The Amplitude Mode in the Quantum Phase Model

We derive the collective low energy excitations of the quantum phase model of interacting lattice bosons within the superfluid state using a dynamical variational approach. We recover the well known sound (or Goldstone) mode and derive a gapped (Higgs type) mode that was overlooked in previous studies of the quantum phase model. This mode is relevant to ultracold atoms in a strong optical lattice potential. We predict the signature of the gapped mode in lattice modulation experiments and show how it evolves with increasing interaction strength.Comment: 4 pages, 3 figure

Brownian Dynamics of a Sphere Between Parallel Walls

We describe direct imaging measurements of a colloidal sphere's diffusion between two parallel surfaces. The dynamics of this deceptively simple hydrodynamically coupled system have proved difficult to analyze. Comparison with approximate formulations of a confined sphere's hydrodynamic mobility reveals good agreement with both a leading-order superposition approximation as well as a more general all-images stokeslet analysis.Comment: 4 pages, 3 figures, REVTeX with PostScript figure

Dynamical properties of ultracold bosons in an optical lattice

We study the excitation spectrum of strongly correlated lattice bosons for the Mott-insulating phase and for the superfluid phase close to localization. Within a Schwinger-boson mean-field approach we find two gapped modes in the Mott insulator and the combination of a sound mode (Goldstone) and a gapped (Higgs) mode in the superfluid. To make our findings comparable with experimental results, we calculate the dynamic structure factor as well as the linear response to the optical lattice modulation introduced by Stoeferle et al. [Phys. Rev. Lett. 92, 130403 (2004)]. We find that the puzzling finite frequency absorption observed in the superfluid phase could be explained via the excitation of the gapped (Higgs) mode. We check the consistency of our results with an adapted f-sum-rule and propose an extension of the experimental technique by Stoeferle et al. to further verify our findings.Comment: 13 pages, 5 figure

Cluster randomised trials in the medical literature: two bibliometric surveys

Background: Several reviews of published cluster randomised trials have reported that about half did not take clustering into account in the analysis, which was thus incorrect and potentially misleading. In this paper I ask whether cluster randomised trials are increasing in both number and quality of reporting. Methods: Computer search for papers on cluster randomised trials since 1980, hand search of trial reports published in selected volumes of the British Medical Journal over 20 years. Results: There has been a large increase in the numbers of methodological papers and of trial reports using the term 'cluster random' in recent years, with about equal numbers of each type of paper. The British Medical Journal contained more such reports than any other journal. In this journal there was a corresponding increase over time in the number of trials where subjects were randomised in clusters. In 2003 all reports showed awareness of the need to allow for clustering in the analysis. In 1993 and before clustering was ignored in most such trials. Conclusion: Cluster trials are becoming more frequent and reporting is of higher quality. Perhaps statistician pressure works

Quantum critical states and phase transitions in the presence of non equilibrium noise

Quantum critical points are characterized by scale invariant correlations and correspondingly long ranged entanglement. As such, they present fascinating examples of quantum states of matter, the study of which has been an important theme in modern physics. Nevertheless very little is known about the fate of quantum criticality under non equilibrium conditions. In this paper we investigate the effect of external noise sources on quantum critical points. It is natural to expect that noise will have a similar effect to finite temperature, destroying the subtle correlations underlying the quantum critical behavior. Surprisingly we find that in many interesting situations the ubiquitous 1/f noise preserves the critical correlations. The emergent states show intriguing interplay of intrinsic quantum critical and external noise driven fluctuations. We demonstrate this general phenomenon with specific examples in solid state and ultracold atomic systems. Moreover our approach shows that genuine quantum phase transitions can exist even under non equilibrium conditions.Comment: 9 pages, 2 figure

