Semiclassical Description of Wavepacket Revival

We test the ability of semiclassical theory to describe quantitatively the revival of quantum wavepackets --a long time phenomena-- in the one dimensional quartic oscillator (a Kerr type Hamiltonian). Two semiclassical theories are considered: time-dependent WKB and Van Vleck propagation. We show that both approaches describe with impressive accuracy the autocorrelation function and wavefunction up to times longer than the revival time. Moreover, in the Van Vleck approach, we can show analytically that the range of agreement extends to arbitrary long times.Comment: 10 pages, 6 figure

Orthogonality Catastrophe in Parametric Random Matrices

We study the orthogonality catastrophe due to a parametric change of the single-particle (mean field) Hamiltonian of an ergodic system. The Hamiltonian is modeled by a suitable random matrix ensemble. We show that the overlap between the original and the parametrically modified many-body ground states, $S$, taken as Slater determinants, decreases like $n^{-k x^2}$, where $n$ is the number of electrons in the systems, $k$ is a numerical constant of the order of one, and $x$ is the deformation measured in units of the typical distance between anticrossings. We show that the statistical fluctuations of $S$ are largely due to properties of the levels near the Fermi energy.Comment: 12 pages, 8 figure

On the semiclassical theory for universal transmission fluctuations in chaotic systems: the importance of unitarity

The standard semiclassical calculation of transmission correlation functions for chaotic systems is severely influenced by unitarity problems. We show that unitarity alone imposes a set of relationships between cross sections correlation functions which go beyond the diagonal approximation. When these relationships are properly used to supplement the semiclassical scheme we obtain transmission correlation functions in full agreement with the exact statistical theory and the experiment. Our approach also provides a novel prediction for the transmission correlations in the case where time reversal symmetry is present

Measuring the Lyapunov exponent using quantum mechanics

We study the time evolution of two wave packets prepared at the same initial state, but evolving under slightly different Hamiltonians. For chaotic systems, we determine the circumstances that lead to an exponential decay with time of the wave packet overlap function. We show that for sufficiently weak perturbations, the exponential decay follows a Fermi golden rule, while by making the difference between the two Hamiltonians larger, the characteristic exponential decay time becomes the Lyapunov exponent of the classical system. We illustrate our theoretical findings by investigating numerically the overlap decay function of a two-dimensional dynamical system.Comment: 9 pages, 6 figure

Spin and e-e interactions in quantum dots: Leading order corrections to universality and temperature effects

We study the statistics of the spacing between Coulomb blockade conductance peaks in quantum dots with large dimensionless conductance g. Our starting point is the ``universal Hamiltonian''--valid in the g->oo limit--which includes the charging energy, the single-electron energies (described by random matrix theory), and the average exchange interaction. We then calculate the magnitude of the most relevant finite g corrections, namely, the effect of surface charge, the ``gate'' effect, and the fluctuation of the residual e-e interaction. The resulting zero-temperature peak spacing distribution has corrections of order Delta/sqrt(g). For typical values of the e-e interaction (r_s ~ 1) and simple geometries, theory does indeed predict an asymmetric distribution with a significant even/odd effect. The width of the distribution is of order 0.3 Delta, and its dominant feature is a large peak for the odd case, reminiscent of the delta-function in the g->oo limit. We consider finite temperature effects next. Only after their inclusion is good agreement with the experimental results obtained. Even relatively low temperature causes large modifications in the peak spacing distribution: (a) its peak is dominated by the even distribution at kT ~ 0.3 Delta (at lower T a double peak appears); (b) it becomes more symmetric; (c) the even/odd effect is considerably weaker; (d) the delta-function is completely washed-out; and (e) fluctuation of the coupling to the leads becomes relevant. Experiments aimed at observing the T=0 peak spacing distribution should therefore be done at kT<0.1 Delta for typical values of the e-e interaction.Comment: 15 pages, 4 figure

