Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: Application to squeezed parametric oscillation beyond the rotating-wave approximation

Open quantum systems can display periodic dynamics at the classical level either due to external periodic modulations or to self-pulsing phenomena typically following a Hopf bifurcation. In both cases, the quantum fluctuations around classical solutions do not reach a quantum-statistical stationary state, which prevents adopting the simple and reliable methods used for stationary quantum systems. Here we put forward a general and efficient method to compute two-time correlations and corresponding spectral densities of time-periodic open quantum systems within the usual linearized (Gaussian) approximation for their dynamics. Using Floquet theory we show how the quantum Langevin equations for the fluctuations can be efficiently integrated by partitioning the time domain into one-period duration intervals, and relating the properties of each period to the first one. Spectral densities, like squeezing spectra, are computed similarly, now in a two-dimensional temporal domain that is treated as a chessboard with one-period x one-period cells. This technique avoids cumulative numerical errors as well as efficiently saves computational time. As an illustration of the method, we analyze the quantum fluctuations of a damped parametrically-driven oscillator (degenerate parametric oscillator) below threshold and far away from rotating-wave approximation conditions, which is a relevant scenario for modern low-frequency quantum oscillators. Our method reveals that the squeezing properties of such devices are quite robust against the amplitude of the modulation or the low quality of the oscillator, although optimal squeezing can appear for parameters that are far from the ones predicted within the rotating-wave approximation.Comment: Comments and constructive criticism are welcom

Interaction of dietary Pediococcus acidilactici and folic acid on growth performance, haematological parameters and non-specific immune response of finger barbel, Acipenser nudiventris

This study was conducted to investigate the effects of dietary Pediococcus acidilactici and folic acid (FA) and their combinations on growth performance, haematological parameters and non-specific immune response of Acipenser nudiventris. 210 individuals (initial body weight: 12.84± 1.53g) were fed seven practical diets: the basal diet as the control diet was supplemented with two levels of P. acidilactici (2 and 3 g per kg diet), FA (2 and 4 mg per kg diet) and their combinations. The results showed that the group fed a combined diet of P. acidilactici and FA (4 mg FA+3 g P. acidilactici per kg diet) showed significant increase in body weight increase (BWI), specific growth rate (SGR), feed conversion ratio (FCR) and condition factor (CF). However, experimental diets had no significant effects on survival rate. Both haematological indices and leucocyte counts were significantly (p<0.05) influenced by dietary P. acidilactici and FA and their combinations. In the group fed 4 mg FA+3 g P. acidilactici, lysozyme activity and total immunoglobulin (Ig) levels significantly increased compared to those fed other diets (p<0.05). Moreover, the fish fed diets supplemented with 2 mg FA+ 3 g P. acidilactici per kg diet had considerably higher immunoglobulin (IgM) level (p<0.05). Under the experimental conditions, dietary P. acidilactici and FA had a synergistic effect on enhancing growth performance and immunity of A. nudiventris

On the motion of spinning test particles in plane gravitational waves

The Mathisson-Papapetrou-Dixon equations for a massive spinning test particle in plane gravitational waves are analysed and explicit solutions constructed in terms of solutions of certain linear ordinary differential equations. For harmonic waves this system reduces to a single equation of Mathieu-Hill type. In this case spinning particles may exhibit parametric excitation by gravitational fields. For a spinning test particle scattered by a gravitational wave pulse, the final energy-momentum of the particle may be related to the width, height, polarisation of the wave and spin orientation of the particle.Comment: 11 page

Deep recurrent networks predicting the gap evolution in adiabatic quantum computing

One of the main challenges in quantum physics is predicting efficiently the dynamics of observables in many-body problems out of equilibrium. A particular example occurs in adiabatic quantum computing, where finding the structure of the instantaneous gap of the Hamiltonian is crucial in order to optimize the speed of the computation. Inspired by this challenge, in this work we explore the potential of deep learning for discovering a mapping from the parameters that fully identify a problem Hamiltonian to the full evolution of the gap during an adiabatic sweep applying different network architectures. Through this example, we find that a limiting factor for the learnability of the dynamics is the size of the input, that is, how the number of parameters needed to identify the Hamiltonian scales with the system size. We demonstrate that a long short-term memory network succeeds in predicting the gap when the parameter space scales linearly with system size. Remarkably, we show that once this architecture is combined with a convolutional neural network to deal with the spatial structure of the model, the gap evolution can even be predicted for system sizes larger than the ones seen by the neural network during training. This provides a significant speedup in comparison with the existing exact and approximate algorithms in calculating the gap

The effect of geometry on charge confinement in three dimensions

We show that, in contrast to the flat case, the Maxwell theory is not confining in the background of the three dimensional BTZ black-hole (covering space). We also study the effect of the curvature on screening behavior of Maxwell-Chern-Simons model in this space-time.Comment: 8 pages. To be published in Europhysics Letter

Deep Learning of Quantum Many-Body Dynamics via Random Driving

Neural networks have emerged as a powerful way to approach many practical problems in quantumphysics. In this work, we illustrate the power of deep learning to predict the dynamics of a quantummany-body system, where the training is based purely on monitoring expectation values of observables under random driving. The trained recurrent network is able to produce accurate predictions for driving trajectories entirely different than those observed during training. As a proof of principle, here we train the network on numerical data generated from spin models, showing that it can learn the dynamics of observables of interest without needing information about the full quantum state.This allows our approach to be applied eventually to actual experimental data generated from aquantum many-body system that might be open, noisy, or disordered, without any need for a detailedunderstanding of the system. This scheme provides considerable speedup for rapid explorations andpulse optimization. Remarkably, we show the network is able to extrapolate the dynamics to times longer than those it has been trained on, as well as to the infinite-system-size limit

Gravitational waves and dragging effects

Linear and rotational dragging effects of gravitational waves on local inertial frames are studied in purely vacuum spacetimes. First the linear dragging caused by a simple cylindrical pulse is investigated. Surprisingly strong transversal effects of the pulse are exhibited. The angular momentum in cylindrically symmetric spacetimes is then defined and confronted with some results in literature. In the main part, the general procedure is developed for studying weak gravitational waves with translational but not axial symmetry which can carry angular momentum. After a suitable averaging the rotation of local inertial frames due to such rotating waves can be calculated explicitly and illustrated graphically. This is done in detail in the accompanying paper. Finally, the rotational dragging is given for strong cylindrical waves interacting with a rotating cosmic string with a small angular momentum.Comment: Scheduled to appear in Class. Quantum Grav. July 200

Massive Schwinger model and its confining aspects on curved space-time

Using a covariant method to regularize the composite operators, we obtain the bosonized action of the massive Schwinger model on a classical curved background. Using the solution of the bosonic effective action, the energy of two static external charges with finite and large distance separation on a static curved space-time is obtained. The confining behavior of this model is also explicitly discussed.Comment: A disscussion about the infrared regularization and also two references are added. Accepted for publication in Phys. Rev. D (2001