systems of solutions are constructed with…
In a quantum system with a smoothly and slowly varying Hamiltonian, which approaches a constant operator at times $t\to \pm \infty$, the transition probabilities between adiabatic states are exponentially small. They are characterized by an…
We apply the asymptotic iteration method (AIM) [J. Phys. A: Math. Gen. 36, 11807 (2003)] to solve new classes of second-order homogeneous linear differential equation. In particular, solutions are found for a general class of eigenvalue…