Dynamics of an inhomogeneous quantum phase transition

We argue that in a second order quantum phase transition driven by an inhomogeneous quench density of quasiparticle excitations is suppressed when velocity at which a critical point propagates across a system falls below a threshold velocity equal to the Kibble-Zurek correlation length times the energy gap at freeze-out divided by $\hbar$. This general prediction is supported by an analytic solution in the quantum Ising chain. Our results suggest, in particular, that adiabatic quantum computers can be made more adiabatic when operated in an "inhomogeneous" way.Comment: 7 pages; version to appear in a special issue of New J. Phy

The scenario of two-dimensional instabilities of the cylinder wake under EHD forcing: A linear stability analysis

We propose to study the stability properties of an air flow wake forced by a dielectric barrier discharge (DBD) actuator, which is a type of electrohydrodynamic (EHD) actuator. These actuators add momentum to the flow around a cylinder in regions close to the wall and, in our case, are symmetrically disposed near the boundary layer separation point. Since the forcing frequencies, typical of DBD, are much higher than the natural shedding frequency of the flow, we will be considering the forcing actuation as stationary. In the first part, the flow around a circular cylinder modified by EHD actuators will be experimentally studied by means of particle image velocimetry (PIV). In the second part, the EHD actuators have been numerically implemented as a boundary condition on the cylinder surface. Using this boundary condition, the computationally obtained base flow is then compared with the experimental one in order to relate the control parameters from both methodologies. After validating the obtained agreement, we study the Hopf bifurcation that appears once the flow starts the vortex shedding through experimental and computational approaches. For the base flow derived from experimentally obtained snapshots, we monitor the evolution of the velocity amplitude oscillations. As to the computationally obtained base flow, its stability is analyzed by solving a global eigenvalue problem obtained from the linearized Navier–Stokes equations. Finally, the critical parameters obtained from both approaches are compared

Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point

We study the adiabatic dynamics of Majorana fermions across a quantum phase transition. We show that the Kibble-Zurek scaling, which describes the density of bulk defects produced during the critical point crossing, is not valid for edge Majorana fermions. Therefore, the dynamics governing an edge state quench is nonuniversal and depends on the topological features of the system. Besides, we show that the localization of Majorana fermions is a necessary ingredient to guaranty robustness against defect production.Comment: Submitted to the Special Issue on "Dynamics and Thermalization in Isolated Quantum Many-Body Systems" in New Journal of Physics. Editors:M. Cazalilla, M. Rigol. New references and some typos correcte

Topological phase transitions between chiral and helical spin textures in a lattice with spin-orbit coupling and a magnetic field

We consider the combined effects of large spin-orbit couplings and a perpendicular magnetic field in a 2D honeycomb fermionic lattice. This system provides an elegant setup to generate versatile spin textures propagating along the edge of a sample. The spin-orbit coupling is shown to induce topological phase transitions between a helical quantum spin Hall phase and a chiral spin-imbalanced quantum Hall state. Besides, we find that the spin orientation of a single topological edge state can be tuned by a Rashba spin-orbit coupling, opening an interesting route towards quantum spin manipulation. We discuss the possible realization of our results using cold atoms trapped in optical lattices, where large synthetic magnetic fields and spin-orbit couplings can be engineered and finely tuned. In particular, this system would lead to the observation of a time-reversal-symmetry-broken quantum spin Hall phase.Comment: 8 pages, 3 figures, Accepted in Europhys. Lett. (Dec 2011

Quenching through Dirac and semi-Dirac points in optical Lattices: Kibble-Zurek scaling for anisotropic Quantum-Critical systems

We propose that Kibble-Zurek scaling can be studied in optical lattices by creating geometries that support, Dirac, Semi-Dirac and Quadratic Band Crossings. On a Honeycomb lattice with fermions, as a staggered on-site potential is varied through zero, the system crosses the gapless Dirac points, and we show that the density of defects created scales as $1/\tau$, where $\tau$ is the inverse rate of change of the potential, in agreement with the Kibble-Zurek relation. We generalize the result for a passage through a semi-Dirac point in $d$ dimensions, in which spectrum is linear in $m$ parallel directions and quadratic in rest of the perpendicular $(d-m)$ directions. We find that the defect density is given by $1 /{\tau^{m\nu_{||}z_{||}+(d-m)\nu_{\perp}z_{\perp}}}$ where $\nu_{||}, z_{||}$ and $\nu_{\perp},z_{\perp}$ are the dynamical exponents and the correlation length exponents along the parallel and perpendicular directions, respectively. The scaling relations are also generalized to the case of non-linear quenching

