Phases and phase transitions in non-equilibrium quantum matter

This thesis focuses on two recent examples of non-equilibrium quantum phase transitions. In the first part we discuss discrete time crystals (DTCs), which are defined by the fact that they spontaneously break discrete time-translation symmetry. In early realizations of DTCs, many-body localization (MBL) played a crucial role in preventing the periodic drive from heating the system to infinite temperature, which would preclude any possibility of symmetry-breaking. This thesis explores the possibility that dissipation may play an equivalent role, allowing for the possibility of time-translation symmetry-breaking without MBL. We describe the results of an experiment exploring DTC order in a doped semiconductor system with significant dissipation, and a potential description of the interplay of driving, dissipation and interactions using a central spin model. In the second part we discuss measurement-induced phase transitions, where the steady-state entanglement can undergo a phase transition as a function of the measurement rate. First we explore the role of the underlying unitary dynamics in the nature of the phase transition. Previous work has revealed an apparent dichotomy between interacting and non-interacting systems, where interacting systems have a phase transition from volume-law to area-law entanglement at a finite critical measurement rate p, whereas the volume-law for non-interacting systems is destroyed at any p > 0. We study this transition for MBL systems, and find an interpolation between these extremes depending on the measurement basis. We discuss the relevance of the emergent integrability characteristic of MBL and how this intersects with the measurements. Next we study the critical properties of this transition in random 1+1D and 2+1D Clifford circuits, aiming to explore connections with percolation. We utilize a graph-state based simulation algorithm, which provides access to geometric properties of entanglement. We find bulk exponents close to percolation, but possible differences in surface behaviour

Transport and entanglement growth in long-range random Clifford circuits

Conservation laws can constrain entanglement dynamics in isolated quantum systems, manifest in a slowdown of higher Rényi entropies. Here, we explore this phenomenon in a class of long-range random Clifford circuits with U(1) symmetry where transport can be tuned from diffusive to superdiffusive. We unveil that the different hydrodynamic regimes reflect themselves in the asymptotic entanglement growth according to S(t)∝t1/z where the dynamical transport exponent z depends on the probability ∝r−α of gates spanning a distance r. For sufficiently small α, we show that the presence of hydrodynamic modes becomes irrelevant such that S(t) behaves similarly in circuits with and without conservation law. We explain our findings in terms of the inhibited operator spreading in U(1)-symmetric Clifford circuits where the emerging light cones can be understood in the context of classical Lévy flights. Our Letter sheds light on the connections between Clifford circuits and more generic many-body quantum dynamics

Disordered monitored free fermions

Scrambling of quantum information in unitary evolution can be hindered due to measurements and localization. Both these effects lead to pinning of the quantum mechanical wavefunction resulting in suppression of entanglement in the steady state. In monitored free-fermionic models the steady state undergoes an entanglement transition from a critical logarithmically to area-law entangled steady state due to the coupling to an environment. However, in an isolated system arbitrarily weak disorder in one dimension leads to Anderson localization. We investigate a free-fermion system in a random field subject to continuous monitoring, which enables us to probe the non-trivial interplay between measurement-induced phases and disorder. Through the careful analysis of the effective central charge, entanglement entropy, and density-density correlations, we show that the critical phase with conformal symmetry is stable under disorder perturbations until a finite critical disorder strength. We find that the universality class of the transition at finite disorder and dissipative coupling is consistent with the Berezinskii-Kosterlitz-Thouless across the extended phase diagram. Furthermore, destructive interference responsible for Anderson localization is destroyed under finite monitoring strength and the steady state orbital wavefunction exhibits a power-law decay. Our results indicate that critical phase is robust to disorder and the area-law phase is distinct from Anderson localization at weak dissipation. Our work opens the avenue to probe this interesting phase transition in experiments involving electrons in quantum dot arrays and nanowires, and allow quantum control of entangled states of electrons.Comment: 11 pages, 11 figures, 1 tabl

