Related papers: Bootstrapping More QM Systems
We propose a double bootstrap procedure for reducing coverage error in the confidence intervals of descriptive statistics for independent and identically distributed functional data. Through a series of Monte Carlo simulations, we compare…
The redistribution of energy levels between energy bands is studied for a family of simple effective Hamiltonians depending on one control parameter and possessing axial symmetry and energy-reflection symmetry. Further study is made on the…
Economists use quantitative trade and spatial models to make counterfactual predictions. Because such predictions often inform policy decisions, it is important to communicate the uncertainty surrounding them. Three key challenges arise in…
Chaotic instanton approach allows to describe analytically the influence of the polychromatic perturbation on quantum properties of nonlinear systems. Double well system with single, multiple and polychromatic kicked perturbation is…
Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We…
We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian…
The notion of a double well potential typically involves two regions of space separated by a repulsive potential barrier. The solution is a wave function that is suppressed in the barrier region and localized in the two surrounding regions.…
Methods that are devised to achieve reversal of quantum dynamics in time have been named "quatum time mirrors". Such a time mirror can be considered as a generalization of Hahn's spin echo to systems with continuous degrees of freedom. We…
A quantum system exhibiting $\mathcal{PT}$ symmetry is a Bose-Einstein condensate in a double-well potential with balanced particle gain and loss, which is described in the mean-field limit by a Gross-Pitaevskii equation with a complex…
We employ magnetocapacitance and far-infrared spectroscopy techniques to study the spectrum of the double-layer electron system in a parabolic quantum well with a narrow tunnel barrier in the centre. For gate-bias-controlled asymmetric…
Bootstrap is a novel and ambitious paradigm for quantum physics. It aims to solve the target problems by exploiting theoretical constraints from general physical principles and self-consistency conditions. The bootstrap philosophy dates…
We use so-called geometrical approach in description of transition from regular motion to chaotic in Hamiltonian systems with potential energy surface that has several local minima. Distinctive feature of such systems is coexistence of…
This article is an introduction to two currently very active research programs, the Conformal Bootstrap and Scattering Amplitudes. Rather than attempting full surveys, the emphasis is on common ideas and methods shared by these two…
This paper analyses the use of bootstrap methods to test for parameter change in linear models estimated via Two Stage Least Squares (2SLS). Two types of test are considered: one where the null hypothesis is of no change and the alternative…
The bootstrap is a method for estimating the distribution of an estimator or test statistic by re-sampling the data or a model estimated from the data. Under conditions that hold in a wide variety of econometric applications, the bootstrap…
We consider small perturbations of a dynamical system on the one-dimensional torus. We derive sharp estimates for the pre-factor of the stationary state, we examine the asymptotic behavior of the solutions of the Hamilton-Jacobi equation…
A new computation method of frequentist $p$-values and Bayesian posterior probabilities based on the bootstrap probability is discussed for the multivariate normal model with unknown expectation parameter vector. The null hypothesis is…
We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…
A simple expression is derived for the band structure of a one-dimensional periodic potential in terms of two solutions of the Schroedinger equation within the unit cell, one with a zero-derivative boundary condition on the left-hand end of…
Using the formalism of extended $N=4$ supersymmetric quantum mechanics we consider the procedure of the construction of multi--well potentials. We demostrate the form--invariance of Hamiltonians entering the supermultiplet, using the…