Monte Carlo Hamiltonian

Jirari, H.; Kröger, H.; Huang, Chaoqun; Jun-qin, Jiang; Luo, X.Q.; Moriarty, K.J.M.

doi:10.1016/s0920-5632(00)91855-3

Cited by 5 publications

(8 citation statements)

References 1 publication

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“…Its working in quantum mechanics has been demonstrated in a number of cases. For the 1-D harmonic oscillator, energy spectrum, wave functions and thermodynamical functions have been found to be in good agreement with the exact results [3][4][5]. Similar results have been obtained for uncoupled as well as coupled harmonic oscillators in 2-D [6,7] and 3-D [8].…”

Section: Exp[−h T/h] |ξ ∼ Lim T→∞ Exp[−e Gr T/h]|ω ω|ξ (2)supporting

confidence: 80%

SPECTRUM AND WAVE FUNCTIONS OF U(1)₂₊₁ LATTICE GAUGE THEORY FROM MONTE CARLO HAMILTONIAN

Hosseinizadeh

Kröger

Melkonyan³

et al. 2011

Mod. Phys. Lett. A

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We address an old problem in lattice gauge theory -the computation of the spectrum and wave functions of excited states. Our method is based on the Hamiltonian formulation of lattice gauge theory. As strategy, we propose to construct a stochastic basis of Bargmann link states, drawn from a physical probability density distribution. Then we compute transition amplitudes between stochastic basis states. From a matrix of transition elements we extract energy spectra and wave functions. We apply this method to U(1) 2+1 lattice gauge theory. We test the method by computing the energy spectrum, wave functions and thermodynamical functions of the electric Hamiltonian of this theory and compare them with analytical results. We observe a reasonable scaling of energies and wave functions in the variable of time. We also present first results on a small lattice for the full Hamiltonian including the magnetic term.

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Section: Exp[−h T/h] |ξ ∼ Lim T→∞ Exp[−e Gr T/h]|ω ω|ξ (2)supporting

confidence: 80%

SPECTRUM AND WAVE FUNCTIONS OF U(1)₂₊₁ LATTICE GAUGE THEORY FROM MONTE CARLO HAMILTONIAN

Hosseinizadeh

Kröger

Melkonyan³

et al. 2011

Mod. Phys. Lett. A

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“…Some years ago, we proposed a new approach [24] (named Monte Carlo Hamiltonian method or MCH) to investigate this problem. A lot of models [24,28,29,30,31,32,33,34] in QM have been used to test the method. This method has also been applied to scalar field theories [35,36,37,38].…”

Section: Monte Carlo Hamiltonianmentioning

confidence: 99%

Bound states and critical behavior of the Yukawa potential

Luo

Kröger

2006

SCI CHINA SER G

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We investigate the bound states of the Yukawa potential V (r) = −λ exp(−αr)/r, using different algorithms: solving the Schrödinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical α = α C , above which no bound state exists. We study the relation between α C and λ for various angular momentum quantum number l, and find in atomic units, α C (l) = λ[A 1 exp(−l/B 1 ) + A 2 exp(−l/B 2 )], with A 1 = 1.020(18), B 1 = 0.443(14), A 2 = 0.170(17), and B 2 = 2.490(180).

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“…[6]. Carrying out these steps allows to construct an effective Hamiltonian, which has turned out to reproduce well low energy physics of a lot of quantum systems [6,7,8,9,10,11,12,13,14,15,16,17].…”

Section: Matrix Elementsmentioning

confidence: 99%

“…its spectrum and eigen states. A lot of models [6,7,8,9,10,11,12,13] in quantum mechanics (QM) have been used to test the method. This method has also been applied to scalar field theories [14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%