Related papers: On Dalgarno and Lewis Perturbation Theory for Scat…
We discuss a many-particle quantum system, which is obtained by adding some nonhermitian but PT (i.e. combined parity and time reversal) invariant interaction to the $A_{N-1}$ rational Calogero model without confining potential. This model…
Discontinuous transitions into absorbing states require an effective mechanism that prevents the stabilization of low density states. They can be found in different systems, such as lattice models or stochastic differential equations (e.g.…
In this paper, we simplify the proof of M. Hamano in \cite{Hamano2018}, scattering theory of the solution to \eqref{NLS system}, by using the method from B. Dodson and J. Murphy in \cite{Dodson2018}. Firstly, we establish a criterion to…
We start from the remark that in wave turbulence theory, exemplified by the cubic twodimensional Schr{\"o}dinger equation (NLS) on the real plane, the regularity of the resonant manifold is linked with dispersive properties of the equation…
It is shown that stochastic processes of diffusion type possess, in all generality, a structure of uncertainty relations and of coherent and squeezed states. This fact is used to obtain, via Nelson stochastic formulation of quantum…
In quantum scattering theory, there exists a relationship between the difference in the scattering phase shifts at threshold and infinity and the number of bound states, which is established by the Levinson theorem. The presence of…
We develop an entangled-probe scattering theory, including quantum detection, that extends the scope of standard scattering approaches. We argue that these probes may be revolutionary in studying entangled matter such as unconventional…
Using the basic ingredient of supersymmetry, we develop a simple alternative approach to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wave functions do not involve tedious…
We present a method for calculating scattering phase shifts which utilizes continuum-discretized states obtained in a bound-state type calculation. The wrong asymptotic behavior of the discretized state is remedied by means of the Green's…
We consider elastic reflection and transmission of electrons by a disordered system characterized by a $2N\!\times\!2N$ scattering matrix $S$. Expressing $S$ in terms of the $N$ radial parameters and of the four $N\!\times\!N$ unitary…
The coherent control of scattering processes is considered, with electron impact dissociation of H$_2^+$ used as an example. The physical mechanism underlying coherently controlled stationary state scattering is exposed by analyzing a…
Here we consider a non-perturbative description of the non-interacting resonant model using a scattering approach employed in JCP 152(24) 244126 (2020). We showed that such description coincides with the standard NEGF and Landauer-Buttiker…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
Recently [Phys. Rev. Lett. {\bf 106}, 093902 (2011)] it has been shown that $\mathcal{PT}$-symmetric scattering systems with balanced gain and loss, undergo a transition from $\mathcal{PT}$-symmetric scattering eigenstates, which are norm…
This review addresses recent developments in nonequilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The…
In this paper, we consider the following inhomogeneous nonlinear Schr\"odinger equation (INLS) \[ i\partial_t u + \Delta u + \mu |x|^{-b} |u|^\alpha u = 0, \quad (t,x)\in \mathbb{R} \times \mathbb{R}^d \] with $b, \alpha>0$. First, we…
We present a lattice method for determining scattering phase shifts and mixing angles for the case of an arbitrary number of coupled channels. Previous nuclear lattice effective field theory simulations were restricted to mixing of up to…
The unitary S-matrix for the space-time non-commutative QED is constructed using the $\star$-time ordering which is needed in the presence of derivative interactions. Based on this S-matrix, perturbation theory is formulated and Feynman…
We study the evolution of angular variable (phase) for general (not necessarily Hamiltonian) perturbations of Hamiltonian systems with one degree of freedom near separatrices of the unperturbed system. To this end, we use averaged system of…
Three-body continuum states are investigated with the hyperspherical method on a Lagrange mesh. The $R$-matrix theory is used to treat the asymptotic behaviour of scattering wave functions. The formalism is developed for neutral as well as…