19 research outputs found

    Local measures of dynamical quantum phase transitions

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    In recent years, dynamical quantum phase transitions (DQPTs) have emerged as a useful theoretical concept to characterize nonequilibrium states of quantum matter. DQPTs are marked by singular behavior in an effective free energy lambda(t), which, however, is a global measure, making its experimental or theoretical detection challenging in general. We introduce two local measures for the detection of DQPTs with the advantage of requiring fewer resources than the full effective free energy. The first, called the real-local effective free energy lambda(M)(t), is defined in real space and is therefore suitable for systems where locally resolved measurements are directly accessible such as in quantum-simulator experiments involving Rydberg atoms or trapped ions. We test lambda(M)(t) in Ising chains with nearest-neighbor and power-law interactions, and find that this measure allows extraction of the universal critical behavior of DQPTs. The second measure we introduce is the momentum-local effective free energy lambda(k)(t), which is targeted at systems where momentum-resolved quantities are more naturally accessible, such as through time-of-flight measurements in ultracold atoms. We benchmark lambda(k)(t) for the Kitaev chain, a paradigmatic system for topological quantum matter, in the presence of weak interactions. Our introduced local measures for effective free energies can further facilitate the detection of DQPTs in modern quantum-simulator experiments

    Non-Standard Errors

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    In statistics, samples are drawn from a population in a data-generating process (DGP). Standard errors measure the uncertainty in estimates of population parameters. In science, evidence is generated to test hypotheses in an evidence-generating process (EGP). We claim that EGP variation across researchers adds uncertainty: Non-standard errors (NSEs). We study NSEs by letting 164 teams test the same hypotheses on the same data. NSEs turn out to be sizable, but smaller for better reproducible or higher rated research. Adding peer-review stages reduces NSEs. We further find that this type of uncertainty is underestimated by participants

    Dynamical quantum phase transitions

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    Ground-level ozone: Evidence of increasing serial dependence in the extremes

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    As exposure to successive episodes of high ground-level ozone concentrations can result in larger changes in respiratory function than occasional exposure buffered by lengthy recovery periods, the analysis of extreme values in a series of ozone concentrations requires careful consideration of not only the levels of the extremes but also of any dependence appearing in the extremes of the series. Increased dependence represents increased health risks and it is thus important to detect any changes in the temporal dependence of extreme values. In this paper we establish the first test for a change point in the extremal dependence of a stationary time series. The test is flexible, easy to use and can be extended along several lines. The asymptotic distributions of our estimators and our test are established. A large simulation study verifies the good finite sample properties. The test allows us to show that there has been a significant increase in the serial dependence of the extreme levels of ground-level ozone concentrations in Bloomsbury (UK) in recent years

    Constructing effective free energies for dynamical quantum phase transitions in the transverse-field Ising chain

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    The theory of dynamical quantum phase transitions represents an attempt to extend the concept of phase transitions to the far from equilibrium regime. While there are many formal analogies to conventional transitions, it is a major question to which extent it is possible to formulate a nonequilibrium counterpart to a Landau-Ginzburg theory. In this paper we take a first step in this direction by constructing an effective free energy for continuous dynamical quantum phase transitions appearing after quantum quenches in the transverse-field Ising chain. Due to unitarity of quantum time evolution this effective free energy becomes a complex quantity transforming the conventional minimization principle of the free energy into a saddle-point equation in the complex plane of the order parameter, which as in equilibrium is the magnetization. We study this effective free energy in the vicinity of the dynamical quantum phase transition by performing an expansion in terms of the complex magnetization and discuss the connections to the equilibrium case. Furthermore, we study the influence of perturbations and signatures of these dynamical quantum phase transitions in spin correlation functions

    Testing liquidity: A statistical theory based on asset staleness

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    Genetic restriction of antigen-presentation dictates allergic sensitization and disease in humanized mice.

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    Immunoglobulin(Ig)E-associated allergies result from misguided immune responses against innocuous antigens. CD4+ T lymphocytes are critical for initiating and perpetuating that process, yet the crucial factors determining whether an individual becomes sensitized towards a given allergen remain largely unknown
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