College of Arts and Scienceshttps://hdl.handle.net/2144/9052019-06-16T11:21:56Z2019-06-16T11:21:56ZMoral critique and philosophical psychologyKatsafanas, Paulhttps://hdl.handle.net/2144/360062019-06-14T16:15:54Z2018-01-01T00:00:00ZMoral critique and philosophical psychology
Katsafanas, Paul
Given the richness of Nietzsche’s texts and the variety of his concerns, picking just two key
topics is no easy task. I am going to focus on two issues that are both obvious and elusive:
obvious, because they are some of Nietzsche’s central concerns, and elusive, because the
literature hasn’t yet come to terms with these topics. Nietzsche’s approach to these topics is
distinctive, his arguments complex and interwoven, so that his discussions can appear
incongruously varied, even contradictory.
2018-01-01T00:00:00ZNatural stabilization of the Higgs boson’s mass and alignmentLane, KennethShepherd, Williamhttps://hdl.handle.net/2144/360052019-06-14T16:15:51ZNatural stabilization of the Higgs boson’s mass and alignment
Lane, Kenneth; Shepherd, William
Current data from the LHC indicate that the 125 GeV Higgs boson, H , is either the single Higgs of the Standard Model or, to a good approximation, an "aligned Higgs." We propose that H is the pseudo-Goldstone dilaton of Gildener and Weinberg. Models based on their mechanism of scale symmetry breaking can naturally account for the Higgs boson's low mass and aligned couplings. We conjecture that they are the only way to achieve a "Higgslike dilaton" that is actually the Higgs boson. These models further imply the existence of additional Higgs bosons in the vicinity of 200 to about 550 GeV. We illustrate our proposal in a version of the two-Higgs-doublet model of Lee and Pilaftsis. Our version of this model is consistent with published precision electroweak and collider physics data. We describe tests to confirm or exclude this model, possibly with available LHC data.
Place after prison: neighborhood attachment and attainment during reentrySimes, Jessica T.https://hdl.handle.net/2144/360042019-06-14T16:15:52ZPlace after prison: neighborhood attachment and attainment during reentry
Simes, Jessica T.
Over 600,000 people leave prison and become residents of neighborhoods across the United States annually. Using a longitudinal survey of people returning to Greater Boston, this study examines disparities in neighborhood attainment after prison. Accounting for levels of pre-prison neighborhood disadvantage, Black and Hispanic respondents moved into significantly more disadvantaged areas than whites. Forty percent of respondents initially moved to only one of two Boston community areas. Housing is an important neighborhood sorting mechanism: living in concentrated disadvantage was more likely for those residing in household arrangements with family or friends, or in emergency or transitional housing. Significantly, neighborhood residence was not attained by all: a quarter of respondents left prison and entered formal institutional settings or lived in extreme social marginality throughout Boston. Housing insecurity, re-incarceration, and profound racial disparities in neighborhood context explain the ecological structure of social inequality in urban neighborhoods in an era of mass incarceration.
Place and punishment: the spatial context of incarcerationSimes, Jessica T.https://hdl.handle.net/2144/359842019-06-14T16:15:49ZPlace and punishment: the spatial context of incarceration
Simes, Jessica T.
OBJECTIVES: Research on race and urban poverty views incarceration as a new and important aspect of social disadvantage in inner-city neighborhoods. However, in quantitative studies of the spatial distribution of imprisonment across neighborhoods, the pattern outside urban areas has not been examined. This paper offers a unique analysis of disaggregated prison admissions and investigates the spatial concentrations and levels of admissions for the entire state of Massachusetts.
METHODS: Spatial regressions estimate census tract-level prison admission rates in relation to racial demographics, social and economic disadvantage, arrest rates, and violent crime; an analysis of outlier neighborhoods examines the surprisingly high admission rates in small cities.
FINDINGS: Regression analysis yields three findings. First, incarceration is highly spatially concentrated: census tracts covering 15% of the state’s population account for half of all prison admissions. Second, across urban and non-urban areas, incarceration is strongly related to concentrated disadvantage and the share of the black population, even after controlling for arrest and crime rates. Third, the analysis shows admission rates in small urban satellite cities and suburbs comprise the highest rates in the sample and far exceed model predictions.
