相关论文: Resummation of not summable series
In this work we explicitly show resurgence relations between perturbative and one instanton sectors of the resonance energy levels for cubic and quartic anharmonic potentials in one-dimensional quantum mechanics. Both systems satisfy the…
Recently the non-perturbative numerical bootstrap method is rapidly developing, especially its application in nonlinear quantum mechanics, many-body physics, lattice models and matrix models. Here we use this numerical bootstrap to study…
The renormalization of effective potential for the noncommutative scalar field theory is investigated to the two-loop approximation. It is seen that the nonplanar diagram does not appear in the one-loop potential. However, nonplanar diagram…
This talk describes the resummation approach in (Fractional) Analytic Perturbation Theory (FAPT) in QCD. First, we make a short historical review of the (F)APT approach and then shortly describe the global scheme of FAPT which allows one to…
This text is about the mathematical use of certain divergent power series. The first part is an introduction to 1-summability. The definitions rely on the formal Borel transform and the Laplace transform along an arbitrary direction of the…
Weak values arise in quantum theory when the result of a weak measurement is conditioned on a subsequent strong measurement. The majority of the trials are discarded, leaving only very few successful events. Intriguingly those can display a…
We consider asymptotics of the ground state energy of heavy atoms and molecules and derive it including Schwinger and Dirac corrections. We consider also related topics: an excessive negative charge, ionization energy and excessive negative…
We show analytically that the perturbative expansion for the free energy of the zero dimensional (quenched) disordered Ising model is Borel-summable in a certain range of parameters, provided that the summation is carried out in two steps:…
By using the WKB quantization we deduce an analytical formula for the energy splitting in a double-well potential which is the usual Landau formula with additional quantum corrections. Then we analyze the accuracy of our formula for the…
A double-well energy expressed as a minimum of two quadratic functions, called phase energies, is studied with taking into account the minimization of the corresponding integral functional. Such integral, as being not sequentially weakly…
The double-well potential is a good example, where we can compute the splitting in the bound state energy of the system due to the tunneling effect with various methods, namely WKB or instanton calculations. All these methods are…
A simple expression for a ground state energy for a two-electron atom is derived. For this, assumption based upon the Niels Bohr ''old'' quantum mechanics idea about electron correlation in a two-electron atom is exploited. Results are…
We consider asymptotics of the ground state energy of heavy atoms and molecules in the self-generatedl magnetic field. Namely, we consider $$ H=((D-A)\cdot\boldsymbol{\sigma})^2-V $$ with $$V=\sum_{1\le m\le M} \frac{Z_m}{|x-y_m|}$$ and a…
We study the quantum Hall states in the lowest Landau level for a single wide quantum well. Due to a separation of charges to opposite sides of the well, a single wide well can be modelled as an effective two level system. We provide…
We examine in detail nonperturbative corrections for low lying energies of a symmetric triple-well potential with non-equivalent vacua, for which there have been disagreement about asymptotic formulas and controversy over the validity of…
We discuss the resummation of the Goldstone boson contributions to the effective potential of the Minimal Supersymmetric Standard Model (MSSM). This eliminates the formal problems of spurious imaginary parts and logarithmic singularities in…
Noncommutative solitons are easier to find in a noncommutative field theory. Similarly, the one-loop quantum corrections to the mass of a noncommutative soliton are easier to compute, in a real scalar theory in 2+1 dimensions. We carry out…
The double well potential is arguably one of the most important potentials in quantum mechanics, because the solution contains the notion of a state as a linear superposition of `classical' states, a concept which has become very important…
We give precise meaning to piecewise constant potentials in non-commutative quantum mechanics. In particular we discuss the infinite and finite non-commutative spherical well in two dimensions. Using this, bound-states and scattering can be…
It was shown that an infinite convergent sequence of improving non-increasing upper bounds to the ground state energy of a slow-moving acoustical polaron can be obtained by means of generalized variational method. The proposed approach is…