Related papers: A generalized scattering theory in quantum mechani…
We consider the scalar wave equation $\square_g \phi$ and the linearized Einstein-scalar field system around generalized Kasner spacetimes with spatial topology $\mathbb{T}^D$. In suitable regimes for the Kasner exponents, it is known that…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
In gravitational scattering the quantum particle probes the Fourier-transforms of a metric. I evaluate the Fourier-transforms of Schwarzschild metrics in standard, harmonic and other coordinate systems in linear and $G^2-$approximations. In…
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical…
The formal scattering theory is developed for the three-particle differential Faddeev equations. The theory is realised along the same line as in the standard two-body case. The solution of the scattering problem is expressed in terms of…
The scattering matrix S of a ballistic chaotic cavity is the direct sum of a `classical' and a `quantum' part, which describe the scattering of channels with typical dwell time smaller and larger than the Ehrenfest time, respectively.…
We develop a statistical theory describing quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynamics is chaotic. This picture is relevant to a variety of systems, ranging from atomic…
We discuss possible applications of the 1-D direct and inverse scattering problem to design of universal quantum gates for quantum computation. The potentials generating some universal gates are described.
Using the implicit function theorem we demonstrate that solutions to the classical part of the relativistic Lippmann-Schwinger equation are in one-to-one correspondence with those of the energy equation of a relativistic two-body system. A…
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a…
Based on the Hamiltonian formalism approach, a generalized L\"uscher's formula for two particle scattering in both the elastic and coupled-channel cases in moving frames is derived from a relativistic Lippmann-Schwinger equation. Some…
Scattering is an important phenomenon which is observed in systems ranging from the micro- to macroscale. In the context of nuclear reaction theory the Heidelberg approach was proposed and later demonstrated to be applicable to many chaotic…
A quantum theory of spherically symmetric thin shells of null dust and their gravitational field is studied. In Nucl. Phys. 603 (2001) 515 (hep-th/0007005), it has been shown how superpositions of quantum states with different geometries…
We study the scattering theory for the Schr\"odinger and wave equations with rough potentials in a scale of homogeneous Sobolev spaces. The first half of the paper concerns with an inverse-square potential in both of subcritical and…
The review chapter starts by a pedagogical introduction to the general concept of the scattering theory: from the fundamental wave-function picture to the second-quantization language, with the aim to clear possible ambiguity in…
The scattering theory of quantum transport relates transport properties of disordered mesoscopic conductors to their transfer matrix $\bbox{T}$. We introduce a novel approach to the statistics of transport quantities which expresses the…
The theory of scattering of atom pairs in a periodic potential is presented for the case of different atoms. When the scattering dynamics is restricted to the lowest Bloch band of the periodic potential, a separation in relative and average…
We develop a new quantum-mechanical approach to scattering a particle on a one-dimensional (1D) system of two identical rectangular potential barriers, which implies modelling the dynamics of its subprocesses -- transmission and reflection…
The connection between the problem of scattering a particle on a one-dimensional $\delta$-potential with the "Einstein's boxes" thought experiment is shown. In both cases, the validity of the superposition principle is limited by Einstein's…
A multiple scattering model of a quantum particle interacting with a random Lorentz gas of fixed point scatterers is established in an Euclidean space of arbitrary dimension. At the core of the model, the scattering amplitude for the point…