Ultracold atoms loaded into optical lattices are nearly ideal experimental realizations of quantum lattice models. Because numerical simulations of fermionic systems are NP hard and no general analytical solution exists, experiments on ultracold fermionic gases in optical lattices could thus be very useful in elucidating the properties of the fermionic Hubbard model and to probe exotic quantum phases, such as d-wave resonating valence bond (RVB) phases. A key ingredient in engineering lattice models and tuning interactions between particles are Feshbach resonances. We discuss the properties of ultracold Fermi gases when crossing a Feshbach resonance and explain the short molecule lifetimes found in recent experiments, as well as the lifting of fermions into higher bands due to entanglement of Bloch states. By relating the double occupancy of the lattice to the temperature, we provide a means for thermometry in fermionic lattice systems, previously not accessible experimentally. Our thermometry results explain the low molecule formation rates and show that current experiments are performed at temperatures higher than expected: considerably lower temperatures are required for fermionic systems to be used as quantum simulators. Work done in collaboration with A. Esposito and M. Troyer.

DNA, the molecule of life, has a wide variety of properties that are of interest also from a purely physics perspective. We will discuss a number of these properties and the associated problems they pose for physicists. These include its equation of state, its phase diagram, the nature of its condensed mesophases, its elastic properties, and the interactions between different DNA molecules.

When nonlinear oscillators with stable limit cycles are subject to periodic forces, these oscillators may become entrained or mode locked to the driving force. Remarkably, a similar phenomenon occurs when the nonlinear oscillators are driven by a random force. In particular, when nonlinear oscillators with different initial conditions are strongly driven with the same random force, their fluctuating behavior may reliably converge to an identical, synchronized response. This analysis suggests experimental procedures for assessing the nonlinear response of biological, chemical, and physical oscillators to fluctuating inputs and provides immediate application to an understanding of the reliable firing of cortical neurons and the processing of neuronal information.

Over the past 80 years there have been many attempts to characterize network structure and its effects on diffusive processes. Much of this work has focused on the spread of infectious disease and epidemiological analogs of the percolation threshold. Unfortunately, the many results for lattices, trees, and even random graphs cannot be applied in this context. Moreover, to be useful, models must provide more detailed information than is captured by a phase diagram. Although the dynamics are almost trivial, the coupling between dynamics and what we usually think of as boundary conditions creates a problem that appears to be irreducibly complex. I will explain why this is so in terms of the assumptions required to derive the usual collective models. I will also define and give examples of structural measures that provide the necessary detailed information. These measures are clearly computationally hard to evaluate, but we may be able to approximate them well through a Monte Carlo approach.

In this talk I will give an overview of the zero-range process (ZRP), a simple hopping particle model in which particles move on a lattice interacting only with other particles at the same site. I will detail some of the interesting features and useful properties of the model and briefly discuss some areas in which it has recently found application. Finally I will present some results on a generalisation of the zero-range process where a small number of long-range interactions are introduced.

In this talk I will be discussing about generation of monochromatic acoustic phonons using ultrafast (femtosecond) laser excitation of GaAs/AlAs superlattices. I will present some experimental results which show the monochromatic nature of the phonons thus generated. Secondly, I will discuss about another possible method for generation of monochromatic acoustic phonons - electrical "pumping" of a GaAs/AlAs superlattice device - a THz SASER. Briefly, I will show some recent results on the SASER device.

We demonstrate spatial separation of carriers with opposite spin orientations in a non-magnetic semiconductor. An ability to manipulate spin of charge carries in a controllable fashion is central to the rapidly developing field of spintronics, as well as for the development of spin-based devices for quantum information processing. However, creation of spin-polarized currents is proven to be a formidable challenge and, previously, required either injection from magnetic materials or application of strong Zeeman magnetic field. We show that in a non-magnetic semiconductor with spin-orbit interactions spins can be spatially separated in a " spin spectrometer " , utilizing difference in momenta and, thus, cyclotron radii, for two spin polarizations. For holes in GaAs almost 100% bipolar spin filtering has been achieved in magnetic focusing geometry with spatial separation of polarized beams by 0.2 microns. We confirmed spin polarization of the injected currents by applying strong Zeeman field and using point contacts as spin filters. Spin-orbit interaction constant has been measured directly in these experiments. The new technique of spin injection/detection opens a possibility to investigate density and electric field dependence of spin-orbit interactions, spin dynamics at a few tenths of picoseconds without RF fields, and shed light on such outstanding problems as " 0.7 anomaly " in quantum point contacts by measuring spin polarization of charge carriers.

In the context of statistical mechanics, duality relates properties of a system at low and high temperatures (strong and weak coupling constants in Euclidean Field Theories), and observables describing order and disorder. Hence duality yields a lot of information about phase diagrams and the nature of phases of some systems, and several self-dual models appear to be solvable. Starting with the work of Kramers and Wannier on 2D Ising Model, a number of models, whose configurations form an abelian group, have been shown to be self-dual, almost all of them two-dimensional. Using a bit of easy commutative algebra, the most general self-dual models on simple lattices will be obtained, also in dimension larger than two. Special properties of self-dual models known earlier and a number of problems will be discussed.

