Related papers: Hall's exact variance decomposition in Bohmian Mec…
We prove new concentration inequalities for quantum spin systems which apply to any local observable measured on any product state or on any state with exponentially decaying correlations. Our results do not require the spins to be arranged…
We study the breakdown of conformal symmetry in a conformally invariant gravitational model. The symmetry breaking is introduced by defining a preferred conformal frame in terms of the large scale characteristics of the universe. In this…
The universal anomalous diffusion scaling is obtained for the semiclassical quantum Hall transition, which has been argued to describe samples with dissipation or correlated impurities. The results explain a discrepancy between existing…
Reliably estimating the uncertainty of a prediction throughout the model lifecycle is crucial in many safety-critical applications. The most common way to measure this uncertainty is via the predicted confidence. While this tends to work…
We investigate the problem of the superuniversality of the phase transition between different quantum Hall plateaus. We construct a set of models which give a qualitative description of this transition in a pure system of interacting…
Infinite sets of inequalities which generalize all the known inequalities that can be used in the majorization step of the Approximating Hamiltonian method are derived. They provide upper bounds on the difference between the quadratic…
Quantum uncertainty is the cornerstone of quantum mechanics which underlies many counterintuitive nonclassical phenomena. Recent studies remarkably showed that it also fundamentally limits nonclassical correlation, and crucially, a…
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be obtainable by such methods. The novel feature of adaptive…
We consider electrons in uniform external magnetic and electric fields which move on a plane whose coordinates are noncommuting. Spectrum and eigenfunctions of the related Hamiltonian are obtained. We derive the electric current whose…
Interpretations of quantum mechanics (QM), or proposals for underlying theories, that attempt to present a definite realist picture, such as Bohmian mechanics, require strong non-local effects. Naively, these effects would violate causality…
The recently so-called deviation scale [C. M. Mabena et al., Phys. Rev. A 99, 013828 (2019)] bridges the connection between the result of the infinitesimal propagation equation (IPE) prediction and that of the single phase screen (SPS)…
In this paper, the deformed Special Relativity, which leads to an essentially new theoretical context of quantum mechanics, is presented. The formulation of the theory arises from a straightforward analogy with the Special Relativity, but…
A test on the numerical accuracy of the semiclassical approximation as a function of the principal quantum number has been performed for the Pullen--Edmonds model, a two--dimensional, non--integrable, scaling invariant perturbation of the…
Quantum coherence is a fundamental common trait of quantum phenomena, from the interference of matter waves to quantum degeneracy of identical particles. Despite its importance, estimating and measuring quantum coherence in generic, mixed…
A brief account of the world view of classical physics is given first. We then recapitulate as to why the Copenhagen interpretation of the quantum mechanics had to renounce most of the attractive features of the clasical world view such as…
We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum walk experiments realized with neutral…
The conventional Hamiltonian $H= p^2+ V_N(x)$, where the potential $V_N(x)$ is a polynomial of degree $N$, has been studied intensively since the birth of quantum mechanics. In some cases, its spectrum can be determined by combining the WKB…
For the random walk among random conductances, we prove that the environment viewed by the particle converges to equilibrium polynomially fast in the variance sense, our main hypothesis being that the conductances are bounded away from…
Bohmian mechanics is a nonlocal hidden-variable interpretation of quantum theory which predicts that particles follow deterministic trajectories in spacetime. Historically, the study of Bohmian trajectories has mainly been restricted to…
The degeneracy of energy levels in a quantum dot of Hall fluid, leading to conductance peaks, can be readily derived from the partition functions of conformal field theory. Their complete expressions can be found for Hall states with both…