Loschmidt echo and fidelity decay near an exceptional point

Non-Hermitian classical and open quantum systems near an exceptional point (EP) are known to undergo strong deviations in their dynamical behavior under small perturbations or slow cycling of parameters as compared to Hermitian systems. Such a strong sensitivity is at the heart of many interesting phenomena and applications, such as the asymmetric breakdown of the adiabatic theorem, enhanced sensing, non-Hermitian dynamical quantum phase transitions and photonic catastrophe. Like for Hermitian systems, the sensitivity to perturbations on the dynamical evolution can be captured by Loschmidt echo and fidelity after imperfect time reversal or quench dynamics. Here we disclose a rather counterintuitive phenomenon in certain non-Hermitian systems near an EP, namely the deceleration (rather than acceleration) of the fidelity decay and improved Loschmidt echo as compared to their Hermitian counterparts, despite large (non-perturbative) deformation of the energy spectrum introduced by the perturbations. This behavior is illustrated by considering the fidelity decay and Loschmidt echo for the single-particle hopping dynamics on a tight-binding lattice under an imaginary gauge field.Comment: 11 pages, 6 figures, to appear in Annalen der Physi

Quantization of a generally covariant gauge system with two super Hamiltonian constraints

The Becci-Rouet-Stora-Tyutin (BRST) operator quantization of a finite-dimensional gauge system featuring two quadratic super Hamiltonian and m linear supermomentum constraints is studied as a model for quantizing generally covariant gauge theories. The proposed model ``completely'' mimics the constraint algebra of General Relativity. The Dirac constraint operators are identified by realizing the BRST generator of the system as a Hermitian nilpotent operator, and a physical inner product is introduced to complete a consistent quantization procedure.Comment: 17 pages. Latex file. Minor changes, two references adde

Multistable Pulse-like Solutions in a Parametrically Driven Ginzburg-Landau Equation

It is well known that pulse-like solutions of the cubic complex Ginzburg-Landau equation are unstable but can be stabilised by the addition of quintic terms. In this paper we explore an alternative mechanism where the role of the stabilising agent is played by the parametric driver. Our analysis is based on the numerical continuation of solutions in one of the parameters of the Ginzburg-Landau equation (the diffusion coefficient $c$), starting from the nonlinear Schr\"odinger limit (for which $c=0$). The continuation generates, recursively, a sequence of coexisting stable solutions with increasing number of humps. The sequence "converges" to a long pulse which can be interpreted as a bound state of two fronts with opposite polarities.Comment: 13 pages, 6 figures; to appear in PR

Isolation of stromal vascular fraction cell suspensions from mouse and human adipose tissues for downstream applications.

This protocol outlines a reliable and versatile approach to isolate stromal vascular fraction cells from different adipose tissues across human and mouse species. A number of downstream applications can then be performed to gain an appreciation of the functional activity of unique adipose tissue-resident cell populations. For complete details on the use and execution of this protocol, please refer to Macdougall et al. (2018)

SL(2,R) model with two Hamiltonian constraints

We describe a simple dynamical model characterized by the presence of two noncommuting Hamiltonian constraints. This feature mimics the constraint structure of general relativity, where there is one Hamiltonian constraint associated with each space point. We solve the classical and quantum dynamics of the model, which turns out to be governed by an SL(2,R) gauge symmetry, local in time. In classical theory, we solve the equations of motion, find a SO(2,2) algebra of Dirac observables, find the gauge transformations for the Lagrangian and canonical variables and for the Lagrange multipliers. In quantum theory, we find the physical states, the quantum observables, and the physical inner product, which is determined by the reality conditions. In addition, we construct the classical and quantum evolving constants of the system. The model illustrates how to describe physical gauge-invariant relative evolution when coordinate time evolution is a gauge.Comment: 9 pages, 1 figure, revised version, to appear in Phys. Rev.