Dynamics of allosteric transitions in GroEL

The chaperonin GroEL-GroES, a machine which helps some proteins to fold, cycles through a number of allosteric states, the $T$ state, with high affinity for substrate proteins (SPs), the ATP-bound $R$ state, and the $R^{\prime\prime}$ ($GroEL-ADP-GroES$) complex. Structures are known for each of these states. Here, we use a self-organized polymer (SOP) model for the GroEL allosteric states and a general structure-based technique to simulate the dynamics of allosteric transitions in two subunits of GroEL and the heptamer. The $T \to R$ transition, in which the apical domains undergo counter-clockwise motion, is mediated by a multiple salt-bridge switch mechanism, in which a series of salt-bridges break and form. The initial event in the $R \to R^{\prime\prime}$ transition, during which GroEL rotates clockwise, involves a spectacular outside-in movement of helices K and L that results in K80-D359 salt-bridge formation. In both the transitions there is considerable heterogeneity in the transition pathways. The transition state ensembles (TSEs) connecting the $T$, $R$, and $R^{\prime\prime}$ states are broad with the the TSE for the $T \to R$ transition being more plastic than the $R\to R^{\prime\prime}$ TSE. The results suggest that GroEL functions as a force-transmitting device in which forces of about (5-30) pN may act on the SP during the reaction cycle.Comment: 32 pages, 10 figures (Longer version than the one published

The dynamic model of enterprise revenue management

The article presents the dynamic model of enterprise revenue management. This model is based on the quadratic criterion and linear control law. The model is founded on multiple regression that links revenues with the financial performance of the enterprise. As a result, optimal management is obtained so as to provide the given enterprise revenue, namely, the values of financial indicators that ensure the planned profit of the organization are acquired

Quantum quenches from integrability: the fermionic pairing model

Understanding the non-equilibrium dynamics of extended quantum systems after the trigger of a sudden, global perturbation (quench) represents a daunting challenge, especially in the presence of interactions. The main difficulties stem from both the vanishing time scale of the quench event, which can thus create arbitrarily high energy modes, and its non-local nature, which curtails the utility of local excitation bases. We here show that nonperturbative methods based on integrability can prove sufficiently powerful to completely characterize quantum quenches: we illustrate this using a model of fermions with pairing interactions (Richardson's model). The effects of simple (and multiple) quenches on the dynamics of various important observables are discussed. Many of the features we find are expected to be universal to all kinds of quench situations in atomic physics and condensed matter.Comment: 10 pages, 7 figure

Effects of random localizing events on matter waves: formalism and examples

A formalism is introduced to describe a number of physical processes that may break down the coherence of a matter wave over a characteristic length scale l. In a second-quantized description, an appropriate master equation for a set of bosonic "modes" (such as atoms in a lattice, in a tight-binding approximation) is derived. Two kinds of "localizing processes" are discussed in some detail and shown to lead to master equations of this general form: spontaneous emission (more precisely, light scattering), and modulation by external random potentials. Some of the dynamical consequences of these processes are considered: in particular, it is shown that they generically lead to a damping of the motion of the matter-wave currents, and may also cause a "flattening" of the density distribution of a trapped condensate at rest.Comment: v3; a few corrections, especially in Sections IV and

Abel-Jacobi maps for hypersurfaces and non commutative Calabi-Yau's

It is well known that the Fano scheme of lines on a cubic 4-fold is a symplectic variety. We generalize this fact by constructing a closed p-form with p=2n-4 on the Fano scheme of lines on a (2n-2)-dimensional hypersurface Y of degree n. We provide several definitions of this form - via the Abel-Jacobi map, via Hochschild homology, and via the linkage class, and compute it explicitly for n = 4. In the special case of a Pfaffian hypersurface Y we show that the Fano scheme is birational to a certain moduli space of sheaves on a p-dimensional Calabi--Yau variety X arising naturally in the context of homological projective duality, and that the constructed form is induced by the holomorphic volume form on X. This remains true for a general non Pfaffian hypersurface but the dual Calabi-Yau becomes non commutative.Comment: 34 pages; exposition of Hochschild homology expanded; references added; introduction re-written; some imrecisions, typos and the orbit diagram in the last section correcte