相关论文: Theory of Perturbations with a Strong Interaction

The perturbation theory with a variational basis is constructed and analyzed.The generalized Gaussian effective potential is introduced and evaluated up to the second order for selfinteracting scalar fields in one and two spatial…

We analyze the optical resonances of a dielectric sphere whose surface has been slightly deformed in an arbitrary way. Setting up a perturbation series up to second order, we derive both the frequency shifts and modified linewidths. Our…

We address the reliability of the Optimized Perturbation Theory (OPT) in the context of the 0-dimensional $O(N)$ scalar field model. The effective potential, the self-energy and the 1PI four-point Green's function for the model are computed…

Recently developed strong-coupling theory open up the possibility of treating quantum-mechanical systems with hard-wall potentials via perturbation theory. To test the power of this theory we study here the exactly solvable quantum…

Trust-region subproblem (TRS) is an important problem arising in many applications such as numerical optimization, Tikhonov regularization of ill-posed problems, and constrained eigenvalue problems. In recent decades, extensive works focus…

In quantum mechanics and quantum field theory perturbation theory generically requires the inclusion of extra contributions non-perturbative in the coupling, such as instantons, to reproduce exact results. We show how full non-perturbative…

We consider the survival probability of a particle in the presence of a finite number of diffusing traps in one dimension. Since the general solution for this quantity is not known when the number of traps is greater than two, we devise a…

Determining the steady state of an open quantum system is crucial for characterizing quantum devices and studying various physical phenomena. Often, computing a single steady state is insufficient, and it is necessary to explore its…

A non-perturbative method which can go beyond the weak coupling perturbation theory is introduced. Essential idea is to formulate a set of exact differential equations as a function of the coupling strength $g$. Unlike other resummation in…

A strictly truncated (weak-coupling) perturbation theory is applied to the attractive Holstein and Hubbard models in infinite dimensions. These results are qualified by comparison with essentially exact Monte Carlo results. The second order…

A partial resummation of perturbation theory is described for field theories containing spin-1/2 particles in states that may be far from thermal equilibrium. This allows the nonequilibrium state to be characterized in terms of…

We develop new perturbation techniques for conducting convergence analysis of various first-order algorithms for a class of nonsmooth optimization problems. We consider the iteration scheme of an algorithm to construct a perturbed…

The production of o(1/g^2) particles in a weakly-coupled theory is believed to be non-perturbatively suppressed. I comment on the prospects of (a) establishing this rigorously, and (b) estimating the effect to exponential accuracy…

We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams…

In this short write-up we argue that self-consistent diagrammatic perturbation theory(i.e. Feynman diagrams) for the one-particle Green function is unable to capture some important qualitative features no matter how self-consistently the…

The present work is motivated by the asymptotic control theory for a system of linear oscillators: the problem is to design a common bounded scalar control for damping all oscillators in asymptotically minimal time. The motion of the system…

Standard derivations of ``time-independent perturbation theory'' of quantum mechanics cannot be applied to the general case where potentials are energy dependent or where the inverse free Green function is a non-linear function of energy.…

The physical aspect of a general perturbation theory is explored. Its role as a physical principle for understanding the interaction among the matters with different levels of hierarchy is appreciated. It is shown that the general…

In order to extract maximal information about cosmology from the large-scale structure of the Universe, one needs to use every bit of signal that can be observed. Beyond the spatial distributions of astronomical objects, the spatial…

The network paradigm is increasingly used to describe the dynamics of complex systems. Here we review the current results and propose future development areas in the assessment of perturbation waves, i.e. propagating structural changes in…