Photonic realization of the relativistic Kronig-Penney model and relativistic Tamm surface states

Photonic analogues of the relativistic Kronig-Penney model and of relativistic surface Tamm states are proposed for light propagation in fibre Bragg gratings (FBGs) with phase defects. A periodic sequence of phase slips in the FBG realizes the relativistic Kronig-Penney model, the band structure of which being mapped into the spectral response of the FBG. For the semi-infinite FBG Tamm surface states can appear and can be visualized as narrow resonance peaks in the transmission spectrum of the grating

Reflectionless Tunnelling of Light in Gradient Optics

We analyse the optical (or microwave) tunnelling properties of electromagnetic waves passing through thin films presenting a specific index profile providing a cut-off frequency, when they are used below this frequency. We show that contrary to the usual case of a square index profile, where tunnelling is accompanied with a strong attenuation of the wave due to reflection, such films present the possibility of a reflectionless tunnelling, where the incoming intensity is totally transmitted

New selective dissolution process to quantify reaction extent and product stability in metakaolin-based geopolymers

A selective dissolution process is developed that can quantify the amount of soluble material, geopolymer gel and remnant unreacted precursor in metakaolin-based geopolymer systems and determine the nanostructural features of the raw materials and geopolymer gel components. The susceptibility of alkalis leachability from the alkaline aluminosilicate hydrate-type gel (N-A-S-H) produced during the geopolymerization is not fully understood. This phenomenon led to deleterious processes from a microstructural, aesthetic and performance point of view. Geopolymers were synthesised using different contents and types of alkalis (M/Al = 0.50–0.83, where M represents Na or K), different contents of soluble silica in the activator (expressed as SiO2/M2O ratio of 1.0, 0.5 and 0.0), and curing temperatures (25 and 50 °C). The selective dissolution process is based on neutral dissolution at pH 7 to extract the soluble materials and acid dissolution using a strong acid at pH 0 to dissolve the geopolymer gel, which provides for the first time a method to quantify the (i) soluble material, (ii) geopolymer gel and (iii) unreacted material in geopolymers. The soluble material provides a reliable indication of the materials that can be removed from the geopolymers in a neutral pH environment and hence the potential for leaching and efflorescence, which is useful for durability prediction and service life. Quantification of remnant unreacted metakaolin determines the reactivity of the precursor and assesses the suitability of different synthesis conditions for varied applications. This work therefore provides a novel and widely applicable approach to determine the susceptibility of geopolymer materials to leaching

Polarisation Patterns and Vectorial Defects in Type II Optical Parametric Oscillators

Previous studies of lasers and nonlinear resonators have revealed that the polarisation degree of freedom allows for the formation of polarisation patterns and novel localized structures, such as vectorial defects. Type II optical parametric oscillators are characterised by the fact that the down-converted beams are emitted in orthogonal polarisations. In this paper we show the results of the study of pattern and defect formation and dynamics in a Type II degenerate optical parametric oscillator for which the pump field is not resonated in the cavity. We find that traveling waves are the predominant solutions and that the defects are vectorial dislocations which appear at the boundaries of the regions where traveling waves of different phase or wave-vector orientation are formed. A dislocation is defined by two topological charges, one associated with the phase and another with the wave-vector orientation. We also show how to stabilize a single defect in a realistic experimental situation. The effects of phase mismatch of nonlinear interaction are finally considered.Comment: 38 pages, including 15 figures, LATeX. Related material, including movies, can be obtained from http://www.imedea.uib.es/Nonlinear/research_topics/OPO

Control of superluminal transit through a heterogeneous medium

We consider pulse propagation through a two component composite medium (metal inclusions in a dielectric host) with or without cavity mirrors. We show that a very thin slab of such a medium, under conditions of localized plasmon resonance, can lead to significant superluminality with detectable levels of transmitted pulse. A cavity containing the heterogeneous medium is shown to lead to subluminal-to-superluminal transmission depending on the volume fraction of the metal inclusions. The predictions of phase time calculations are verified by explicit calculations of the transmitted pulse shapes. We also demonstrate the independence of the phase time on system width and the volume fraction under specific conditions.Comment: 21 Pages,5 Figures (Published in Journal of Modern Optics