Related papers: Bootstrapping More QM Systems
Polynomial systems over the binary field have important applications, especially in symmetric and asymmetric cryptanalysis, multivariate-based post-quantum cryptography, coding theory, and computer algebra. In this work, we study the…
For many relevant statistics of multivariate time series, no valid frequency domain bootstrap procedures exist. This is mainly due to the fact that the distribution of such statistics depends on the fourth-order moment structure of the…
We present a theoretical treatment of overdamped Brownian motion on a multidimensional tilted periodic potential that is analogous to the tight-binding model of quantum mechanics. In our approach we expand the continuous Smoluchowski…
Random matrix theory is a useful tool in the study of the physics of multiple scattering systems, often striking a balance between computation speed and physical rigour. Propagation of waves through thick disordered media, as arises in for…
Existing frequency domain methods for bootstrapping time series have a limited range. Consider for instance the class of spectral mean statistics (also called integrated periodograms) which includes many important statistics in time series…
A sixth order quadrupole boson Hamiltonian is treated through a time dependent variational principle approach choosing as trial function a coherent state with respect to zeroth $b^{\dagger}_0$ and second $b^{\dagger}_2+b^{\dagger}_{-2}$…
We present a phase-space method for the Bose-Hubbard model based on the Q-function representation. In particular, we consider two model Hamiltonians in the mean-field approximation; the first is the standard "one site" model where quantum…
A new model for the double well potential is presented in the paper. In the new potential, the exchanging rate could be easily calculated by the perturbation method in supersymmetric quantum mechanics. It gives good results whether the…
Motivated by recent progress on non-Hermitian topological band theories, we study the energy spectrum of a generic two-band non-Hermitian Hamiltonian. We prove rigorously that the complex energy spectrum of such a non-Hermitian Hamiltonian…
Recently, an application of the numerical bootstrap method to quantum mechanics was proposed, and it successfully reproduces the eigenstates of various systems. However, it is unclear why this method works. In order to understand this…
Following a `bottom-up approach' in understanding many-particle effects and dynamics we provide a systematic ab initio study of the dependence of the breathing dynamics of ultracold bosons in a 1D harmonic trap on the number of bosons…
Statistics derived from the eigenvalues of sample covariance matrices are called spectral statistics, and they play a central role in multivariate testing. Although bootstrap methods are an established approach to approximating the laws of…
We study anisotropies of helicity modulus, excitation spectrum, sound velocity and angle-resolved luminescence spectrum in a two-dimensional system of interacting excitons in a periodic potential. Analytical expressions for anisotropic…
In the realm of contemporary physics, the bootstrap method is typically associated with an optimization-based approach to problem-solving. This method leverages our understanding of a specific physical problem, which is used as the…
We employ a magnetocapacitance technique to study the spectrum of the soft two-subband (or double-layer) electron system in a parabolic quantum well with a narrow tunnel barrier in the centre. In this system unbalanced by gate depletion, at…
We study the interplay between electronic interactions and quasiperiodicity in a one-dimensional narrow-band system, focusing on ground-state and low-energy excitation properties. Using band projection as low-energy effective approach, we…
A bootstrap procedure for constructing prediction bands for a stationary functional time series is proposed. The procedure exploits a general vector autoregressive representation of the time-reversed series of Fourier coefficients appearing…
We give a detailed account of an $\it{ab}$ $\it{initio}$ spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the…
In this article, we explore the construction of Hamiltonians with long-range interactions and their corrections using the short-range behavior of the wave function. A key aspect of our investigation is the examination of the one-particle…
We develop the multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB), a variational numerically exact ab-initio method for studying the quantum dynamics and stationary properties of bosonic systems. ML-MCTDHB…