CONCLUSION: Mass incarceration emerged not just to manage distinctively urban social problems but was characteristic of a broader mode of governance evident in communities often far-removed from deep inner-city poverty. These notably high levels and concentrations in small cities should be accounted for when developing theories of concentrated disadvantage or policies designed to ameliorate the impacts of mass incarceration on communities.
Decay of superfluid currents in a moving system of strongly interacting bosonsPolkovnikov, AnatoliAltman, E.Demler, E.Halperin, B.Lukin, M. D.https://hdl.handle.net/2144/359802019-06-14T16:15:48Z2005-06-01T00:00:00ZDecay of superfluid currents in a moving system of strongly interacting bosons
Polkovnikov, Anatoli; Altman, E.; Demler, E.; Halperin, B.; Lukin, M. D.
We analyze the stability and decay of supercurrents of strongly interacting bosons on optical lattices. At the mean-field level, the system undergoes an irreversible dynamic phase transition, whereby the current decays beyond a critical phase gradient that depends on the interaction strength. At commensurate filling the transition line smoothly interpolates between the classical modulational instability of weakly interacting bosons and the equilibrium Mott transition at zero current. Below the mean-field instability, the current can decay due to quantum and thermal phase slips. We derive asymptotic expressions of the decay rate near the critical current. In a three-dimensional optical lattice this leads to very weak broadening of the transition. In one and two dimensions the broadening leads to significant current decay well below the mean-field critical current. We show that the temperature scale below which quantum phase slips dominate the decay of supercurrents is easily within experimental reach.
2005-06-01T00:00:00ZNonequilibrium Gross-Pitaevskii dynamics of boson lattice modelsPolkovnikov, AnatoliSachdev, SubirGirvin, S. M.https://hdl.handle.net/2144/359792019-06-14T16:15:31Z2002-11-01T00:00:00ZNonequilibrium Gross-Pitaevskii dynamics of boson lattice models
Polkovnikov, Anatoli; Sachdev, Subir; Girvin, S. M.
Motivated by recent experiments on trapped ultracold bosonic atoms in an optical lattice potential, we consider the nonequilibrium dynamic properties of such bosonic systems for a number of experimentally relevant situations. When the number of bosons per lattice site is large, there is a wide parameter regime where the effective boson interactions are strong, but the ground state remains a superfluid (and not a Mott insulator): we describe the conditions under which the dynamics in this regime can be described by a discrete Gross-Pitaevskii equation. We describe the evolution of the phase coherence after the system is initially prepared in a Mott insulating state, and then allowed to evolve after a sudden change in parameters places it in a regime with a superfluid ground state. We also consider initial conditions with a “π phase” imprint on a superfluid ground state (i.e., the initial phases of neighboring wells differ by π), and discuss the subsequent appearance of the density wave order and “Schrödinger cat,” i.e., macroscopic quantum interference, states.
2002-11-01T00:00:00ZEmpowerment in a controlling place: youth program facilitators and resistance to school disciplineGreenberg, Max A.https://hdl.handle.net/2144/359782019-06-14T16:15:53ZEmpowerment in a controlling place: youth program facilitators and resistance to school discipline
Greenberg, Max A.
Research has described a nearly monolithic culture of control that shapes the disciplinary practices and experiences of youth in urban schools. However, existing research does not adequately account for the diverse actions of school-based adults in relation to school discipline. Drawing on four years of fieldwork in violence prevention programs implemented in classrooms throughout Los Angeles Unified School District (LAUSD), this study explores how program facilitators create and sustain a cultural frame of empowerment within the context of the culture of control. As the findings reveal, facilitators narrowed and refined empowerment, emphasizing student anonymity and leveling classroom authority. This enactment of empowerment temporarily subverted disciplinary and punitive mechanisms in ways that meaningfully impacted individuals. This article applies the theoretical framework of cultural heterogeneity to educational contexts, arguing that while schools are sites of an overarching culture of control, school-based adults enact multiple, often conflicting cultural frames.
