相关论文: Borel-Pade vs Borel-Weniger method: a QED and a QC…
A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been…
Linear recurrent sequences are those whose elements are defined as linear combinations of preceding elements, and finding recurrence relations is a fundamental problem in computer algebra. In this paper, we focus on sequences whose elements…
The supersymmetric reformulation of physical observables in the Chalker-Coddington model (CC) for the plateau transition in the integer quantum Hall effect leads to a reformulation of its critical properties in terms of a 2D non-compact…
Strongly-correlated quantum many-body systems are difficult to study and simulate classically. We recently proposed a variational quantum eigensolver (VQE) based on the multiscale entanglement renormalization ansatz (MERA) with tensors…
I summarize what is known about the Euler-Heisenberg Lagrangian and its multiloop corrections for scalar and spinor QED, in various types of constant fields, and in various dimensions. Particular attention is given to the asymptotic…
QED based on $\theta$-unexpanded noncomutative space-time in contrast with the noncommutative QED based on $\theta$-expanded U(1) gauge theory via the Seiberg-Witten map, is one-loop renormalizable. Meanwhile it suffers from asymptotic…
Inspired by the method of smoothed asymptotics developed by Terence Tao, we introduce a new ultra-violet regularisation scheme for loop integrals in quantum field theory which we call $\eta$ regularisation. This allows us to reveal a…
We propose an extension of Wenzel-Kramers-Brillouin (WKB) approximation for solving the Schr\"odinger equation. A set of coupled differential equations is obtained by considering an ansatz of the wave function with an auxiliary condition on…
The tensor train approximation of electronic wave functions lies at the core of the QC-DMRG (Quantum Chemistry Density Matrix Renormalization Group) method, a recent state-of-the-art method for numerically solving the $N$-electron…
The semi-classical discrete truncated Wigner approximation (dTWA) has recently been proposed as a simulation method for spin-$1/2$ systems. While it appears to provide a powerful approach which shows promising results in higher dimensions…
We prove that formal WKB solutions of Schr\"odinger equations on Riemann surfaces are resurgent. Specifically, they are Borel summable in almost all directions and their Borel transforms admit endless analytic continuation away from a…
A new resummation scheme in scalar field theories is proposed by combining parquet resummation techniques and flow equations, which is characterized by a hierarchy structure of the Bethe--Salpeter (BS) equations. The new resummation scheme…
The renormalization group method is applied for obtaining the asymptotic form of the wave function of the quantum anharmonic oscillator by resumming the perturbation series. It is shown that the resumed series is the cumulant of the naive…
Block coordinate descent (BCD) methods approach optimization problems by performing gradient steps along alternating subgroups of coordinates. This is in contrast to full gradient descent, where a gradient step updates all coordinates…
The mergings of energy levels associated with the breaking of PT symmetry in the model of Bender and Boettcher, and in its generalisation to incorporate a centrifugal term, are analysed in detail. Even though conventional WKB techniques…
We apply the linear $\delta$-expansion (LDE), originally developed as a nonperturbative, analytical approximation scheme in quantum field theory, to problems involving noninteracting electrons in disordered solids. The initial idea that the…
We study the zero-dimensional prototype of the path integrals in quantum mechanics and quantum field theory, with the action $S(\phi)=\frac{\sigma }{2}\phi^{2}+\frac{\lambda}{4}\phi^{4}$. Using the Lefschetz thimble decomposition and the…
Some general properties of local $\zeta$-function procedures to renormalize some quantities in $D$-dimensional (Euclidean) Quantum Field Theory in curved background are rigorously discussed for positive scalar operators $-\Delta + V(x)$ in…
We present a covariant decomposition of Einstein's Field Equations which is particularly suitable for perturbations of spherically symmetric -- and general locally rotationally symmetric -- spacetimes. Based upon the utility of the 1+3…
We apply the truncated Wigner method to the process of three-body recombination in ultracold Bose gases. We find that within the validity regime of the Wigner truncation for two-body scattering, three-body recombination can be treated using…