Topological Blocking in Quantum Quench Dynamics

We study the non-equilibrium dynamics of quenching through a quantum critical point in topological systems, focusing on one of their defining features: ground state degeneracies and associated topological sectors. We present the notion of 'topological blocking', experienced by the dynamics due to a mismatch in degeneracies between two phases and we argue that the dynamic evolution of the quench depends strongly on the topological sector being probed. We demonstrate this interplay between quench and topology in models stemming from two extensively studied systems, the transverse Ising chain and the Kitaev honeycomb model. Through non-local maps of each of these systems, we effectively study spinless fermionic $p$-wave paired superconductors. Confining the systems to ring and toroidal geometries, respectively, enables us to cleanly address degeneracies, subtle issues of fermion occupation and parity, and mismatches between topological sectors. We show that various features of the quench, which are related to Kibble-Zurek physics, are sensitive to the topological sector being probed, in particular, the overlap between the time-evolved initial ground state and an appropriate low-energy state of the final Hamiltonian. While most of our study is confined to translationally invariant systems, where momentum is a convenient quantum number, we briefly consider the effect of disorder and illustrate how this can influence the quench in a qualitatively different way depending on the topological sector considered.Comment: 18 pages, 11 figure

Interaction of substrate uridyl 3',5'-adenosine with ribonuclease A: a molecular dynamics study

A wealth of information available from x-ray crystallographic structures of enzyme-ligand complexes makes it possible to study interactions at the molecular level. However, further investigation is needed when i) the binding of the natural substrate must be characterized, because ligands in the stable enzyme-ligand complexes are generally inhibitors or the analogs of substrate and transition state, and when ii) ligand binding is in part poorly characterized. We have investigated these aspects in the binding of substrate uridyl 3',5'-adenosine (UpA) to ribonuclease A (RNase A). Based on the systematically docked RNase A-UpA complex resulting from our previous study, we have undertaken a molecular dynamics simulation of the complex with solvent molecules. The molecular dynamics trajectories of this complex are analyzed to provide structural explanations for varied experimental observations on the ligand binding at the B2 subsite of ribonuclease A. The present study suggests that B2 subsite stabilization can be effected by different active site groups, depending on the substrate conformation. Thus when adenosine ribose pucker is O4'-endo, Gln69 and Glu111 form hydrogen-bonding contacts with adenine base, and when it is C2'-endo, Asn71 is the only amino acid residue in direct contact with this base. The latter observation is in support of previous mutagenesis and kinetics studies. Possible roles for the solvent molecules in the binding subsites are described. Furthermore, the substrate conformation is also examined along the simulation pathway to see if any conformer has the properties of a transition state. This study has also helped us to recognize that small but concerted changes in the conformation of the substrate can result in substrate geometry favorable for 2',3' cyclization. The identified geometry is suitable for intraligand proton transfer between 2'-hydroxyl and phosphate oxygen atom. The possibility of intraligand proton transfer as suggested previously and the mode of transfer before the formation of cyclic intermediate during transphosphorylation are discussed

Insights into the Fold Organization of TIM Barrel from Interaction Energy Based Structure Networks

There are many well-known examples of proteins with low sequence similarity, adopting the same structural fold. This aspect of sequence-structure relationship has been extensively studied both experimentally and theoretically, however with limited success. Most of the studies consider remote homology or “sequence conservation” as the basis for their understanding. Recently “interaction energy” based network formalism (Protein Energy Networks (PENs)) was developed to understand the determinants of protein structures. In this paper we have used these PENs to investigate the common non-covalent interactions and their collective features which stabilize the TIM barrel fold. We have also developed a method of aligning PENs in order to understand the spatial conservation of interactions in the fold. We have identified key common interactions responsible for the conservation of the TIM fold, despite high sequence dissimilarity. For instance, the central beta barrel of the TIM fold is stabilized by long-range high energy electrostatic interactions and low-energy contiguous vdW interactions in certain families. The other interfaces like the helix-sheet or the helix-helix seem to be devoid of any high energy conserved interactions. Conserved interactions in the loop regions around the catalytic site of the TIM fold have also been identified, pointing out their significance in both structural and functional evolution. Based on these investigations, we have developed a novel network based phylogenetic analysis for remote homologues, which can perform better than sequence based phylogeny. Such an analysis is more meaningful from both structural and functional evolutionary perspective. We believe that the information obtained through the “interaction conservation” viewpoint and the subsequently developed method of structure network alignment, can shed new light in the fields of fold organization and de novo computational protein design

