Related papers: Schwinger's Propagator Is Only A Green's Function
In this paper, we establish quantitative Green's function estimates for some higher dimensional lattice quasi-periodic (QP) Schr\"odinger operators. The resonances in the estimates can be described via a pair of symmetric zeros of certain…
A revised iterative method based on Green function defined by quadratures along a single trajectory is proposed to solve the low-lying quantum wave function for Schroedinger equation. Specially a new expression of the perturbed energy is…
We study the Schwinger pair production in confining theories. The production rate in an external electric field E is numerically evaluated by using the holographic description. There exist two kinds of critical values of the electric field,…
Non locality appearing in QFT during the free evolution of localized field states and in the Feynman propagator function is analyzed. It is shown to be connected to the initial non local properties present at the level of quantum states and…
We present an elementary nonperturbative method to obtain Green's functions (GFs) for timelike momenta. We assume there are no singularities in the first and third quadrants of the complex plane of space momentum components and perform a 3d…
We consider the process of electron-positron pair production in the presence of strong electric backgrounds being rapidly switched on and off and examine the total particle yield. For sufficiently sharp field profiles, the particle number…
We evaluate the propagator of scalar and spinor in three dimensional quantum electrodynamics with the use of Ward-Identity for soft-photon emission vertex.We work well in position space to treat infrared divergences in our model.…
We present new scale-free quantitative unique continuation principles for Schr\"odinger operators. They apply to linear combinations of eigenfunctions corresponding to eigenvalues below a prescribed energy, and can be formulated as an…
We obtain a complete series solution of stationary Schr\"odinger's equation in the general quantum systems. It is exact in the sense that any approximation means is not used, or that the whole corrections or contributions from all order…
Probabilities of a pair of fermions and bosons creation in a static and spatially uniform electric field E are represented in the Schwinger formulas by infinite series. It is believed that in weak fields the main contribution to the…
We prove that 3-dimensional Schrodinger operator with slowly decaying sparse potential has an a.c. spectrum that fills positive half-line. A new kind of WKB asymptotics for Green's function is found. The absense of positive eigenvalues is…
Particle production induced by a time-dependent background is well understood as the projection of the time-evolved initial state onto a set of final states. While the asymptotic initial and final states are well defined in the usual way,…
Our goal is to develop spectral and scattering theories for the one-dimensional Schr\"odinger operator with a long-range potential $q(x)$, $x\geq 0$. Traditionally, this problem is studied with a help of the Green-Liouville approximation.…
Pair-creation of charged particles in a strong gauge-field background - the renowned Schwinger effect - can strongly alter the efficiency of gauge-field production during axion inflation. It is therefore crucial to have a clear…
In scalar QED we study the Schwinger pair production from an initial ensemble of charged bosons when an electric field is turned on for a finite period together with or without a constant magnetic field. The scalar QED Hamiltonian depends…
The propagator which evolves the wave-function in NRQM, can be expressed as a matrix element of a time evolution operator: i.e $ G_{\rm NR}(x)= \langle{\mathbf{x}_2}|{U_{\rm NR}(t)}|{\mathbf{x}_1}\rangle$ in terms of the orthonormal…
A quantum kinetic equation has been derived for the description of pair production in a time-dependent homogeneous electric field $E(t)$. As a source term, the Schwinger mechanism for particle creation is incorporated. Possible particle…
In the probability representation of quantum mechanics, quantum states are represented by a classical probability distribution, the marginal distribution function (MDF), whose time dependence is governed by a classical evolution equation.…
We present an experimental realisation of the direct scheme for measuring the Wigner function of a single quantized light mode. In this method, the Wigner function is determined as the expectation value of the photon number parity operator…
The vacuum persistence probability, $P_{vac}(t)$, for a system of charged fermions in a fixed, external, and spatially homogeneous electric field, was derived long ago by Schwinger; $w = -log[P_{vac}(t)]/ (V t)$ has often been identified as…