Effective interactions and large-scale diagonalization for quantum dots

The widely used large-scale diagonalization method using harmonic oscillator basis functions (an instance of the Rayleigh-Ritz method, also called a spectral method, configuration-interaction method, or ``exact diagonalization'' method) is systematically analyzed using results for the convergence of Hermite function series. We apply this theory to a Hamiltonian for a one-dimensional model of a quantum dot. The method is shown to converge slowly, and the non-smooth character of the interaction potential is identified as the main problem with the chosen basis, while on the other hand its important advantages are pointed out. An effective interaction obtained by a similarity transformation is proposed for improving the convergence of the diagonalization scheme, and numerical experiments are performed to demonstrate the improvement. Generalizations to more particles and dimensions are discussed.Comment: 7 figures, submitted to Physical Review B Single reference error fixe

Casimir-Foucault interaction: Free energy and entropy at low temperature

It was recently found that thermodynamic anomalies which arise in the Casimir effect between metals described by the Drude model can be attributed to the interaction of fluctuating Foucault (or eddy) currents [Phys. Rev. Lett. 103, 130405 (2009)]. We show explicitly that the two leading terms of the low-temperature correction to the Casimir free energy of interaction between two plates, are identical to those pertaining to the Foucault current interaction alone, up to a correction which is very small for good metals. Moreover, a mode density along real frequencies is introduced, showing that the Casimir free energy, as given by the Lifshitz theory, separates in a natural manner in contributions from eddy currents and propagating cavity modes, respectively. The latter have long been known to be of little importance to the low-temperature Casimir anomalies. This convincingly demonstrates that eddy current modes are responsible for the large temperature correction to the Casimir effect between Drude metals, predicted by the Lifshitz theory, but not observed in experiments.Comment: 10 pages, 1 figur

Analytical and Numerical Demonstration of How the Drude Dispersive Model Satisfies Nernst's Theorem for the Casimir Entropy

In view of the current discussion on the subject, an effort is made to show very accurately both analytically and numerically how the Drude dispersive model, assuming the relaxation is nonzero at zero temperature (which is the case when impurities are present), gives consistent results for the Casimir free energy at low temperatures. Specifically, we find that the free energy consists essentially of two terms, one leading term proportional to T^2, and a next term proportional to T^{5/2}. Both these terms give rise to zero Casimir entropy as T -> 0, thus in accordance with Nernst's theorem.Comment: 11 pages, 4 figures; minor changes in the discussion. Contribution to the QFEXT07 proceedings; matches version to be published in J. Phys.

Complexity without chaos: Plasticity within random recurrent networks generates robust timing and motor control

It is widely accepted that the complex dynamics characteristic of recurrent neural circuits contributes in a fundamental manner to brain function. Progress has been slow in understanding and exploiting the computational power of recurrent dynamics for two main reasons: nonlinear recurrent networks often exhibit chaotic behavior and most known learning rules do not work in robust fashion in recurrent networks. Here we address both these problems by demonstrating how random recurrent networks (RRN) that initially exhibit chaotic dynamics can be tuned through a supervised learning rule to generate locally stable neural patterns of activity that are both complex and robust to noise. The outcome is a novel neural network regime that exhibits both transiently stable and chaotic trajectories. We further show that the recurrent learning rule dramatically increases the ability of RRNs to generate complex spatiotemporal motor patterns, and accounts for recent experimental data showing a decrease in neural variability in response to stimulus onset

Casimir Force on Real Materials - the Slab and Cavity Geometry

We analyse the potential of the geometry of a slab in a planar cavity for the purpose of Casimir force experiments. The force and its dependence on temperature, material properties and finite slab thickness are investigated both analytically and numerically for slab and walls made of aluminium and teflon FEP respectively. We conclude that such a setup is ideal for measurements of the temperature dependence of the Casimir force. By numerical calculation it is shown that temperature effects are dramatically larger for dielectrics, suggesting that a dielectric such as teflon FEP whose properties vary little within a moderate temperature range, should be considered for experimental purposes. We finally discuss the subtle but fundamental matter of the various Green's two-point function approaches present in the literature and show how they are different formulations describing the same phenomenon.Comment: 24 pages, 11 figures; expanded discussion, one appendix added, 1 new figure and 10 new references. To appear in J. Phys. A: Math. Theo

Gaussians for Electronic and Rovibrational Quantum Dynamics

The assumptions underpinning the adiabatic Born-Oppenheimer (BO) approximation are broken for molecules interacting with attosecond laser pulses, which generate complicated coupled electronic-nuclear wavepackets that generally will have components of electronic and dissociation continua as well as bound-state contributions. The conceptually most straightforward way to overcome this challenge is to treat the electronic and nuclear degrees of freedom on equal quantum-mechanical footing by not invoking the BO approximation at all. Explicitly correlated Gaussian (ECG) basis functions have proved successful for non-BO calculations of stationary molecular states and energies, reproducing rovibrational absorption spectra with very high accuracy. In this paper, we present a proof-of-principle study of the ability of fully flexible ECGs (FFECGs) to capture the intricate electronic and rovibrational dynamics generated by short, high-intensity laser pulses. By fitting linear combinations of FFECGs to accurate wave function histories obtained on a large real-space grid for a regularized 2D model of the hydrogen atom and for the 2D Morse potential we demonstrate that FFECGs provide a very compact description of laser-driven electronic and rovibrational dynamics

How students in high school experience the use of music in physical education

Masteroppgave - Lektor i kroppsøving og idrettsfag - 202