Ecohydraulic modelling of anabranching rivers

In this paper we provide the first quantitative evidence of the spatial complexity of habitat diversity across the flow regime for locally anabranching channels, and their potential increased biodiversity value in comparison to managed single-thread rivers. Ecohydraulic modelling is used to provide evidence for the potential ecological value of anabranching channels. Hydraulic habitat (biotopes) of an anabranched reach of the River Wear at Wolsingham, UK is compared with an adjacent artificially straightened single-thread reach downstream. 2D hydraulic modelling was undertaken across the flow regime. Simulated depth and velocity data were used to calculate Froude number (Fr) index; known to be closely associated with biotope type, allowing biotope maps to be produced for each flow simulation using published Fr limits. The gross morphology of the anabranched reach appears to be controlling flow hydraulics, creating a complex and diverse biotope distribution at low and intermediate flows. This contrasts markedly with the near uniform biotope pattern modelled for the heavily modified single-thread reach. As discharge increases the pattern of biotopes altered to reflect a generally higher energy system, interestingly, however, a number of low energy biotopes were activated through the anabranched reach as new sub-channels became inundated and this process is creating valuable refugia for macroinvertebrates and fish, during times of flood. In contrast, these low energy areas were not seen in the straightened single thread reach. Model results suggest that anabranched channels have a vital role to play in regulating flood energy on river systems and in creating and maintaining hydraulic habitat diversity

Surface Enhanced Second Harmonic Generation from Macrocycle, Catenane, and Rotaxane Thin Films: Experiments and Theory

Surface enhanced second harmonic generation (SE SHG) experiments on molecular structures, macrocycles, catenanes, and rotaxanes, deposited as monolayers and multilayers by vacuum sublimation on silver, are reported. The measurements show that the molecules form ordered thin films, where the highest degree of order is observed in the case of macrocycle monolayers and the lowest in the case of rotaxane multilayers. The second harmonic generation activity is interpreted in terms of electric field induced second harmonic (EFISH) generation where the electric field is created by the substrate silver atoms. The measured second order nonlinear optical susceptibility for a rotaxane thin film is compared with that obtained by considering only EFISH contribution to SHG intensity. The electric field on the surface of a silver layer is calculated by using the Delphi4 program for structures obtained with TINKER molecular mechanics/dynamics simulations. An excellent agreement is observed between the calculated and the measured SHG susceptibilities.

Chirality Quantum Phase Transition in the Dirac oscillator

We study a relativistic spin-1/2 fermion subjected to a Dirac oscillator coupling and a constant magnetic field. An interplay between opposed chirality interactions culminates in the appearance of a relativistic quantum phase transition, which can be fully characterized. We obtain analytical expressions for the energy gap, order parameter, and canonical quantum fluctuations across the critical point. Moreover, we also discuss the effect of this phase transition on the statistics of the chiral bosonic ensemble, where its super- or sub-Poissonian nature can be controled by means of external parameters. Finally, we study the entanglement properties between the degrees of freedom in the relativistic ground state, where an interesting transition between a bi-separable and a genuinely tripartite entangled state occurs.Comment: RevTex4 file, color figures, submitted for publicatio

Modeling the series of (n x 2) Si-rich reconstructions of beta-SiC(001): a prospective atomic wire?

We perform ab initio plane wave supercell density functional calculations on three candidate models of the (3 x 2) reconstruction of the beta-SiC(001) surface. We find that the two-adlayer asymmetric-dimer model (TAADM) is unambiguously favored for all reasonable values of Si chemical potential. We then use structures derived from the TAADM parent to model the silicon lines that are observed when the (3 x 2) reconstruction is annealed (the (n x 2) series of reconstructions), using a tight-binding method. We find that as we increase n, and so separate the lines, a structural transition occurs in which the top addimer of the line flattens. We also find that associated with the separation of the lines is a large decrease in the HOMO-LUMO gap, and that the HOMO state becomes quasi-one-dimensional. These properties are qualititatively and quantitatively different from the electronic properties of the original (3 x 2) reconstruction.Comment: 22 pages, including 6 EPS figure

A lattice model for the kinetics of rupture of fluid bilayer membranes

We have constructed a model for the kinetics of rupture of membranes under tension, applying physical principles relevant to lipid bilayers held together by hydrophobic interactions. The membrane is characterized by the bulk compressibility (for expansion), the thickness of the hydrophobic part of the bilayer, the hydrophobicity and a parameter characterizing the tail rigidity of the lipids. The model is a lattice model which incorporates strain relaxation, and considers the nucleation of pores at constant area, constant temperature, and constant particle number. The particle number is conserved by allowing multiple occupancy of the sites. An equilibrium ``phase diagram'' is constructed as a function of temperature and strain with the total pore surface and distribution as the order parameters. A first order rupture line is found with increasing tension, and a continuous increase in proto-pore concentration with rising temperature till instability. The model explains current results on saturated and unsaturated PC lipid bilayers and thicker artificial bilayers made of diblock copolymers. Pore size distributions are presented for various values of area expansion and temperature, and the fractal dimension of the pore edge is evaluated.Comment: 15 pages, 8 figure