Magnetic field tuning of charge and spin order in the cuprate superconductorsPolkovnikov, AnatoliSachdev, S.Vojta, M.Demler, E.https://hdl.handle.net/2144/359772019-06-14T16:15:38Z2002-08-30T00:00:00ZMagnetic field tuning of charge and spin order in the cuprate superconductors
Polkovnikov, Anatoli; Sachdev, S.; Vojta, M.; Demler, E.
Recent neutron scattering, nuclear magnetic resonance, and scanning tunneling microscopy experiments have yielded valuable new information on the interplay between charge and spin density wave order and superconductivity in the cuprate superconductors, by using a perpendicular magnetic field to tune the ground state properties. We compare the results of these experiments with the predictions of a theory which assumed that the ordinary superconductor was proximate to a quantum transition to a superconductor with co-existing spin/charge density wave order.
2002-08-30T00:00:00ZGeometric speed limit of accessible many-body state preparationBukov, MarinSels, DriesPolkovnikov, Anatolihttps://hdl.handle.net/2144/359762019-06-14T15:18:51Z2019-02-20T00:00:00ZGeometric speed limit of accessible many-body state preparation
Bukov, Marin; Sels, Dries; Polkovnikov, Anatoli
We analyze state preparation within a restricted space of local control parameters between adiabatically connected states of control Hamiltonians. We formulate a conjecture that the time integral of energy fluctuations over the protocol duration is bounded from below by the geodesic length set by the quantum geometric tensor. The conjecture implies a geometric lower bound for the quantum speed limit (QSL). We prove the conjecture for arbitrary, sufficiently slow protocols using adiabatic perturbation theory and show that the bound is saturated by geodesic protocols, which keep the energy variance constant along the trajectory. Our conjecture implies that any optimal unit-fidelity protocol, even those that drive the system far from equilibrium, are fundamentally constrained by the quantum geometry of adiabatic evolution. When the control space includes all possible couplings, spanning the full Hilbert space, we recover the well-known Mandelstam-Tamm bound. However, using only accessible local controls to anneal in complex models such as glasses or to target individual excited states in quantum chaotic systems, the geometric bound for the quantum speed limit can be exponentially large in the system size due to a diverging geodesic length. We validate our conjecture both analytically by constructing counter-diabatic and fast-forward protocols for a three-level system, and numerically in nonintegrable spin chains and a nonlocal SYK model.
2019-02-20T00:00:00ZCluster truncated Wigner approximation in strongly interacting systemsWurtz, JonathanPolkovnikov, AnatoliSels, Drieshttps://hdl.handle.net/2144/359752019-06-14T15:17:35Z2018-08-01T00:00:00ZCluster truncated Wigner approximation in strongly interacting systems
Wurtz, Jonathan; Polkovnikov, Anatoli; Sels, Dries
We present a general method by which linear quantum Hamiltonian dynamics with exponentially many degrees of freedom is replaced by approximate classical nonlinear dynamics with the number of degrees of freedom (phase space dimensionality) scaling polynomially in the system size. This method is based on generalization of the truncated Wigner approximation (TWA) to a higher dimensional phase space, where phase space variables are associated with a complete set of quantum operators spanning finite size clusters. The method becomes asymptotically exact with increasing cluster size. The crucial feature of TWA is fluctuating initial conditions, which we approximate by a Gaussian distribution. We show that such fluctuations dramatically increase accuracy of TWA over traditional cluster mean-field approximations. In this way we can treat on equal footing quantum and thermal fluctuations as well as compute entanglement and various equal and non-equal time correlation functions. The main limitation of the method is exponential scaling of the phase space dimensionality with the cluster size, which can be significantly reduced by using the language of Schwinger bosons and can likely be further reduced by truncating the local Hilbert space variables. We demonstrate the power of this method analyzing dynamics in various spin chains with and without disorder and show that we can capture such phenomena as long time hydrodynamic relaxation, many-body localization and the ballistic spread of entanglement.