Semiclassical approach to fidelity amplitude

The fidelity amplitude is a quantity of paramount importance in echo type experiments. We use semiclassical theory to study the average fidelity amplitude for quantum chaotic systems under external perturbation. We explain analytically two extreme cases: the random dynamics limit --attained approximately by strongly chaotic systems-- and the random perturbation limit, which shows a Lyapunov decay. Numerical simulations help us bridge the gap between both extreme cases.Comment: 10 pages, 9 figures. Version closest to published versio

Aerosol-Assisted CVD-Grown PdO Nanoparticle-Decorated Tungsten Oxide Nanoneedles Extremely Sensitive and Selective to Hydrogen

We report for the first time the successful synthesis of palladium (Pd) nanoparticle (NP)-decorated tungsten trioxide (WO3) nanoneedles (NNs) via a two-step aerosol-assisted chemical vapor deposition approach. Morphological, structural, and elemental composition analysis revealed that a Pd(acac)2 precursor was very suitable to decorate WO3 NNs with uniform and well-dispersed PdO NPs. Gas-sensing results revealed that decoration with PdO NPs led to an ultrasensitive and selective hydrogen (H2) gas sensor (sensor response peaks at 1670 at 500 ppm of H2) with low operating temperature (150 °C). The response of decorated NNs is 755 times higher than that of bare WO3 NNs. Additionally, at a temperature near that of the ambient temperature (50 °C), the response of this sensor toward the same concentration of H2 was 23, which is higher than that of some promising sensors reported in the literature. Finally, humidity measurements showed that PdO/WO3 sensors displayed low-cross-sensitivity toward water vapor, compared to bare WO3 sensors. The addition of PdO NPs helps to minimize the effect of ambient humidity on the sensor response

Coulomb blockade conductance peak fluctuations in quantum dots and the independent particle model

We study the combined effect of finite temperature, underlying classical dynamics, and deformations on the statistical properties of Coulomb blockade conductance peaks in quantum dots. These effects are considered in the context of the single-particle plus constant-interaction theory of the Coulomb blockade. We present numerical studies of two chaotic models, representative of different mean-field potentials: a parametric random Hamiltonian and the smooth stadium. In addition, we study conductance fluctuations for different integrable confining potentials. For temperatures smaller than the mean level spacing, our results indicate that the peak height distribution is nearly always in good agreement with the available experimental data, irrespective of the confining potential (integrable or chaotic). We find that the peak bunching effect seen in the experiments is reproduced in the theoretical models under certain special conditions. Although the independent particle model fails, in general, to explain quantitatively the short-range part of the peak height correlations observed experimentally, we argue that it allows for an understanding of the long-range part.Comment: RevTex 3.1, 34 pages (including 13 EPS and PS figures), submitted to Phys. Rev.

Normalizing single-cell RNA sequencing data: challenges and opportunities

Single-cell transcriptomics is becoming an important component of the molecular biologist's toolkit. A critical step when analyzing data generated using this technology is normalization. However, normalization is typically performed using methods developed for bulk RNA sequencing or even microarray data, and the suitability of these methods for single-cell transcriptomics has not been assessed. We here discuss commonly used normalization approaches and illustrate how these can produce misleading results. Finally, we present alternative approaches and provide recommendations for single-cell RNA sequencing users

The Addition Spectrum and Koopmans' Theorem for Disordered Quantum Dots

We investigate the addition spectrum of disordered quantum dots containing spinless interacting fermions using the self-consistent Hartree-Fock approximation. We concentrate on the regime r_s >~1, with finite dimensionless conductance g. We find that in this approximation the peak spacing fluctuations do not scale with the mean single particle level spacing for either Coulomb or nearest neighbour interactions when r_s >~1. We also show that Koopmans' approximation to the addition spectrum can lead to errors that are of order the mean level spacing or larger, both in the mean addition spectrum peak spacings, and in the peak spacing fluctuations.Comment: 35 pages including 22 figures (eps