Machine learning methods are increasingly being employed as surrogate models in place of computationally expensive and slow numerical integrators for a bevy of applications in the natural sciences. However, while the ...
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Zero-noise extrapolation is a quantum error mitigation technique that has typically been studied under the ideal approximation that the noise acting on a quantum device is not time correlated. In this paper, we invest...
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Zero-noise extrapolation is a quantum error mitigation technique that has typically been studied under the ideal approximation that the noise acting on a quantum device is not time correlated. In this paper, we investigate the feasibility and performance of zero-noise extrapolation in the presence of time-correlated noise. We show that, in contrast to white noise, time-correlated noise is harder to mitigate via zero-noise extrapolation because it is difficult to scale the noise level without also modifying its spectral distribution. This limitation is particularly strong if “local” gate-level methods are applied for noise scaling. However, we find that “global” noise-scaling methods, e.g., global unitary folding, can be sufficiently reliable even in the presence of time-correlated noise.
Studies in the collective motility of organisms use a range of analytical approaches to formulate continuous kinetic models of collective dynamics from rules or equations describing agent interactions. However, the de...
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We study the complexity for an open quantum system. Our system is a harmonic oscillator coupled to a one-dimensional massless scalar field, which acts as the bath. Specifically, we consider the reduced density matrix ...
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We study the complexity for an open quantum system. Our system is a harmonic oscillator coupled to a one-dimensional massless scalar field, which acts as the bath. Specifically, we consider the reduced density matrix by tracing out the bath degrees of freedom for both regular and inverted oscillators and compute the complexity of purification (COP) and complexity by using the operator-state mapping. We find that when the oscillator is regular, the COP saturates quickly for both underdamped and overdamped oscillators. Interestingly, when the oscillator is underdamped, we discover a kink-like behavior for the saturation value of the COP with a varying damping coefficient. For the inverted oscillator, we find a linear growth of the COP with time for all values of the bath-system interaction. However, when the interaction is increased the slope of the linear growth decreases, implying that the unstable nature of the system can be regulated by the bath.
We combine the newly-constructed Galerkin difference basis with the energy-based discontinuous Galerkin method for wave equations in second order form. The approximation properties of the resulting method are excellen...
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作者:
Torquato, SalvatoreDepartment of Chemistry
Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States
Understanding time-dependent diffusion processes in multiphase media is of great importance in physics, chemistry, materials science, petroleum engineering and biology. Consider the time-dependent problem of mass tran...
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Understanding time-dependent diffusion processes in multiphase media is of great importance in physics, chemistry, materials science, petroleum engineering and biology. Consider the time-dependent problem of mass transfer of a solute between two phases and assume that the solute is initially distributed in one phase (phase 2) and absent from the other (phase 1). We desire the fraction of total solute present in phase 1 as a function of time, S(t), which we call the spreadability, since it is a measure of the spreadability of diffusion information as a function of time. We derive exact direct-space formulas for S(t) in any Euclidean space dimension d in terms of the autocovariance function as well as corresponding Fourier representations of S(t) in terms of the spectral density, which are especially useful when scattering information is available experimentally or theoretically. These are singular results because they are rare examples of mass transport problems where exact solutions are possible. We derive closed-form general formulas for the short- and long-time behaviors of the spreadability in terms of crucial small- and large-scale microstructural information, respectively. The long-time behavior of S(t) enables one to distinguish the entire spectrum of microstructures that span from hyperuniform to nonhyperuniform media. For hyperuniform media, disordered or not, we show that the "excess" spreadability, S(∞) − S(t), decays to its long-time behavior exponentially faster than that of any nonhyperuniform two-phase medium, the "slowest" being antihyperuniform media. The stealthy hyperuniform class is characterized by an excess spreadability with the fastest decay rate among all translationally invariant microstructures. We obtain exact results for S(t) for a variety of specific ordered and disordered model microstructures across dimensions that span from hyperuniform to antihyperuniform media. Moreover, we establish a remarkable connection between the spreadability
This paper investigates the finite-thickness effect of two superimposed fluids on bubbles and spikes in Richtmyer–Meshkov instability(RMI) for arbitrary Atwood numbers by using the method of the small parameter expan...
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This paper investigates the finite-thickness effect of two superimposed fluids on bubbles and spikes in Richtmyer–Meshkov instability(RMI) for arbitrary Atwood numbers by using the method of the small parameter expansion up to the second order. When the thickness of the two fluids tends to be infinity, our results can reproduce the classical results where RMI happens at the interface separating two semi-infinity-thickness fluids of different densities. It is found that the thickness has a large influence on the amplitude evolution of bubbles and spikes compared with those in classical RMI. Based on the thickness relationship of the two fluids, the thickness effect on bubbles and spikes for four cases is discussed. The thickness encourages(or reduces)the growth of bubbles or spikes, depending on not only Atwood number, but also the relationship of the thickness ratio of the heavy and light fluids, which is explicitly determined in this paper.
The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space R3+ is rigorously proved under a Navier-slip boundary condition for velocit...
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We show how a complete mathematical model of a physical process can be learned directly from data via a hybrid approach combining three simple and general ingredients: physical assumptions of smoothness, locality, and...
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Dynamical quantum phase transitions are non-analyticities in a dynamical free energy (or return rate) which occur at critical times. Although extensively studied in one dimension, the exact nature of the non-analytici...
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