Multilevel blocking Monte Carlo simulations for quantum dots

This article provides an introduction to the ideas behind the multilevel blocking (MLB) approach to the fermion sign problem in path-integral Monte Carlo simulations, and also gives a detailed discussion of MLB results for quantum dots. MLB can turn the exponential severity of the sign problem into an algebraic one, thereby enabling numerically exact studies of otherwise inaccessible systems. Low-temperature simulation results for up to eight strongly correlated electrons in a parabolic 2D quantum dot are presented.Comment: 10 Pages, includes 4 figures and mprocl.st

Parameter identification in a semilinear hyperbolic system

We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and contraction arguments. We then investigte the inverse problem of recovering the unknown nonlinear damping law from additional boundary measurements of the pressure drop along the pipe. This coefficient inverse problem is shown to be ill-posed and a variational regularization method is considered for its stable solution. We prove existence of minimizers for the Tikhonov functional and discuss the convergence of the regularized solutions under an approximate source condition. The meaning of this condition and some arguments for its validity are discussed in detail and numerical results are presented for illustration of the theoretical findings

Relieving the fermionic and the dynamical sign problem: Multilevel Blocking Monte Carlo simulations

This article gives an introduction to the multilevel blocking (MLB) approach to both the fermion and the dynamical sign problem in path-integral Monte Carlo simulations. MLB is able to substantially relieve the sign problem in many situations. Besides an exposition of the method, its accuracy and several potential pitfalls are discussed, providing guidelines for the proper choice of certain MLB parameters. Simulation results are shown for strongly interacting electrons in a 2D parabolic quantum dot, the real-time dynamics of several simple model systems, and the dissipative two-state dynamics (spin-boson problem).Comment: Review, 20 pages REVTeX, incl. 7 figure

Doping- and size-dependent suppression of tunneling in carbon nanotubes

We study the effect of doping in the suppression of tunneling observed in multi-walled nanotubes, incorporating as well the influence of the finite dimensions of the system. A scaling approach allows us to encompass the different values of the critical exponent $\alpha$ measured for the tunneling density of states in carbon nanotubes. We predict that further reduction of $\alpha$ should be observed in multi-walled nanotubes with a sizeable amount of doping. In the case of nanotubes with a very large radius, we find a pronounced crossover between a high-energy regime with persistent quasiparticles and a low-energy regime with the properties of a one-dimensional conductor.Comment: 4 pages, 2 figures, LaTeX file, pacs: 71.10.Pm, 71.20.Tx, 72.80.R

Resonant tunneling in a Luttinger liquid for arbitrary barrier transmission

A numerically exact dynamical quantum Monte Carlo approach has been developed and applied to transport through a double barrier in a Luttinger liquid with arbitrary transmission. For strong transmission, we find broad Fabry-Perot Coulomb blockade peaks, with a lineshape parametrized by a single parameter, but at sufficiently low temperatures, non-Lorentzian universal lineshapes characteristic of coherent resonant tunneling emerge, even for strong interactions. For weak transmission, our data supports the recently proposed correlated sequential tunneling picture and is consistent with experimental results on intrinsic nanotube dots.Comment: 4 pages, 4 figure

Corporal Punishment in Public Schools: Does It Violate the Eighth Amendment

Ingraham v. Wright, 525 F.2d 909 (5th Cir.) (en banc), cert. granted, 96 S. Ct. 2200 (1976). Few would deny the extensive authority possessed by the states to establish, regulate, and supervise the educational systems within their respective domains. However well-established that authority may be, states and school officials unmistakably remain subject to the provisions of the Federal Constitution via the supremacy clause. The Supreme Court of the United States has voiced its unequivocal affirmance of this concept: In our system, state-operated schools may not be enclaves of totalitarianism. School officials do not possess absolute authority over their students. Students in school as well as out of a school are \u27persons\u27 under our Constitution. Acknowledgement of constitutional rights of students compels the recognition of a cause of action under 42 U.S.C. § 1983 for the deprivation of these rights by state officials. The simplicity of the above statements is quite deceptive. The complexity of pursuing this cause of action lies primarily in the task of sustaining the allegation that the specific commissions or omissions of the state officials did indeed violate a constitutional guarantee. This was the obstacle faced by the plaintiffs in Ingraham v. Wright, who unsuccessfully attempted to demonstrate that the corporal punishment authorized and administered by defendant school officials deprived them of their constitutional right to be free from cruel and unusual punishment as guaranteed by the eighth amendment to the Constitution. The relative ease with which the Ingraham court dismissed the plaintiffs\u27 section 1983 allegations based on the eighth amendment was not commensurate with the soundness of their contentions. The viability of such contentions is the purpose to which this comment is dedicated