Time-independent Constant Research Articles

Entanglement island and Page curve in wedge holography

Entanglement islands play an essential role in the recent breakthrough in resolving the black hole information paradox. However, whether entanglement islands can exist in massless gravity theories is controversial. It is found that entanglement islands disappear in the initial model of wedge holography with massless gravity on the brane. As a result, the entanglement entropy of Hawking radiation becomes a time-independent constant, and there is no Page curve. In this paper, we recover massless entanglement islands in wedge holography with suitable DGP gravity or higher derivative gravity on the branes. We study two typical cases. In the first case, we consider a black hole on the strong-gravity brane and a bath on the weak-gravity brane. It is similar to the usual double holography with non-gravitational baths. In the second case, we discuss two black holes on the two branes with the same gravitational strength. We recover massless entanglement islands and non-trivial Page curves in both cases. We also argue that the entanglement island is consistent with massless gravity. Our results strongly support that entanglement islands can exist in long-range theories of gravity.

Continuous-Time Insider Trading with Risk-Neutral Insider under Imperfect Observation

A model of insider trading in continuous time in which a risk-neutral insider possesses long-lived imperfect information on a risk asset is studied. By conditional expectation theory and filtering theory, we turn it into a model with insider knowing complete information about the asset with a revised risky value and deduce its linear Bayesian equilibrium consisting of optimal insider trading strategy and semistrong pricing rule. It shows that, in the equilibrium, as the degree of insider observing the signal of the risky asset value is more and more accurate, market depth, trading intensity, and residual information are all decreasing and the total expectation profit of the insider is increasing and that the information about the asset value incorporated into the equilibrium price, which has nothing to do with the volatility of noise trades, is increasing as time goes by, but not all information of asset value is incorporated into the price in the final disclosed time due to the incompleteness of insider’s observation, though the market depth is still a time-independent constant. Some simulations are illustrated to show these features. However, it is an open question of how to make maximal profit if the insider is risk-averse.

Fluctuation–dissipation relation for a quantum Brownian oscillator in a parametrically squeezed thermal field

In this paper we study the nonequilibrium evolution of a quantum Brownian oscillator, modeling the internal degree of freedom of a harmonic atom or an Unruh–DeWitt detector, coupled to a nonequilibrium and nonstationary quantum field bath and inquire whether a fluctuation–dissipation relation (FDR) can exist after/if it approaches equilibration. This is a nontrivial issue because a squeezed field bath cannot reach equilibration and yet, as this work shows, the system oscillator indeed can, which is a necessary condition for FDRs. We discuss three different settings: (A) The bath field essentially remains in a squeezed thermal state throughout, whose squeeze parameter is a mode- and time-independent constant. This situation is often encountered in quantum optics and quantum thermodynamics. (B) The bath field is initially in a thermal state, but is subjected to a parametric process leading to mode- and time-dependent squeezing. This scenario is encountered in cosmology and dynamical Casimir effects. The squeezing in the bath in both types of processes will affect the oscillator’s nonequilibrium evolution. We show that at late times it approaches equilibration and this stationarity condition warrants the existence of a FDR. The trait of squeezing is marked by the oscillator’s effective equilibrium temperature, and the proportionality factor in the FDR is only related to the stationary component of the noise kernel of the bath field. Setting (C) is more subtle: A finite system–bath coupling strength can set the oscillator in a squeezed state even though the bath field is stationary and does not engage in any parametric process. The squeezing of the system in this case is in general time-dependent but becomes constant when the internal dynamics is fully relaxed. We begin with comments on the broad range of physical processes involving squeezed thermal baths and end with some remarks on the significance of FDRs in capturing the essence of quantum backreaction in nonequilibrium and stochastic systems.

How a four-dimensional de Sitter solution remains outside the swampland

We argue that, in the presence of time-dependent fluxes and quantum corrections, four-dimensional de Sitter solutions should appear in the type IIB string landscape and not in the swampland. Our construction considers generic choices of local and non-local quantum terms and satisfies the no-go and the swampland criteria, the latter being recently upgraded using the trans-Planckian cosmic censorship. Interestingly, both time-independent Newton constant and moduli stabilization may be achieved in such backgrounds even in the presence of time-dependent fluxes and internal spaces. However, once the time-dependence is switched off, any four-dimensional solution with de Sitter isometries appears to have no simple effective field theory descriptions and is back in the swampland.