Today, almost any cutting-edge nanoscience effort includes extensive atomic resolution electron microscopy. Recent technological advances in the field of transmission electron microscopy (such as aberration correction) have increased the spatial resolution into the sub-Ångstrom range, the energy resolution into the sub-eV range, and the sensitivity to resolve single atoms. Atomic-scale analysis plays a unique role in discovering how structures function on the nanoscale.

Virginia Tech is addressing this fundamental characterization need by the establishment of a new user facility with its core facility – a ‘FEI Titan’ scanning / transmission electron microscope (S/TEM), a dedicated aberration corrector system with state-of-the-art imaging (HRTEM phase contrast, exit-wave reconstruction, HAADF-STEM ‘Z-contrast’, tomography, …) and spectroscopic capabilities (EDX, EELS, EFTEM). The application of these techniques will provide critical information to understand phenomena on the nanoscale. I will briefly discuss the exciting new electron microscopy research opportunities that exist now at Virginia Tech. The ‘strategic plan‘ includes attaching a spherical aberration (CS) corrector for the image plane and the application of new state-of-the-art experimental methodologies.

As an example, I will show how advanced TEM has been used to describe a comprehensive picture of the general light emitting mechanism of commercially available high-brightness InGaN/GaN based green light emitting diodes (LED). For the first time, the local indium stoichiometry has been linked to the local electronic structure inside the quantum well (QW) structure. This challenge was addressed by application of high-resolution TEM (HRTEM), reconstruction of the exit wave (EWR), annular dark field (ADF) TEM, and Z-contrast imaging (HAADF-STEM) to characterize the atom distribution. Furthermore, valence electron energy loss spectroscopy (VEELS) has determined local band gap fluctuations.

Finally, I briefly would like to focus on how we will achieve atomic resolution in 3-D electron microscopy (electron tomography) in the near future.

Classical equilibrium simulations of biomolecules struggle to sample a space of configurations that is globally sparse, yet locally very dense. Slow (in computer time) transitions between locally stable conformations exacerbate problems of initial state bias and statistical error that plague all simulations. I will discuss a new method to assess these types of errors, in which the sampled configurations are divided up to build a structural histogram. The statistical properties of the structural histogram then offer a unique view of the sampling of the simulation.

Single molecule magnets (SMMs) are magnetic nanostructures that consist of a core of strongly exchange-coupled transition metal ions with a large collective magnetic moment per molecule, thus far up to 26 Bohr magnetons, and a predominantly uniaxial magnetic anisotropy. Their molecular nature enables experimental studies of nearly monodisperse ensembles of nanomagnets with well-defined size, shape, chemical composition, and magnetic anisotropy. Specifically, quantum tunneling of the magnetization (QTM) has been clearly demonstrated and studied in these materials. This talk will present studies of QTM that combine microwave spectroscopy (10-50 GHz) with high sensitivity micro-Hall effect magnetometry using integrated (EPR and magnetometry) sensors. This method enables the monitoring of spin- state populations in the presence of microwave radiation and a direct measure of the energy splitting between high-spin states. It also enables characterization of the energy relaxation rate and decoherence time of these superposition states.

The description of excited states in solid is a challenging and important problem in condensed matter physics as the transport and the optical properties of materials are related to the excited states. Until recently the density functional theory (DFT) based on the local density approximation (LDA) has been the choice of method in the atomistic first principle material simulations. In spite of its success in the describing the ground state properties, such as lattice constants, bulk moduli, etc., the commonly used LDA method vastly underestimates the electron band gap. In my talk I will discuss recent developments in the screened-exchange (sX) density functional method as an approach to address the band gap problem in LDA. Inclusion of short-range exact exchange interaction within DFT formalism improves the band gap dramatically. I will present the comparison of LDA and sX formalism and the electron-electron interaction in sX DFT to provide the physical picture behind such a large band gap correction. I will also present sX DFT applications to various semiconductor systems.

We explore a broad class of single species models, trying to quantitatively estimate various aspects of reaction kinetics. Among the questions we have been studying are estimates of rare events probabilities and classification of absorbing phase transitions.

We develop a rigorous, simple, and efficient method to calculate the rare event statistics in reaction-diffusion systems. To this end, we develop a Hamiltonian formulation of reaction-diffusion dynamics. Although the system is specified by a set of rules, rather than a Hamiltonian, one may nevertheless show that there is a certain canonical Hamiltonian associated with the systems dynamics.

As for absorbing phase transitions, we suggest a simple scheme, making it possible to have, at least, an educated guess regarding the universality class of a reaction-diffusion model at hand. The scheme is based on the topology of phase portraits of the system's Hamiltonian.