2018-08-01T00:00:00ZDynamic trapping near a quantum critical pointKolodrubetz, MichaelKatz, EmanuelPolkovnikov, Anatolihttps://hdl.handle.net/2144/359742019-06-14T15:18:30Z2015-02-26T00:00:00ZDynamic trapping near a quantum critical point
Kolodrubetz, Michael; Katz, Emanuel; Polkovnikov, Anatoli
The study of dynamics in closed quantum systems has been revitalized by the emergence of experimental systems that are well-isolated from their environment. In this paper, we consider the closed-system dynamics of an archetypal model: spins driven across a second-order quantum critical point, which are traditionally described by the Kibble-Zurek mechanism. Imbuing the driving field with Newtonian dynamics, we find that the full closed system exhibits a robust new phenomenon—dynamic critical trapping—in which the system is self-trapped near the critical point due to efficient absorption of field kinetic energy by heating the quantum spins. We quantify limits in which this phenomenon can be observed and generalize these results by developing a Kibble-Zurek scaling theory that incorporates the dynamic field. Our findings can potentially be interesting in the context of early universe physics, where the role of the driving field is played by the inflaton or a modulus field.
2015-02-26T00:00:00ZDynamical stability of a many-body Kapitza pendulumCitro, RobertaDalla Torre, Emanuele G.D'Alessio, LucaPolkovnikov, AnatoliBabadi, MehrtashOka, TakashiDemler, Eugenehttps://hdl.handle.net/2144/359732019-06-14T15:17:40Z2015-09-01T00:00:00ZDynamical stability of a many-body Kapitza pendulum
Citro, Roberta; Dalla Torre, Emanuele G.; D'Alessio, Luca; Polkovnikov, Anatoli; Babadi, Mehrtash; Oka, Takashi; Demler, Eugene
We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine–Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investigate the stability phase diagram through an analytic high-frequency expansion, a self-consistent variational approach, and a numeric semiclassical calculation. Classical and quantum experiments are proposed to verify the validity of our results.
2015-09-01T00:00:00ZQuantum versus classical annealing: insights from scaling theory and results for spin glasses on 3-regular graphsLiu, Cheng-WeiPolkovnikov, AnatoliSandvik, Anders W.https://hdl.handle.net/2144/359722019-06-14T15:18:28Z2015-04-07T00:00:00ZQuantum versus classical annealing: insights from scaling theory and results for spin glasses on 3-regular graphs
Liu, Cheng-Wei; Polkovnikov, Anatoli; Sandvik, Anders W.
We discuss an Ising spin glass where each S=1/2 spin is coupled antiferromagnetically to three other spins (3-regular graphs). Inducing quantum fluctuations by a time-dependent transverse field, we use out-of-equilibrium quantum Monte Carlo simulations to study dynamic scaling at the quantum glass transition. Comparing the dynamic exponent and other critical exponents with those of the classical (temperature-driven) transition, we conclude that quantum annealing is less efficient than classical simulated annealing in bringing the system into the glass phase. Quantum computing based on the quantum annealing paradigm is therefore inferior to classical simulated annealing for this class of problems. We also comment on previous simulations where a parameter is changed with the simulation time, which is very different from the true Hamiltonian dynamics simulated here.
2015-04-07T00:00:00ZUniversal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineeringBukov, MarinD'Alessio, LucaPolkovnikov, Anatolihttps://hdl.handle.net/2144/359702019-06-14T15:18:04Z2015-03-01T00:00:00ZUniversal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering
Bukov, Marin; D'Alessio, Luca; Polkovnikov, Anatoli
We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian. These classes cover systems, such as the Kapitza pendulum, the Harper–Hofstadter model of neutral atoms in a magnetic field, the Haldane Floquet Chern insulator and others. In all setups considered, we discuss both the infinite-frequency limit and the leading finite-frequency corrections to the Floquet Hamiltonian. We provide a short overview of Floquet theory focusing on the gauge structure associated with the choice of stroboscopic frame and the differences between stroboscopic and non-stroboscopic dynamics. In the latter case, one has to work with dressed operators representing observables and a dressed density matrix. We also comment on the application of Floquet Theory to systems described by static Hamiltonians with well-separated energy scales and, in particular, discuss parallels between the inverse-frequency expansion and the Schrieffer–Wolff transformation extending the latter to driven systems.