Information transfer with a gravitating bath

Late-time dominance of entanglement islands plays a critical role in addressing the information paradox for black holes in AdS coupled to an asymptotic non-gravitational bath. A natural question is how this observation can be extended to gravitational systems. To gain insight into this question, we explore how this story is modified within the context of Karch-Randall braneworlds when we allow the asymptotic bath to couple to dynamical gravity. We find that because of the inability to separate degrees of freedom by spatial location when defining the radiation region, the entanglement entropy of radiation emitted into the bath is a time-independent constant, consistent with recent work on black hole information in asymptotically flat space. If we instead consider an entanglement entropy between two sectors of a specific division of the Hilbert space, we then find non-trivial time-dependence, with the Page time a monotonically decreasing function of the brane angle---provided both branes are below a particular angle. However, the properties of the entropy depend discontinuously on this angle, which is the first example of such discontinuous behavior for an AdS brane in AdS space.

Poisson's ratio of PDMS thin films

Despite the fact that a small uncertainty in PDMS Poisson's ratio leads to significant errors in traction force microscopy, there is a clear lack of data for PDMS films at the scale of 100 μm, a relevant size scale frequently employed in cell mechanics studies. Equally important is the need for consideration of the viscoelastic nature of PDMS, as no mechanical property - including Poisson's ratio - can be taken as a time-independent constant. The foremost challenge for addressing these issues is the difficulty of carrying out stress relaxation tests on miniature PDMS samples accompanied by non-contact strain measurement with a very high spatiotemporal resolution. This study introduces such a stress relaxation platform incorporating i) the proper means for the application of necessary boundary conditions, ii) a high-precision in load measurement, and iii) a non-contact, local strain measurement technique based on single particle tracking. During stretching, images were recorded at a rate of 18 Hz with a 40 μm spatial resolution. Microsphere-embedded PDMS films as thin as 125 and 155 μm were prepared to study the Poisson's ratio by a local strain microscope. After tracing the displacement of microspheres by a single particle tracking method and using a strain mapping, Poisson's ratio for 155-μm-thick PDMS was found to decrease from 0.483 ± 0.034 to 0.473 ± 0.040 over a period of 20 min. For 125-μm-thick PDMS, this reduction took place from 0.482 ± 0.041 to 0.468 ± 0.038. Moreover, a non-monotonic reduction was observed in both cases. This negative correlation between Poisson's ratio and relaxation time was found to be statistically significant for both thicknesses with p < 0.001. The viscoelastic behavior was further characterized through the Burgers model. With a measurement field of 597 × 550 μm2, this study emphasizes the importance of the local investigation of mechanical properties. Furthermore, the dependence of transverse strain on a film thickness difference of 30 μm was measured to determine the sensitivity of local strain tracking. The inherent high resolution of the proposed approach enables one to measure deformations more precisely and to observe the temporal evolution of the Poisson's ratio that has not been observed before. In addition to the high-precision determination of PDMS Poisson's ratio, this work also offers a promising pathway for the accurate and time-dependent determination of the mechanical properties of other soft materials, where similar ambiguities exist regarding the mechanical behavior.

Ensemble controllability and discrimination of perturbed bilinear control systems on connected, simple, compact Lie groups

The controllability of bilinear systems is well understood for finite dimensional isolated systems where the control can be implemented exactly. However when perturbations are present some interesting theoretical questions are raised. We consider in this paper a control system whose control cannot be implemented exactly but is shifted by a time independent constant in a discrete list of possibilities. We prove under general hypothesis that the collection of possible systems (one for each possible perturbation) is simultaneously controllable with a common control. The result is extended to the situations where the perturbations are constant over a common, long enough, time frame. We apply the result to the controllability of quantum systems. Furthermore, some examples and a convergence result are presented for the situation where an infinite number of perturbations occurs. In addition, the techniques invoked in the proof allow us to obtain generic necessary and sufficient conditions for ensemble controllability.

Construction of Lagrangian and Hamiltonian structures starting from one constant of motion

The problem of the construction of Lagrangian and Hamiltonian structures starting from two first-order equations of motion is presented. This approach requires the knowledge of one (time independent) constant of motion for the dynamical system only. The Hamiltonian and Lagrangian structures are constructed, the Hamilton–Jacobi equation is then written and solved, and the second (time dependent) constant of the motion for the problem is explicitly exhibited.