Dimensional hybridity in measurement-induced criticality

Entanglement transitions in quantum dynamics present a novel class of phase transitions in non-equilibrium systems. When a many-body quantum system undergoes hybrid quantum dynamics, consisting of unitary evolution interspersed with monitored random measurements, the steady-state can exhibit a phase transition between volume- and area-law entanglement. The role of dimension in the nature of these transitions is an open problem. There is a dimensional correspondence between measurement-induced transitions in non-unitary quantum circuits in $d$ spatial dimensions and classical statistical mechanical models in $d+1$ dimensions, where the time dimension in the quantum problem is mapped to a spatial dimension in the classical model. In this work we show that the role of dimension is considerably richer by unveiling a form of `dimensional hybridity': critical properties of the steady-state entanglement are governed by a combination of exponents consistent with $d$-dimensional percolation and $(d+1)$-dimensional percolation. We uncover this dimensional hybridity in 1+1D and 2+1D circuits using a graph-state based simulation algorithm where the entanglement structure is encoded in an underlying graph, providing access to the geometric structure of entanglement. We locate the critical point using the tripartite information, revealing area-law entanglement scaling at criticality, and showing that the entanglement transition coincides with the purification transition. The emergence of this `dimensional hybridity' in these non-unitary quantum circuits sheds new light on the universality of measurement-induced transitions, and opens the way for analyzing the quantum error correcting properties of random unitary circuits in higher dimensions.Comment: 17 pages, 15 figures. Updated estimates of surface exponents $\eta_\parallel$ and $\eta_\bot

The legacy of 20th Century landscape change on today’s woodland carabid communities

Aim For many species, the effects of landscape change can involve a time lag and result in an extinction debt. The landscape matrix plays a vital role in supporting species populations. However, the importance of the historical composition and configuration of landscape mosaics has received little attention, with studies focusing on the effects of loss and fragmentation of single (focal) habitat over time. We investigated the importance of historical and contemporary landscape heterogeneity (composition and configuration) to identify how landscape change has, and is continuing to have, an effect on current woodland carabid communities. Location Lowland Britain. Methods Carabids were sampled from woodlands in 36 tetrads of 4 km2. Ordination methods analysed current community response to representations of contemporary and historical (1930’s) landscape heterogeneity. The effects of 80 years of landscape change on current carabid assemblages were compared among tetrads. Results Results are consistent with an extinction debt; carabid communities correlated significantly with the historical composition and configuration of the landscape, but not contemporary landscape configuration. Community assemblages have been shaped, and many species remain affiliated with landscape conditions that no longer exist, notably, large patches of broadleaf woodland and semi-natural grassland. Recent introduction of conifer plantations has had a negative effect on the abundance of many woodland species. For many common, slow-dispersing species, contemporary and historical landscapes offered sub-optimum woodland coverage indicating a lag effect that exceeds 80 years. Increased arable landcover and loss of semi-natural grassland and heathland points towards an ongoing detrimental impact on carabid populations. Main conclusions Compared with focal-habitat studies, the landscape mosaic approach provides a more comprehensive understanding of the effects of widespread landscape change on species communities. Conservation guidance includes new planting, maintenance and restoration of semi-natural habitats, implemented across multiple spatial scales and where feasible, considering both historical and contemporary landscape heterogeneity

Study of the auto-ignition phenomenon of PRFs under HCCI conditions in a RCEM by means of spectroscopy

