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Related papers: Bootstrapping Simple QM Systems

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Recently, a novel bootstrap method for numerical calculations in matrix models and quantum mechanical systems is proposed. We apply the method to certain quantum mechanical systems derived from some well-known local toric Calabi-Yau…

High Energy Physics - Theory · Physics 2022-12-08 Bao-ning Du , Min-xin Huang , Pei-xuan Zeng

Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…

Statistics Theory · Mathematics 2025-04-02 Guoyu Zhang , Dandan Jiang , Fang Yao

Symmetries play a central role in quantum many-body physics, yet uncovering them systematically remains challenging. We introduce a bootstrap framework designed to reconstruct the representation theory of hidden finite group symmetries of…

Quantum Physics · Physics 2026-04-03 Chen Bai , Zihan Zhou , Bastien Lapierre , Shinsei Ryu

In this review, we aim to utilize the bootstrap method to study models that have received significant interest in high energy theory and holography recently. Matrix bootstrap is proposed to determine the range of the solution up to an…

General Relativity and Quantum Cosmology · Physics 2026-05-19 Shu Luo

Finding a method to combine the numerical bootstrap with the analytic lightcone bootstrap is an important goal to advance the conformal bootstrap program. We propose a hybrid bootstrap method to do just that. The numerical and analytic…

High Energy Physics - Theory · Physics 2022-02-16 Ning Su

We employ the technique of perturbative analytic null bootstrap to obtain the energy eigenvalues and ladder operators of the sextic anharmonic oscillator up to second order in the coupling. We confirm our results by deriving the same from…

Quantum Physics · Physics 2023-09-26 Renjan Rajan John , Krishna Priya R

We construct a non-perturbative approach based on quantum averaging combined with resonant transformations to detect the resonances of a given Hamiltonian and to treat them. This approach, that generalizes the rotating-wave approximation,…

Quantum Physics · Physics 2007-05-23 M. Amniat-Talab , S. Guerin , H. R. Jauslin

In this paper, we employ the bootstrap method, a technique that relies on consistency relations instead of direct diagonalization, to determine the expectation values in quantum many-body systems. We then use these values to assess the…

Quantum Physics · Physics 2025-06-23 Jiaju Zhang , Arash Jafarizadeh , M. A. Rajabpour

Smooth model potentials with parameters selected to reproduce the spectrum of one-electron atoms are used to approximate the singular Coulomb potential. Even when the potentials do not mimic the Coulomb singularity, much of the spectrum is…

Chemical Physics · Physics 2016-10-28 Cristina E. González-Espinoza , Paul. W Ayers , Jacek Karwowski , Andreas Savin

Statistical multispecies models of multiarea marine ecosystems use a variety of data sources to estimate parameters using composite or weighted likelihood functions with associated weighting issues and questions on how to obtain variance…

Applications · Statistics 2012-02-16 Lorna Taylor , Verena M. Trenkel , Vojtech Kupca , Gunnar Stefansson

The bootstrap program for 1+1-dimensional integrable Quantum Field Theories (QFT's) is developed to a large extent for the Homogeneous sine-Gordon (HSG) models. This program can be divided into various steps, which include the computation…

High Energy Physics - Theory · Physics 2007-05-23 Olalla A. Castro-Alvaredo

We study the effectiveness of the numerical bootstrap techniques recently developed in arXiv:2004.10212 for quantum mechanical systems. We find that for a double well potential the bootstrap method correctly captures non-perturbative…

High Energy Physics - Theory · Physics 2022-01-19 Jyotirmoy Bhattacharya , Diptarka Das , Sayan Kumar Das , Ankit Kumar Jha , Moulindu Kundu

A stable physical system has an energy spectrum that is bounded from below. For quantum systems, the dangerous states of unboundedly low energies should decouple and become null. We propose the principle of nullness and apply it to the…

High Energy Physics - Theory · Physics 2023-01-03 Wenliang Li

Efficient sampling from ensembles of Hamiltonian cycles is critical for predicting the thermodynamic properties of compact polymers, with applications including modeling protein and RNA folding and designing soft materials. Although…

Quantum Physics · Physics 2026-03-16 Davide Rattacaso , Daniel Jaschke , Antonio Trovato , Ilaria Siloi , Simone Montangero

We consider quantum systems consisting of a linear chain of n harmonic oscillators coupled by a nearest neighbour interaction of the form $-q_r q_{r+1}$ ($q_r$ refers to the position of the $r$th oscillator). In principle, such systems are…

Mathematical Physics · Physics 2009-02-27 G. Regniers , J. Van der Jeugt

Quantum Monte Carlo methods are powerful tools for studying quantum many-body systems but face difficulties in accessing excited states and in treating sign problems. We present a continuous-time path-integral Monte Carlo method for…

Strongly Correlated Electrons · Physics 2025-12-16 Abhishek Karna , Hansen S. Wu , Shailesh Chandrasekharan , Ribhu K. Kaul

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…

Methodology · Statistics 2019-02-21 Miles Lopes , Andrew Blandino , Alexander Aue

We study the isotropic and anisotropic Hamiltonian of two coupled harmonic oscillators from an algebraic approach of the $SU(1,1)$ and $SU(2)$ groups. In order to obtain the energy spectrum and eigenfunctions of this problem, we write its…

Quantum Physics · Physics 2024-10-02 J. C. Vega , D. Ojeda-Guillén , R. D. Mota

Identifying the Hamiltonian of a quantum system from experimental data is considered. General limits on the identifiability of model parameters with limited experimental resources are investigated, and a specific Bayesian estimation…

Quantum Physics · Physics 2019-10-15 S. G. Schirmer , F. C. Langbein

. The choice of a suitable random matrix model of a complex system is very sensitive to the nature of its complexity. The statistical spectral analysis of various complex systems requires, therefore, a thorough probing of a wide range of…

Statistical Mechanics · Physics 2009-10-31 Pragya Shukla