Determination of Shear and Bulk Moduli of Viscoelastic Solids from the Indirect Tension Creep Test

Because of its efficiency in analyzing complex viscoelastic problems, the finite-element (FE) analysis has been widely used to identify the time- and rate-dependent effects of viscoelastic materials on various structural conditions. When performing the FE analysis on a viscoelastic structure, most FE programs require fundamental material properties, shear and bulk moduli, of the given viscoelastic material as their input. However, the shear and bulk modulus tests are difficult to perform, so they have been commonly estimated from a single material test on the basis of the assumption that the Poisson’s ratio of viscoelastic materials is a time-independent constant. Such an assumption, however, might not be suitable because the Poisson’s ratio of the viscoelastic materials is also a function of time. Therefore, this study developed computation algorithms for determining the time-dependent Poisson’s ratio and shear and bulk moduli of asphalt mixtures, which have been well recognized as a viscoelastic materia...

Estimation of mean seabed roughness in a tidal channel with an extended log-fit method

An extended log-fit method is developed to estimate mean seabed roughness length z 0 from a number of current profiles measured near the seabed in the absence of surface waves. With this new method, the mean seabed roughness length z 0 is estimated by fitting the logarithmic distribution, k ( z ) = A ln ( z / z 0 ) , to a time-independent dimensionless mean velocity profile k( z) that is derived from the number of current profiles, where A is a time-independent constant. The field data were collected at a mean water depth of 16 m in a tidal channel. An Acoustic Doppler Profiler (ADP) was used to continuously measure tidal current profiles at 16 levels above the seabed for 10 min, every 10 min over a period of 13 days. On the basis of collected field data, it is found that the bed roughness lengths estimated from individual velocity profiles are extremely fluctuating and profile-dependent. In contrast, the mean roughness lengths estimated with this extended log-fit method are shown much less fluctuating and proven more accurate. This study also investigates the sensitivity of the current shear velocity u ¯ * to different bed roughness lengths.

Global picture of self-similar and non-self-similar decay in Burgers turbulence

This paper continues earlier investigations of the decay of Burgers turbulence in one dimension from Gaussian random initial conditions of the power-law spectral type E0(k) approximately |k|(n). Depending on the power n , different characteristic regions are distinguished. The main focus of this paper is to delineate the regions in wave number k and time t in which self-similarity can (and cannot) be observed, taking into account small-k and large-k cutoffs. The evolution of the spectrum can be inferred using physical arguments describing the competition between the initial spectrum and the new frequencies generated by the dynamics. For large wave numbers, we always have a k(-2) region, associated with the shocks. When n is less than 1, the large-scale part of the spectrum is preserved in time and the global evolution is self-similar, so that scaling arguments perfectly predict the behavior in time of the energy and integral scale. If n is larger than 2, the spectrum tends for long times to a universal scaling form independent of the initial conditions, with universal behavior k(2) at small wave numbers. In the interval 2<n the leading behavior is self-similar, independent of n and with universal behavior k(2) at small wave number. When 1<n<2, the spectrum has three scaling regions: first, a |k|(n) region at very small k's with a time-independent constant; second, a k(2) region at intermediate wave numbers; finally, the usual k(-2) region. In the remaining interval n<-3 the small-k cutoff dominates and n also plays no role. We find also (numerically) the subleading term approximately k(2) in the evolution of the spectrum in the interval -3<n<1. High-resolution numerical simulations have been performed confirming both scaling predictions and analytical asymptotic theory.

Exact coherent state transition elements for the squeezed harmonic oscillator

The squeezed harmonic oscillator Hamiltonian H = ωa†a + αa2 + α*a†2 is analysed, where a† and a are harmonic oscillator creation and annihilation operators, ω is real, and α is a time independent constant. For the case that ω2 − 4|α|2 > 0 it is known that the Hamiltonian possesses real and positive eigenvalues. The exact eigenstates are constructed by using a Bogoliubov transformation to express them in terms of the algebra and states of the harmonic oscillator. Known properties of these states are reviewed and new results are derived. Modified coherent states are constructed from the exact eigenstates and shown to yield a unit projection operator for the original harmonic oscillator Hilbert space via generalized Gaussian integrals. Transition elements between harmonic oscillator coherent states are then evaluated exactly by using the properties of the modified coherent state projection operator.

