3,095 research outputs found

    Intellectual Property Rights in Japan

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    Quantum Quenches in Free Field Theory: Universal Scaling at Any Rate

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    Quantum quenches display universal scaling in several regimes. For quenches which start from a gapped phase and cross a critical point, with a rate slow compared to the initial gap, many systems obey Kibble-Zurek scaling. More recently, a different scaling behaviour has been shown to occur when the quench rate is fast compared to all other physical scales, but still slow compared to the UV cutoff. We investigate the passage from fast to slow quenches in scalar and fermionic free field theories with time dependent masses for which the dynamics can be solved exactly for all quench rates. We find that renormalized one point functions smoothly cross over between the regimes.Comment: 40 pages; v2: a bit late, but it includes minor modifications to match published versio

    Smooth and fast versus instantaneous quenches in quantum field theory

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    We examine in detail the relationship between smooth fast quantum quenches, characterized by a time scale δt\delta t, and {\em instantaneous quenches}, within the framework of exactly solvable mass quenches in free scalar field theory. Our earlier studies \cite{dgm1,dgm2} highlighted that the two protocols remain distinct in the limit δt→0\delta t \rightarrow 0 because of the relation of the quench rate to the UV cut-off, i.e., 1/δt≪Λ1/\delta t\ll\Lambda always holds in the fast smooth quenches while 1/δt∼Λ1/\delta t\sim\Lambda for instantaneous quenches. Here we study UV finite quantities like correlators at finite spatial distances and the excess energy produced above the final ground state energy. We show that at late times and large distances (compared to the quench time scale) the smooth quench correlator approaches that for the instantaneous quench. At early times, we find that for small spatial separation and small δt\delta t, the correlator scales universally with δt\delta t, exactly as in the scaling of renormalized one point functions found in earlier work. At larger separation, the dependence on δt\delta t drops out. The excess energy density is finite (for finite mδtm\delta t) and scales in a universal fashion for all dd. However, the scaling behaviour produces a divergent result in the limit mδt→0m\delta t \rightarrow 0 for d≥4d\ge4, just as in an instantaneous quench, where it is UV divergent for d≥4d \geq 4. We argue that similar results hold for arbitrary interacting theories: the excess energy density produced is expected to diverge for scaling dimensions Δ>d/2\Delta > d/2.Comment: 52 pages; v2: minor modifications to match published versio

    An exactly solvable quench protocol for integrable spin models

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    Quantum quenches in continuum field theory across critical points are known to display different scaling behaviours in different regimes of the quench rate. We extend these results to integrable lattice models such as the transverse field Ising model on a one-dimensional chain and the Kitaev model on a two-dimensional honeycomb lattice using a nonlinear quench protocol which allows for exact analytical solutions of the dynamics. Our quench protocol starts with a finite mass gap at early times and crosses a critical point or a critical region, and we study the behaviour of one point functions of the quenched operator at the critical point or in the critical region as a function of the quench rate. For quench rates slow compared to the initial mass gap, we find the expected Kibble-Zurek scaling. In contrast, for rates fast compared to the mass gap, but slow compared to the inverse lattice spacing, we find scaling behaviour similar to smooth fast continuum quenches. For quench rates of the same order of the lattice scale, the one point function saturates as a function of the rate, approaching the results of an abrupt quench. The presence of an extended critical surface in the Kitaev model leads to a variety of scaling exponents depending on the starting point and on the time where the operator is measured. We discuss the role of the amplitude of the quench in determining the extent of the slow (Kibble-Zurek) and fast quench regimes, and the onset of the saturation.Comment: 54 pages, 13 figures; v2: added analytic argument for Kitaev mode

    Hospitalization and Treatment of the Mentally Ill: Ohio's New Mental Health Law

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    Synthesis of timed circuits using BDDs*

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    Journal ArticleThis paper presents a tool which synthesizes timed circuits from reduced state graphs. Using timing information to reduce state graphs can lead to significantly smaller and faster circuits. The tool uses implicit techniques (binary decision diagrams) to represent these graphs. This allows us to synthesize larger, more complex systems which may be intractable with an explicit representation. We are also able to create a parameterized family of solutions, facilitating technology mapping

    New verification method for embedded systems

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    Journal ArticleAbstract-Verification of embedded systems is complicated by the fact that they are composed of digital hardware, analog sensors and actuators, and low level software. In order to verify the interaction of these heterogeneous components, it would be beneficial to have a single modeling formalism that is capable of representing all of these components. To address this need, this paper describes an extended labeled hybrid Petri net (LHPN) model that includes constructs for Boolean, discrete, and continuous variables as well as constructs to model timing. This paper also presents a method to verify these extended LHPNs. Finally, this paper presents a case study to illustrate the application of this model to the verification of a fault-tolerant temperature sensor
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