Related papers: Rayleigh-Schr\"{o}dinger Perturbation Theory Based…
We study the accuracy of analytical wave function based many-body methods derived by energy minimization of a Jastrow-Feenberg ansatz for electrons (`Fermi hypernetted chain / Euler Lagrange' approach). Approximations to avoid the…
We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the…
This paper presents a comprehensive investigation of the problem of a harmonic oscillator with time-depending frequencies in the framework of the Vlasov theory and the Wigner function apparatus for quantum systems in the phase space. A new…
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…
We re-derive the Schr\"{o}dinger-Robertson uncertainty principle for the position and momentum of a quantum particle. Our derivation does not directly employ commutation relations, but works by reduction to an eigenvalue problem related to…
The behaviour of internal waves propagating in a background shear flow is studied in the case where the direction of shear is orthogonal to gravity. Ray-tracing theory is used to predict properties of the wave state at locations where…
We perform a variational calculation in the SU(N) Yang Mills theory in 3+1 dimensions. Our trial variational states are explicitly gauge invariant, and reduce to simple Gaussian states in the zero coupling limit. Our main result is that the…
We present a systematic study of the Rayleigh--Ritz variational method for quantum oscillators in the Segal--Bargmann space. We rigorously derive the normalizability condition $|\alpha| < \tfrac{1}{2}$ for generalized Gaussian trial…
In this manuscript, we investigate the analytical solution of the time-dependent Schr\"odinger equation for a harmonic oscillator with time-dependent mass and frequency, coupled with angular-dependent potential energy by utilizing the Dunkl…
We demonstrate the application of transition state theory to wave packet dynamics in metastable Schr\"odinger systems which are approached by means of a variational ansatz for the wave function and whose dynamics is described within the…
This paper is devoted to development of perturbation theory for studying the properties of graphene sheet of finite size, at nonzero temperature and chemical potential. The perturbation theory is based on the tight-binding Hamiltonian and…
Conventional weak-coupling Rayleigh-Schr\"odinger perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale analysis, a powerful and sophisticated…
For accurate ab initio description of Rydberg excited states the study suggests generating the appropriate diffuse basis functions by a cheap variational optimization of virtual orbitals of the corresponding ion core. By following this…
The stationary background flow in the spherically symmetric infall of a compressible fluid, coupled to the space-time defined by the static Schwarzschild metric, has been subjected to linearized perturbations. The perturbative procedure is…
An effective field theory approach is developed for calculating the thermodynamic properties of a field theory at high temperature $T$ and weak coupling $g$. The effective theory is the 3-dimensional field theory obtained by dimensional…
The ``close limit,'' a method based on perturbations of Schwarzschild spacetime, has proved to be a very useful tool for finding approximate solutions to models of black hole collisions. Calculations carried out with second order…
We reexamine the general solution of a Schr\"{o}dinger equation in the presence of a time-dependent linear potential in configuration space based on the Lewis-Riesenfeld framework. For comparison, we also solve the problem in momentum space…
We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results…
For the generalized statistical mechanics based on the Tsallis entropy, a variational perturbation approximation method with the principle of minimal sensitivity is developed by calculating the generalized free energy up to the third order…
In this contribution we present an exploratory study of several novel methods for numerical stochastic perturbation theory. For the investigation we consider observables defined through the gradient flow in the simple {\phi}^4 theory.