2015-03-01T00:00:00ZUniversal dynamic scaling in three-dimensional Ising spin glassesLiu, Cheng-WeiPolkovnikov, AnatoliSandvik, Anders W.Young, A. P.https://hdl.handle.net/2144/359682019-06-14T15:18:27Z2015-08-19T00:00:00ZUniversal dynamic scaling in three-dimensional Ising spin glasses
Liu, Cheng-Wei; Polkovnikov, Anatoli; Sandvik, Anders W.; Young, A. P.
We use a nonequilibrium Monte Carlo simulation method and dynamical scaling to study the phase transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity v (temperature change versus time) in Monte Carlo simulations starting at a high temperature. This approach has the advantage that the equilibrium limit does not have to be strictly reached for a scaling analysis to yield critical exponents. For the dynamic exponent we obtain z=5.85(9) for bimodal couplings distribution and z=6.00(10) for the Gaussian case. Assuming universal dynamic scaling, we combine the two results and obtain z=5.93±0.07 for generic 3D Ising spin glasses.
2015-08-19T00:00:00ZFrom quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamicsD'Alessio, LucaKafri, YarivPolkovnikov, AnatoliRigol, Marcoshttps://hdl.handle.net/2144/359672019-06-14T15:17:46Z2016-01-01T00:00:00ZFrom quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
D'Alessio, Luca; Kafri, Yariv; Polkovnikov, Anatoli; Rigol, Marcos
This review gives a pedagogical introduction to the eigenstate thermalization hypothesis (ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first part, ETH is introduced as a natural extension of ideas from quantum chaos and random matrix theory (RMT). To this end, we present a brief overview of classical and quantum chaos, as well as RMT and some of its most important predictions. The latter include the statistics of energy levels, eigenstate components, and matrix elements of observables. Building on these, we introduce the ETH and show that it allows one to describe thermalization in isolated chaotic systems without invoking the notion of an external bath. We examine numerical evidence of eigenstate thermalization from studies of many-body lattice systems. We also introduce the concept of a quench as a means of taking isolated systems out of equilibrium, and discuss results of numerical experiments on quantum quenches. The second part of the review explores the implications of quantum chaos and ETH to thermodynamics. Basic thermodynamic relations are derived, including the second law of thermodynamics, the fundamental thermodynamic relation, fluctuation theorems, the fluctuation–dissipation relation, and the Einstein and Onsager relations. In particular, it is shown that quantum chaos allows one to prove these relations for individual Hamiltonian eigenstates and thus extend them to arbitrary stationary statistical ensembles. In some cases, it is possible to extend their regimes of applicability beyond the standard thermal equilibrium domain. We then show how one can use these relations to obtain nontrivial universal energy distributions in continuously driven systems. At the end of the review, we briefly discuss the relaxation dynamics and description after relaxation of integrable quantum systems, for which ETH is violated. We present results from numerical experiments and analytical studies of quantum quenches at integrability. We introduce the concept of the generalized Gibbs ensemble and discuss its connection with ideas of prethermalization in weakly interacting systems.
2016-01-01T00:00:00ZNegative mass corrections in a dissipative stochastic environmentD'Alessio, LucaKafri, YarivPolkovnikov, Anatolihttps://hdl.handle.net/2144/359662019-06-14T15:17:34Z2016-02-01T00:00:00ZNegative mass corrections in a dissipative stochastic environment
D'Alessio, Luca; Kafri, Yariv; Polkovnikov, Anatoli
We study the dynamics of a macroscopic object interacting with a dissipative stochastic environment using an adiabatic perturbation theory. The perturbation theory reproduces known expressions for the friction coefficient and, surprisingly, gives an additional negative mass correction. The effect of the negative mass correction is illustrated by studying a harmonic oscillator interacting with a dissipative stochastic environment. While it is well known that the friction coefficient causes a reduction of the oscillation frequency, we show that the negative mass correction can lead to its enhancement. By studying an exactly solvable model of a magnet coupled to a spin environment evolving under standard non-conserving dynamics we show that the effect is present even beyond the validity of the adiabatic perturbation theory.