High precision study of the structure of [formula omitted] supersymmetric Yang–Mills quantum mechanics

The spectrum of D = 4 supersymmetric Yang–Mills quantum mechanics is computed with high accuracy in all channels of angular momentum and fermion number. Localized and nonlocalized states coexists in certain channels as a consequence of the supersymmetric interactions with flat valleys. All states fall into well identifiable supermultiplets providing an explicit realization of supersymmetry on the spectroscopic level. An accidental degeneracy among some supermultiplets has been found. Regularized Witten index converges to a time-independent constant which agrees with earlier calculations.

On the Long-Time Behavior of Unsplit Perfectly Matched Layers

This paper shows how to eliminate an undesirable long-time linear growth of the electromagnetic field in a class of unsplit perfectly matched layers (PML) typically used as absorbing boundary conditions in computational electromagnetics codes. For the new PML equations, we give energy arguments that show the fields in the layer are bounded by a time-independent constant, hence they are long-time stable. Numerical experiments confirm the elimination of the linear growth, and the long-time boundedness of the fields.

Routine α-Amylase Assay Using Protected 4-Nitrophenyl-1,4-α-d-maltoheptaoside and a Novel α-Glucosidase

In contrast to numerous methods for measuring alpha-amylase activity, the approved IFCC reference method offers an invariable time-independent constant product pattern, thus avoiding possibly changing stoichiometric calculations. However, reference methods do not lend themselves to routine use, so that such methods need to be modified. Ethylidene-blocked 4-nitrophenylmaltoheptaoside (EPS-G7) is degraded to glucose and 4-nitrophenol in a coupled assay with a bacterial alpha-glucosidase under the following measurement conditions: 3.5 mmol/L EPS-G7, 7.1 kU/L alpha-glucosidase, 70 mmol/L sodium chloride, 1 mmol/L calcium chloride, 50 mmol/L HEPES, pH 7.15, at 37 degrees C. The increase of absorbance is continuously monitored for 3 min at 405 nm after a lag phase of 2 min. Catalytic concentrations up to 15-fold higher than the upper reference limit can be determined without dilution. Precision studies in manual performance show CVs of 1.4-2. 6% (within-run) and 1.9-2.8% (day-to-day). There was no interference from 100 mmol/L glucose, 30 mmol/L triacylglycerols, 610 micromol/L bilirubin, and 2.95 g/L hemoglobin. The method closely correlates with other chromogenic assays. The preliminary 0.95 reference interval for adults, not dependent on age and sex, is 33.6-96.2 U/L. The procedure is a robust adaptation of the reference method to routine use at 37 degrees C with increased sensitivity, fewer interferences, and reduced cost.

Dissipative quantum transport in a quantum wire.

We have carried out a real-time path-integral calculation of quantum transport of an electron through a dissipative quantum wire, which is modeled by a parabolic potential in one of the directions. The interaction between the electron and the phonons is treated in terms of an ordered expansion. At the linear order the problem is solved exactly. We present a detailed derivation of the influence of functional formalism within this model. We study the quantum dynamics of the electron under an external force nonperturbatively with various initial conditions. The electron drifting velocity is found to depend on the external force linearly, and consists of a sum of two terms. One term is a time-independent constant while the other oscillates with time. The drifting velocity remains the same for different initial conditions and the oscillation has a characteristic period. We found that while the confinement does not appear to influence the long time drifting velocity within the linear model, it does have very complicated nontrivial effects when nonlinear terms are included. A formalism is established to include the confining potential within a general model of the electron-phonon coupling. \textcopyright{} 1996 The American Physical Society.

Time integrals of input signal and output signal in linear measurement systems

The proportionality relation between the time integral of the input signal and that of the output signal is derived in a linear measurement system with lumped parameters and in a system with distributed parameters. The relation is equivalent to that of signals in a most simple case in which the input signal is a time-independent constant and the output signal is proportional to the magnitude of the input signal. In a system with distributed parameters, the relation is valid for signals averaged over surfaces through which they are transmitted in or out. The relation is also valid even when the linear system shows time delay, overshoot or damped vibration.