An investigation of the effects of contour conditions and fuel properties on the auto-ignition and combustion process under HCCI conditions is presented in this study. A parametric variation of initial temperature, intake pressure, compression ratio, oxygen concentration and equivalence ratio has been carried out for Primary Reference Fuels in a Rapid Compression Expansion Machine while applying spectroscopy. The results have also been contrasted with natural chemiluminescence measurements. Additionally, the experiments have been simulated in CHEMKIN and the results derived from the optical techniques have been compared with the results from the chemical kinetics of the process, validating the chemical kinetic mechanism and an additional sub-model of excited OH . Two different scenarios can be seen according to the results from the spectrograph. For very lean or very low-temperature combustions no peak of OH is seen at 310 nm of wavelength, proving that the luminosity came from the CO continuum rather than from the OH . However, for more intense combustions (richer equivalence ratios, higher temperatures or lower EGR rates) spectrography shows a clear peak of OH that has much longer time of life than the corresponding to the CO continuum. The main chemical reaction that causes this two scenarios has been identified as H þ HO2 ) 2OH. The increase of relevance of this reaction at high combustion temperatures causes a higher OH accumulation, which leads to a brighter OH emission. Finally, for low temperature combustions the CO continuum out-shines the OH radiation so the light emitted by this radical cannot be detected by means of natural chemiluminescence. 201The authors would like to thank different members of the LAV team of the ETH-Zurich for their contribution to this work. The authors are grateful to the Universitat Politecnica de Valencia for financing the Ph.D. studies of W. Vera-Tudela (FPI SP1 grant 30/05/2012) and his stay at ETH-Zurich (grant 30/12/2014). Finally, the authors would like to thank the Spanish Ministry of Education for financing the Ph.D. studies of Dario Lopez-Pintor (grant FPU13/02329) and his stay at ETH-Zurich (grant EST14/00626).Desantes Fernández, JM.; García Oliver, JM.; Vera-Tudela-Fajardo, WM.; López Pintor, D.; Schneider, B.; Boulouchos, K. (2016). Study of the auto-ignition phenomenon of PRFs under HCCI conditions in a RCEM by means of spectroscopy. Applied Energy. 179:389-400. https://doi.org/10.1016/j.apenergy.2016.06.134S38940017

A study of phase transformation at the surface of a zirconia ceramic

Yttria Partially Stabilized Zirconia (YPSZ) is one of the most important engineering ceramic materials in that it displays a whole host of outstanding structural and functional properties. Of particular importance for load-bearing applications is the remarkable fracture toughness of YPSZ that arises from its ability to undergo martensitic transformation, a phase transformation that is dependent on stress, temperature, time, humidity, grain size, and the proximity of an interface. The present study was aimed at revealing the influence of the thermal ageing on the tetragonal to monoclinic phase transformation in the near-surface regions of YPSZ. In order to perform qualitative and quantitative characterisation of the phase composition, three principal microscopic techniques were employed: atomic force microscopy, depth resolved Raman micro-spectroscopy, and synchrotron X-ray diffraction. Satisfactory consistency was achieved between the results obtained using different techniques. Moreover, the data obtained in this way displayed complementarity that provided valuable input for the development of thermodynamic modelling of the complex inter-dependence between phase state and processing history of zirconia ceramics

Spatio-temporal Models of Lymphangiogenesis in Wound Healing

Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis), very few have been proposed for the regeneration of the lymphatic network. Lymphangiogenesis is a markedly different process from angiogenesis, occurring at different times and in response to different chemical stimuli. Two main hypotheses have been proposed: 1) lymphatic capillaries sprout from existing interrupted ones at the edge of the wound in analogy to the blood angiogenesis case; 2) lymphatic endothelial cells first pool in the wound region following the lymph flow and then, once sufficiently populated, start to form a network. Here we present two PDE models describing lymphangiogenesis according to these two different hypotheses. Further, we include the effect of advection due to interstitial flow and lymph flow coming from open capillaries. The variables represent different cell densities and growth factor concentrations, and where possible the parameters are estimated from biological data. The models are then solved numerically and the results are compared with the available biological literature.Comment: 29 pages, 9 Figures, 6 Tables (39 figure files in total

Investigating the viability of genetic screening/testing for RA susceptibility using combinations of five confirmed risk loci

Objective. Five loci—the shared epitope (SE) of HLA-DRB1, the PTPN22 gene, a locus on 6q23, the STAT4 gene and a locus mapping to the TRAF1/C5 genetic region—have now been unequivocally confirmed as conferring susceptibility to RA. The largest single effect is conferred by SE. We hypothesized that combinations of susceptibility alleles may increase risk over and above that of any individual locus alone