相关论文: Bootstrapping microcanonical ensemble in classical…
We test the bootstrap approach for determining the spectrum of one dimensional Hamiltonians, following the recent approach of Han, Hartnoll, and Kruthoff. We focus on comparing the bootstrap method data to known analytical predictions for…
Recently, novel numerical computation on quantum mechanics by using a bootstrap method was proposed by Han, Hartnoll, and Kruthoff. We consider whether this method works in systems with a $\theta$-term, where the standard Monte-Carlo…
We show that for a particular model, the quantum mechanical bootstrap is capable of finding exact results. We consider a solvable system with Hamiltonian $H=SZ(1-Z)S$, where $Z$ and $S$ satisfy canonical commutation relations. While this…
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…
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…
We test the bootstrap approach for determining the spectrum of one dimensional Hamiltonians. In this paper we focus on problems that have a two parameter search space in the bootstrap approach: the double well and a periodic potential…
Large $N$ matrix quantum mechanics is central to holographic duality but not solvable in the most interesting cases. We show that the spectrum and simple expectation values in these theories can be obtained numerically via a `bootstrap'…
We study the quantum-mechanical bootstrap as it applies to the bound states of several central potentials in three dimensions. As part of this effort, we show how the bootstrap approach may be applied to ``non-algebraic'' potentials, such…
We consider matrix quantum mechanics with multiple bosonic matrices, including those obtained from dimensional reduction of Yang-Mills theories. Using the matrix bootstrap, we study simple observables like $\langle \mathop{tr} X^2 \rangle$…
Recently, the ``Bootstrap" technique was applied in Quantum Mechanics to solve the eigenspectra of Hermitian Hamiltonians and extended to non-Hermitian PT-symmetric systems. However, its application has been limited to real spectra. In this…
In this work we report on a new bootstrap method for quantum mechanical problems that closely mirrors the setup from conformal field theory (CFT). We use the equations of motion to develop an analogue of the conformal block expansion for…
We study the effect of anharmonicity in quantum anharmonic oscillators, by computing the energy gap between the ground and the 1st excited state using the numerical bootstrap method. Based on perturbative formulae of limiting coupling…
A numerical bootstrap method is proposed to provide rigorous and nontrivial bounds in general quantum many-body systems with locality. In particular, lower bounds on ground state energies of local lattice systems are obtained by imposing…
Selftrapping has been traditionally studied on the assumption that quasiparticles interact with harmonic phonons and that this interaction is linear in the displacement of the phonon. To complement recent semiclassical studies of…
We study "the Caged Anisotropic Harmonic Oscillator", which is a new example of a superintegrable, or accidentally degenerate Hamiltonian. The potential is that of the harmonic oscillator with rational frequency ratio (l:m:n), but…
The bootstrap method aims to solve problems by imposing constraints on the space of physical observables, which often follow from physical assumptions such as positivity and symmetry. Here, we employ a bootstrap approach to study…
The bootstrap is a technique recently developed to get energy eigenvalues of bound states and correlation functions. There are three crucial steps - recursive equations, positivity constraints, search space. We calculate recursive equations…
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…
Bootstrap methods, initially developed for solving statistical and quantum field theories, have recently been shown to capture the discrete spectrum of quantum mechanical problems, such as the single particle Schr\"odinger equation with an…
We describe in detail a mathematical framework in which statistical ensembles of hybrid classical-quantum systems can be properly described. We show how a maximum entropy principle can be applied to derive the microcanonical ensemble of…