Effects of one-dimensional random rough surfaces on ultrasonic backscatter: Utility of phase-screen and Fresnel approximations

The effects of one-dimensional randomly rough surface corrugations on the time-dependent backscatter predicted by a simple model of the interaction of ultrasound with the microstructure of a sample are studied. Changes in the wave field that are due to surface topography, were calculated and compared by three different schemes: (1) the boundary integral element (BIE) method, (2) the phase-screen approximation (PSA), and (3) the PSA combined with the Fresnel approximation (which, as we report, yields an analytic series solution). Although the second and third schemes are easy to implement and accurate in some important cases, they are uncontrolled approximations that do not systematically estimate the resulting errors. The BIE method provides increasingly precise answers for a given model (at the cost of increasingly large numerical calculations) and was used to estimate the range of validity for the approximate methods. It is shown that the time evolution of the backscattered signal is approximately the same for the PSA as for the BIE calculations, aside from an overall time-independent constant. It is also shown that the approximate constant of proportionality depends strongly on the frequency, the correlation length, and the rms height; it is much less affected by the radius or the focal length of the probe. The constant of proportionality is presented both graphically and as a semiempirical formula and can be used to estimate and correct the error of the simpler PSA calculation.

Generalized Hamiltonian structures for systems in three dimensions with a rescalable constant of motion

The generalized Hamiltonian structures of several three-dimensional dynamical systems of interest in physical applications are considered. In general, Hamiltonians exist only for systems that possess at least one time-independent constant of motion. Systems with only time-dependent constants of motion may sometimes be rescaled and their constant of motion made time-independent. When this is possible, the transformed system may be cast in a generalized Hamiltonian formalism with non-canonical structure functions.

Local and Ensemble Dynamics of Linked Populations

In a recent issue of the Journal of Animal Ecology, Bascompte & Sole (1994) investigated the effect of introducing immigration between a number of populations each represented by a simple one-step map. They conclude that this linkage generally serves to destabilize individual populations, increasing their propensity to exhibit chaotic fluctuations, but tending to reduce the variance of the ensemble. Although not mentioned by Bascompte & Sole, there have been several other recent papers on linkage between potentially chaotic populations (e.g. McCallum 1992; Gonzalez-Andujar & Perry 1993a,b; Stone 1993). These papers suggest that linkage between simple maps tends to decrease the likelihood of chaotic fluctuations, rather than increase it, as Bascompte & Sole suggest. These studies use a smaller number of populations than considered by Bascompte & Sole or simply consider immigration to be a time-independent constant. Even so, they suggest that Bascompte & Soles conclusion about local dynamics should be tempered. While linkage does have an effect on local dynamics, it is not clear that there is a general rule governing the nature of this effect. For the simplest case, where immigration is a constant, Ruxton (1993) provides an example where introducing low levels of immigration can induce chaos in a model population which would show a regular cycle if isolated. However, higher levels of immigration recover a simple cycle again. Bascompte & Sole also conclude that ensemble dynamics are 'stabilized' by the addition of linkage, in that the variance decreases and the resultant total population resembles a steady state with added noise. This appears at odds with my own observation of 10 linked maps where the global dynamics commonly appear as a simple cycle (Ruxton 1994). However, a reconciliation of these two, apparently contradictory, observations may be found in the work of de Roos, McCauley & Wilson (1991) who considered a predator-prey interaction on a discrete lattice. If movement takes place only between adjacent sites then they observed a noisy signal around a roughly constant population. However, when all lattice sites were equally available for movement, then large amplitude cycles were obtained. A similar situation appears to apply to our linked populations. I allow dispersal to all populations equally and obtain regular cycles whereas Bascompte and Sole allow movement only between neighbouring populations and obtain a 'noisy equilibrium'. Hence, although Bascompte and Sole are correct in concluding that the number of subpopulations has an important effect on the behaviour of the ensemble, the degree of linkage between individual populations should also be emphasized as an equally important ecological parameter. One of the most developed areas for exploration of the way linkage between populations affects dynamics lies in the field of human childhood diseases. Here, in contrast to most other areas, firmly grounded theoretical models can be combined with a considerable amount of data (e.g. Sugihara, Grenfell & May 1990; Grenfell 1992).