Black Holes in Non-flat Backgrounds: the Schwarzschild Black Hole in the Einstein Universe

As an example of a black hole in a non-flat background a composite static spacetime is constructed. It comprises a vacuum Schwarzschild spacetime for the interior of the black hole across whose horizon it is matched on to the spacetime of Vaidya representing a black hole in the background of the Einstein universe. The scale length of the exterior sets a maximum to the black hole mass. To obtain a non-singular exterior, the Vaidya metric is matched to an Einstein universe. The behaviour of scalar waves is studied in this composite model.Comment: 8 pages, 3 postscript figures, minor corrections Journal Ref: accepted for Physical Review

Coexistence of superfluid and Mott phases of lattice bosons

Recent experiments on strongly-interacting bosons in optical lattices have revealed the co-existence of spatially-separated Mott-insulating and number-fluctuating phases. The description of this inhomogeneous situation is the topic of this Letter. We establish that the number-fluctuating phase forms a superfluid trapped between the Mott-insulating regions and derive the associated collective mode structure. We discuss the interlayer's crossover between two- and three-dimensional behavior as a function of the lattice parameters and estimate the critical temperatures for the transition of the superfluid phase to a normal phase

Geometric Finiteness and Non-quasinormal Modes of the BTZ Black Hole

The BTZ black hole is geometrically finite. This means that its three dimensional hyperbolic structure as encoded in its metric is in 1-1 correspondence with the Teichmuller space of its boundary, which is a two torus. The equivalence of different Teichmuller parameters related by the action of the modular group therefore requires the invariance of the monodromies of the solutions of the wave equation around the inner and outer horizons in the BTZ background. We show that this invariance condition leads to the non-quasinormal mode frequencies discussed by Birmingham and Carlip.Comment: 8 Pages, Latex file, minor changes in the text, journal versio

Dirac Quasinormal modes of Schwarzschild black hole

The quasinormal modes (QNMs) associated with the decay of Dirac field perturbation around a Schwarzschild black hole is investigated by using continued fraction and Hill-determinant approaches. It is shown that the fundamental quasinormal frequencies become evenly spaced for large angular quantum number and the spacing is given by $\omega_{\lambda+1}- \omega_{\lambda}=0.38490-0.00000i$. The angular quantum number has the surprising effect of increasing real part of the quasinormal frequencies, but it almost does not affect imaginary part, especially for low overtones. In addition, the quasinormal frequencies also become evenly spaced for large overtone number and the spacing for imaginary part is $Im(\omega_{n+1})-Im(\omega_n)\approx -i/4M$ which is same as that of the scalar, electromagnetic, and gravitational perturbations.Comment: 14 pages, 5 figure

The dynamics of condensate shells: collective modes and expansion

We explore the physics of three-dimensional shell-shaped condensates, relevant to cold atoms in "bubble traps" and to Mott insulator-superfluid systems in optical lattices. We study the ground state of the condensate wavefunction, spherically-symmetric collective modes, and expansion properties of such a shell using a combination of analytical and numerical techniques. We find two breathing-type modes with frequencies that are distinct from that of the filled spherical condensate. Upon trap release and subsequent expansion, we find that the system displays self-interference fringes. We estimate characteristic time scales, degree of mass accumulation, three-body loss, and kinetic energy release during expansion for a typical system of Rb87

Oscillatory pairing of fermions in spin-split traps

As a means of realizing oscillatory pairing between fermions, we study superfluid pairing between two fermion "spin" species that are confined to adjustable spin-dependent trapping potentials. Focusing on the one-dimensional limit, we find that with increasing separation between the spin-dependent traps the fermions exhibit distinct phases, including a fully paired phase, a spin-imbalanced phase with oscillatory pairing, and an unpaired fully spin-polarized phase. We obtain the phase diagram of fermions in such a spin-split trap and discuss signatures of these phases in cold-atom experiments.Comment: 5 pages, 5 figures, RevTe