Expansion dynamics in the one-dimensional Fermi-Hubbard model

Expansion dynamics of interacting fermions in a lattice are simulated within the one-dimensional (1D) Hubbard model, using the essentially exact time-evolving block decimation (TEBD) method. In particular, the expansion of an initial band-insulator state is considered. We analyze the simulation results based on the dynamics of a two-site two-particle system, the so-called Hubbard dimer. Our findings describe essential features of a recent experiment on the expansion of a Fermi gas in a two-dimensional lattice. We show that the Hubbard-dimer dynamics, combined with a two-fluid model for the paired and non-paired components of the gas, gives an efficient description of the full dynamics. This should be useful for describing dynamical phenomena of strongly interacting Fermions in a lattice in general.Comment: Fig. 9 changed, text + supplementary material revise

Hopping modulation in a one-dimensional Fermi-Hubbard Hamiltonian

We consider a strongly repulsive two-component Fermi gas in a one-dimensional (1D) optical lattice described in terms of a Hubbard Hamiltonian. We analyze the response of the system to a periodic modulation of the hopping amplitude in presence of large two body interaction. By (essentially) exact simulations of the time evolution, we find a non-trivial double occupancy frequency dependence. We show how the dependence relates to the spectral features of the system given by the Bethe ansatz. The discrete nature of the spectrum is clearly reflected in the double occupancy after long enough modulation time. We also discuss the implications of the 1D results to experiments in higher dimensional systems.Comment: 4 pages, 5 figures; minor changes in the text, updated references

Bionic models for identification of biological systems

This article proposes a clinical decision support system that processes biomedical data. For this purpose a bionic model has been designed based on neural networks, genetic algorithms and immune systems. The developed system has been tested on data from pregnant women. The paper focuses on the approach to enable selection of control actions that can minimize the risk of adverse outcome. The control actions (hyperparameters of a new type) are further used as an additional input signal. Its values are defined by a hyperparameter optimization method. A software developed with Python is briefly described

Generalized Hartree-Fock Theory for Interacting Fermions in Lattices: Numerical Methods

We present numerical methods to solve the Generalized Hartree-Fock theory for fermionic systems in lattices, both in thermal equilibrium and out of equilibrium. Specifically, we show how to determine the covariance matrix corresponding to the Fermionic Gaussian state that optimally approximates the quantum state of the fermions. The methods apply to relatively large systems, since their complexity only scales quadratically with the number of lattice sites. Moreover, they are specially suited to describe inhomogenous systems, as those typically found in recent experiments with atoms in optical lattices, at least in the weak interaction regime. As a benchmark, we have applied them to the two-dimensional Hubbard model on a 10x10 lattice with and without an external confinement.Comment: 16 pages, 22 figure

The fidelity approach to the Hubbard model

We use the fidelity approach to quantum critical points to study the zero temperature phase diagram of the one-dimensional Hubbard model. Using a variety of analytical and numerical techniques, we analyze the fidelity metric in various regions of the phase diagram, with particular care to the critical points. Specifically we show that close to the Mott transition, taking place at on-site repulsion U=0 and electron density n=1, the fidelity metric satisfies an hyper-scaling form which we calculate. This implies that in general, as one approaches the critical point U=0, n=1, the fidelity metric tends to a limit which depends on the path of approach. At half filling, the fidelity metric is expected to diverge as U^{-4} when U is sent to zero.Comment: 8 pages, 4 figures, added results on the hyper-scaling form of the fidelity metri

Unanswered ethical and scientific questions for trials of invasive interventions for coronary disease: The case of single vessel disease

Trials in the 1990s demonstrated that medical therapy is as effective as invasive therapies for treating single-vessel coronary disease. Yet more recent studies enrolling patients with this condition have focused on evaluating only invasive approaches, namely, stenting versus coronary artery bypass surgery. Several ethical and scientific questions remain unanswered regarding the conduct of these later trials. Were they justified? Why wasn't a medical therapy arm included? Were subjects informed about the availability of medical therapy as an equivalent option? Was optimized medical therapy given prior to randomization? The absence of clear answers to these questions raises the possibility of serious bias in favor of invasive interventions. Considering that medical therapy is underutilized in patients with coronary disease, efforts should focus more on increasing utilization of medical therapy and proper selection of noninvasive interventions

Stamp transferred suspended graphene mechanical resonators for radio-frequency electrical readout

We present a simple micromanipulation technique to transfer suspended graphene flakes onto any substrate and to assemble them with small localized gates into mechanical resonators. The mechanical motion of the graphene is detected using an electrical, radio-frequency (RF) reflection readout scheme where the time-varying graphene capacitor reflects a RF carrier at f=5-6 GHz producing modulation sidebands at f +/- fm. A mechanical resonance frequency up to fm=178 MHz is demonstrated. We find both hardening/softening Duffing effects on different samples, and obtain a critical amplitude of ~40 pm for the onset of nonlinearity in graphene mechanical resonators. Measurements of the quality factor of the mechanical resonance as a function of DC bias voltage Vdc indicate that dissipation due to motion-induced displacement currents in graphene electrode is important at high frequencies and large Vdc

Control of microwave signals using circuit nano-electromechanics

Waveguide resonators are crucial elements in sensitive astrophysical detectors [1] and circuit quantum electrodynamics (cQED) [2]. Coupled to artificial atoms in the form of superconducting qubits [3, 4], they now provide a technologically promising and scalable platform for quantum information processing tasks [2, 5-8]. Coupling these circuits, in situ, to other quantum systems, such as molecules [9, 10], spin ensembles [11, 12], quantum dots [13] or mechanical oscillators [14, 15] has been explored to realize hybrid systems with extended functionality. Here, we couple a superconducting coplanar waveguide resonator to a nano-coshmechanical oscillator, and demonstrate all-microwave field controlled slowing, advancing and switching of microwave signals. This is enabled by utilizing electromechanically induced transparency [16-18], an effect analogous to electromagnetically induced transparency (EIT) in atomic physics [19]. The exquisite temporal control gained over this phenomenon provides a route towards realizing advanced protocols for storage of both classical and quantum microwave signals [20-22], extending the toolbox of control techniques of the microwave field.Comment: 9 figure

A tool to balance benefit and harm when deciding about adjuvant therapy

Adjuvant therapy aims to prevent outgrowth of residual disease but can induce serious side effects. Weighing conflicting treatment effects and communicating this information with patients is not elementary. This study presents a scheme balancing benefit and harm of adjuvant therapy vs no adjuvant therapy. It is illustrated by the available evidence on adjuvant pelvic external beam radiotherapy (RT) for intermediate-risk stage I endometrial carcinoma patients. The scheme comprises five outcome possibilities of adjuvant therapy: patients who benefit from adjuvant therapy (some at the cost of complications) vs those who neither benefit nor contract complications, those who do not benefit but contract severe complications, or those who die. Using absolute risk differences, a fictive cohort of 1000 patients receiving adjuvant RT is categorised. Three large randomised clinical trials were included. Recurrences will be prevented by adjuvant RT in 60 patients, a majority of 908 patients will neither benefit nor suffer severe radiation-induced harm but 28 patients will suffer severe complications due to adjuvant RT and an expected four patients will die. This scheme readily summarises the different possible treatment outcomes and can be of practical value for clinicians and patients in decision making about adjuvant therapies