2016-02-01T00:00:00ZSchrieffer-Wolff Transformation for periodically driven systems: strongly correlated systems with artificial gauge fieldsBukov, MarinKolodrubetz, MichaelPolkovnikov, Anatolihttps://hdl.handle.net/2144/359652019-06-14T15:14:34Z2016-03-21T00:00:00ZSchrieffer-Wolff Transformation for periodically driven systems: strongly correlated systems with artificial gauge fields
Bukov, Marin; Kolodrubetz, Michael; Polkovnikov, Anatoli
We generalize the Schrieffer-Wolff transformation to periodically driven systems using Floquet theory. The method is applied to the periodically driven, strongly interacting Fermi-Hubbard model, for which we identify two regimes resulting in different effective low-energy Hamiltonians. In the nonresonant regime, we realize an interacting spin model coupled to a static gauge field with a nonzero flux per plaquette. In the resonant regime, where the Hubbard interaction is a multiple of the driving frequency, we derive an effective Hamiltonian featuring doublon association and dissociation processes. The ground state of this Hamiltonian undergoes a phase transition between an ordered phase and a gapless Luttinger liquid phase. One can tune the system between different phases by changing the amplitude of the periodic drive.
2016-03-21T00:00:00ZHeating and many-body resonances in a periodically driven two-band systemBukov, MarinHeyl, MarkusHuse, David A.Polkovnikov, Anatolihttps://hdl.handle.net/2144/359642019-06-14T15:18:17Z2016-04-18T00:00:00ZHeating and many-body resonances in a periodically driven two-band system
Bukov, Marin; Heyl, Markus; Huse, David A.; Polkovnikov, Anatoli
We study the dynamics and stability in a strongly interacting resonantly driven two-band model. Using exact numerical simulations, we find a stable regime at large driving frequencies where the time evolution is governed by a local Floquet Hamiltonian that is approximately conserved out to very long times. For slow driving, on the other hand, the system becomes unstable and heats up to infinite temperature. While thermalization is relatively fast in these two regimes (but to different “temperatures”), in the crossover between them we find slow nonthermalizing time evolution: temporal fluctuations become strong and temporal correlations long lived. Microscopically, we trace back the origin of this nonthermalizing time evolution to the properties of rare Floquet many-body resonances, whose proliferation at lower driving frequency removes the approximate energy conservation, and thus produces thermalization to infinite temperature.
2016-04-18T00:00:00ZSlow quenches in a quantum Ising chain: dynamical phase transitions and topologySharma, ShraddhaDivakaran, UmaPolkovnikov, AnatoliDutta, Amithttps://hdl.handle.net/2144/359632019-06-14T15:18:10Z2016-04-28T00:00:00ZSlow quenches in a quantum Ising chain: dynamical phase transitions and topology
Sharma, Shraddha; Divakaran, Uma; Polkovnikov, Anatoli; Dutta, Amit
We study the slow quenching dynamics (characterized by an inverse rate τ−1) of a one-dimensional transverse Ising chain with nearest neighbor ferromagentic interactions across the quantum critical point (QCP) and analyze the Loschmidt overlap measured using the subsequent temporal evolution of the final wave function (reached at the end of the quenching) with the final time-independent Hamiltonian. Studying the Fisher zeros of the corresponding generalized “partition function,” we probe nonanalyticities manifested in the rate function of the return probability known as dynamical phase transitions (DPTs). In contrast to the sudden quenching case, we show that DPTs survive in the subsequent temporal evolution following the quenching across two critical points of the model for a sufficiently slow rate; furthermore, an interesting “lobe” structure of Fisher zeros emerge. We have also made a connection to topological aspects studying the dynamical topological order parameter [νD(t)] as a function of time (t) measured from the instant when the quenching is complete. Remarkably, the time evolution of νD(t) exhibits drastically different behavior following quenches across a single QCP and two QCPs. In the former case, νD(t) increases stepwise by unity at every DPT (i.e., ΔνD=1). In the latter case, on the other hand, νD(t) essentially oscillates between 0 and 1 (i.e., successive DPTs occur with ΔνD=1 and ΔνD=−1, respectively), except for instants where it shows a sudden jump by a factor of unity when two successive DPTs carry a topological charge of the same sign.
2016-04-28T00:00:00Z