Microscopic theory of the Andreev gap

We present a microscopic theory of the Andreev gap, i.e. the phenomenon that the density of states (DoS) of normal chaotic cavities attached to superconductors displays a hard gap centered around the Fermi energy. Our approach is based on a solution of the quantum Eilenberger equation in the regime $t_D\ll t_E$, where $t_D$ and $t_E$ are the classical dwell time and Ehrenfest-time, respectively. We show how quantum fluctuations eradicate the DoS at low energies and compute the profile of the gap to leading order in the parameter $t_D/t_E$ .Comment: 4 pages, 3 figures; revised version, more details, extra figure, new titl

Simulation and Theory of Ions at Atmospherically Relevant Aqueous Liquid-Air Interfaces

Chemistry occurring at or near the surfaces of aqueous droplets and thin films in the atmosphere influences air quality and climate. Molecular dynamics simulations are becoming increasingly useful for gaining atomic-scale insight into the structure and reactivity of aqueous interfaces in the atmosphere. Here we review simulation studies of atmospherically relevant aqueous liquid-air interfaces, with an emphasis on ions that play important roles in the chemistry of atmospheric aerosols. In addition to surveying results from simulation studies, we discuss challenges to the refinement and experimental validation of the methodology for simulating ion adsorption to the air-water interface, and recent advances in elucidating the driving forces for adsorption. We also review the recent development of a dielectric continuum theory that is capable of reproducing simulation and experimental data on ion behavior at aqueous interfaces

Detuning-dependent Properties and Dispersion-induced Instabilities of Temporal Dissipative Kerr Solitons in Optical Microresonators

Temporal-dissipative Kerr solitons are self-localized light pulses sustained in driven nonlinear optical resonators. Their realization in microresonators has enabled compact sources of coherent optical frequency combs as well as the study of dissipative solitons. A key parameter of their dynamics is the effective-detuning of the pump laser to the thermally- and Kerr-shifted cavity resonance. Together with the free spectral range and dispersion, it governs the soliton-pulse duration, as predicted by an approximate analytical solution of the Lugiato-Lefever equation. Yet, a precise experimental verification of this relation was lacking so far. Here, by measuring and controlling the effective-detuning, we establish a new way of stabilizing solitons in microresonators and demonstrate that the measured relation linking soliton width and detuning deviates by less than 1 % from the approximate expression, validating its excellent predictive power. Furthermore, a detuning-dependent enhancement of specific comb lines is revealed, due to linear couplings between mode-families. They cause deviations from the predicted comb power evolution, and induce a detuning-dependent soliton recoil that modifies the pulse repetition-rate, explaining its unexpected dependence on laser-detuning. Finally, we observe that detuning-dependent mode-crossings can destabilize the soliton, leading to an unpredicted soliton breathing regime (oscillations of the pulse) that occurs in a normally-stable regime. Our results test the approximate analytical solutions with an unprecedented degree of accuracy and provide new insights into dissipative-soliton dynamics.Comment: Updated funding acknowledgement

DMFT vs Second Order Perturbation Theory for the Trapped 2D Hubbard-Antiferromagnet

In recent literature on trapped ultracold atomic gases, calculations for 2D-systems are often done within the Dynamical Mean Field Theory (DMFT) approximation. In this paper, we compare DMFT to a fully two-dimensional, self-consistent second order perturbation theory for weak interactions in a repulsive Fermi-Hubbard model. We investigate the role of quantum and of spatial fluctuations when the system is in the antiferromagnetic phase, and find that, while quantum fluctuations decrease the order parameter and critical temperatures drastically, spatial fluctuations only play a noticeable role when the system undergoes a phase transition, or at phase boundaries in the trap. We conclude from this that DMFT is a good approximation for the antiferromagnetic Fermi-Hubbard model for experimentally relevant system sizes.Comment: 4 pages, 5 figure

Symplectic algorithm for constant-pressure molecular dynamics using a Nose-Poincare thermostat

We present a new algorithm for isothermal-isobaric molecular-dynamics simulation. The method uses an extended Hamiltonian with an Andersen piston combined with the Nos'e-Poincar'e thermostat, recently developed by Bond, Leimkuhler and Laird [J. Comp. Phys., 151, (1999)]. This Nos'e-Poincar'e-Andersen (NPA) formulation has advantages over the Nos'e-Hoover-Andersen approach in that the NPA is Hamiltonian and can take advantage of symplectic integration schemes, which lead to enhanced stability for long-time simulations. The equations of motion are integrated using a Generalized Leapfrog Algorithm and the method is easy to implement, symplectic, explicit and time reversible. To demonstrate the stability of the method we show results for test simulations using a model for aluminum.Comment: 7 page

Quantum analogues of Hardy's nonlocality paradox

Hardy's nonlocality is a "nonlocality proof without inequalities": it exemplifies that quantum correlations can be qualitatively stronger than classical correlations. This paper introduces variants of Hardy's nonlocality in the CHSH scenario which are realized by the PR-box, but not by quantum correlations. Hence this new kind of Hardy-type nonlocality is a proof without inequalities showing that superquantum correlations can be qualitatively stronger than quantum correlations.Comment: minor fixe

Single-file dynamics with different diffusion constants

We investigate the single-file dynamics of a tagged particle in a system consisting of N hardcore interacting particles (the particles cannot pass each other) which are diffusing in a one-dimensional system where the particles have different diffusion constants. For the two particle case an exact result for the conditional probability density function (PDF) is obtained for arbitrary initial particle positions and all times. The two-particle PDF is used to obtain the tagged particle PDF. For the general N-particle case (N large) we perform stochastic simulations using our new computationally efficient stochastic simulation technique based on the Gillespie algorithm. We find that the mean square displacement for a tagged particle scales as the square root of time (as for identical particles) for long times, with a prefactor which depends on the diffusion constants for the particles; these results are in excellent agreement with very recent analytic predictions in the mathematics literature.Comment: 9 pages, 5 figures. Journal of Chemical Physics (in press

Simulating adiabatic evolution of gapped spin systems

We show that adiabatic evolution of a low-dimensional lattice of quantum spins with a spectral gap can be simulated efficiently. In particular, we show that as long as the spectral gap \Delta E between the ground state and the first excited state is any constant independent of n, the total number of spins, then the ground-state expectation values of local operators, such as correlation functions, can be computed using polynomial space and time resources. Our results also imply that the local ground-state properties of any two spin models in the same quantum phase can be efficiently obtained from each other. A consequence of these results is that adiabatic quantum algorithms can be simulated efficiently if the spectral gap doesn't scale with n. The simulation method we describe takes place in the Heisenberg picture and does not make use of the finitely correlated state/matrix product state formalism.Comment: 13 pages, 2 figures, minor change

Audio-guided mindfulness training in schools and its effect on academic attainment: Contributing to theory and practice

We report the results of a randomized trial (N = 337) examining the effectiveness of a daily audio-guided MBI in raising academic achievement in 16 volunteer classrooms across two socio-demographically diverse United States primary schools. The study's findings were that, over the intervention period, improvements in Math scores, Social Studies scores and Grade Point Averages (GPA) were generally higher for students in intervention classrooms. However, confidence intervals were wide and there was pre-existing variability between schools and grades, resulting in few significant differences as a result of the intervention and generally low effect sizes. Through a careful discussion of the study's results, the paper contributes to theory by generating a comprehensive agenda for follow-up research. The study also contributes to practice by reporting on the effectiveness of technology-enabled mindfulness training because participating teachers seemed able to implement the intervention with almost no further training or need for hiring external mindfulness experts