Analytical regularisation for confined quantum fields between parallel surfaces

Zeta-regularisation for exact-WKB resolution of a general 1D Schrödinger equation

We review an exact analytical resolution method for general one-dimensional (1D) quantal anharmonic oscillators: stationary Schrödinger equations with polynomial potentials. It is an exact form of WKB treatment involving spectral (usual) vs "classical" (newer) zeta-regularisations in parallel. The central results are a set of Bohr--Sommerfeld-like but exact quantisation conditions, directly drawn from Wronskian identities, and appearing to extend Bethe-Ansatz formulae of integrable systems. Such exact quantisation conditions do not just select the eigenvalues; some evaluate the spectral determ…

Entanglement purification of nonlocal quantum-dot-confined electrons assisted by double-sided optical microcavities

We present a nondestructive parity-check detector (PCD) scheme for two single-electron quantum dots embedded in double-sided optical microcavities. Using a polarization-entangled photon pair, the PCD works in a parallel style and is robust to the phase fluctuation of the optical path length. In addition, we present an economic entanglement purification protocol for electron pairs with our nondestructive PCD. The parties in quantum communication can increase the purification efficiency and simultaneously decrease the quantum source consumed for some particular fidelity thresholds. Therefore, ou…

具有空间变化有效质量的平行板间大质量标量场的卡西米尔效应

Casimir effect for a massive scalar field confined between parallel plates with a spatially varying effective mass

研究平行板间大质量标量场在位置依赖有效质量下的卡西米尔效应，通过求解克莱因 - 戈登方程获精确模式，经量子化和正则化评估真空能量，结果表明两种贡献在不同区域有不同表现，建立了与量子真空现象联系并提供新框架。

An intuitive picture of the Casimir effect

The Casimir effect, which predicts the emergence of an attractive force between two parallel, highly reflecting plates in vacuum, plays a vital role in various fields of physics, from quantum field theory and cosmology to nanophotonics and condensed matter physics. Nevertheless, Casimir forces still lack an intuitive explanation and current derivations rely on regularisation procedures to remove infinities. Starting from special relativity and treating space and time coordinates equivalently, this paper overcomes no-go theorems of quantum electrodynamics and obtains a local relativistic quantu…

Parallel transport in an entangled ring

This paper defines a notion of parallel transport in a lattice of quantum particles, such that the transformation associated with each link of the lattice is determined by the quantum state of the two particles joined by that link. We focus particularly on a one-dimensional lattice--a ring--of entangled rebits, which are binary quantum objects confined to a real state space. We consider states of the ring that maximize the correlation between nearest neighbors, and show that some correlation must be sacrificed in order to have non-trivial parallel transport around the ring. An analogy is made …

Exact Solution for Chameleon Field, Self-Coupled Through the Ratra-Peebles Potential with n = 1 and Confined Between Two Parallel Plates

We calculate the chameleon field profile, confined between two parallel plates, filled with air at pressure $P = 10^{-4}\,{\rm mbar}$ and room temperature and separated by the distance $L$, in the chameleon field theory with Ratra--Peebles self--interaction potential with index $n = 1$. We give the exact analytical solution in terms of Jacobian elliptic functions, depending on the mass density of the ambient matter. The obtained analytical solution can be used in qBounce experiments, measuring transition frequencies between quantum gravitational states of ultracold neutrons and also for the ca…