Related papers: Absorbing Boundary Condition as Limiting Case of I…
The quantum Zeno effect -- suppression of decay by frequent measurements -- was believed to occur only when the response of the detector is so quick that the initial tiny deviation from the exponential decay law is detectable. However, we…
There is a common expectation that the big-bang singularity must be resolved in quantum gravity but it is not clear how this can be achieved. A major obstacle here is the difficulty of interpreting wave-functions in quantum gravity. The…
Optomechanics allows the transduction of weak forces to optical fields, with many efforts approaching the standard quantum limit. We consider force-sensing using a mirror-in-the-middle setup and use two coupled cavity modes originated from…
We study the reach of direct detection experiments for large bound states (containing $10^4$ or more dark nucleons) of Asymmetric Dark Matter. We consider ordinary nuclear recoils, excitation of collective modes (phonons), and electronic…
We define a measuring device (detector) of the coordinate of quantum particle as an absorbing wall that cuts off the particle's wave function. The wave function in the presence of such detector vanishes on the detector. The trace the…
Here we embark on a thorough investigation of the magneto-optical absorption in semiconducting {\em spherical} quantum dots characterized by a confining harmonic potential and an applied magnetic field in the symmetric gauge. This is done…
We investigate and prove Lieb-Oxford bounds in one dimension by studying convex potentials that approximate the ill-defined Coulomb potential. A Lieb-Oxford inequality establishes a bound of the indirect interaction energy for electrons in…
Any proposed solution to the "screen problem" in quantum mechanics -- the challenge of predicting the joint distribution of particle arrival times and impact positions -- must align with the extensive data obtained from scattering…
We prove the expected disturbance caused to a quantum system by a sequence of randomly ordered two-outcome projective measurements is upper bounded by the square root of the probability that at least one measurement in the sequence accepts.…
Abstarct: Boundary effects caused by the boundary interactions in various integrable field theories on a half line are discussed at the classical as well as the quantum level. Only the so-called ``integrable" boundary interactions are…
IR/UV mixing (a mechanism causing ultraviolet quantum-gravity effects to manifest themselves also in a far-infrared regime) is a rare case of feature found in several approaches to the quantum-gravity problem. We here derive the…
Let $\Omega \subset\mathbb{R}^N$ ($N\geq 3$) be a $C^2$ bounded domain and $\Sigma \subset \partial\Omega$ be a $C^2$ compact submanifold without boundary, of dimension $k$, $0\leq k \leq N-1$. We assume that $\Sigma = \{0\}$ if $k = 0$ and…
In this article, we study the impact of a change in the type of boundary conditions of an elliptic boundary value problem. In the context of the conductivity equation we consider a reference problem with mixed homogeneous Dirichlet and…
Quantum sensing is commonly described as a constrained optimization problem: maximize the information gained about an unknown quantity using a limited number of particles. Important sensors including gravitational-wave interferometers and…
We consider the phenomenon of eigenvalue absorption for a many body Hamiltonian, which depends on a parameter. The conditions on pair potentials, which guarantee that the eigenvalues approaching the bottom of the continuous spectrum become…
A quantum neutral particle, constrained to move on a conical surface, is used as a toy model to explore bound states due to both a inverse squared distance potential and a $\delta$-function potential, which appear naturally in the model.…
Detection of axion dark matter heavier than a meV is hindered by its small wavelength, which limits the useful volume of traditional experiments. This problem can be avoided by directly detecting in-medium excitations, whose $\sim…
Let $\Omega$ be an open set in Euclidean space $\R^m,\, m=2,3,...$, and let $v_{\Omega}$ denote the torsion function for $\Omega$. It is known that $v_{\Omega}$ is bounded if and only if the bottom of the spectrum of the Dirichlet Laplacian…
We consider approximating the solution of the Helmholtz exterior Dirichlet problem for a nontrapping obstacle, with boundary data coming from plane-wave incidence, by the solution of the corresponding boundary value problem where the…
Most embeddings of the Standard Model into a more unified theory, in particular the ones based on supergravity or superstrings, predict the existence of a hidden sector of particles which have only very weak interactions with the visible…