scholarly journals Energy redistribution and spatiotemporal evolution of correlations after a sudden quench of the Bose-Hubbard model

2020 ◽  
Vol 6 (40) ◽  
pp. eaba9255
Author(s):  
Yosuke Takasu ◽  
Tomoya Yagami ◽  
Hiroto Asaka ◽  
Yoshiaki Fukushima ◽  
Kazuma Nagao ◽  
...  
Keyword(s):  
Hubbard Model ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Nonequilibrium Dynamics ◽  
Many Body ◽  
Energy Redistribution ◽  
Particle Correlation ◽  
Far From Equilibrium ◽  
Quantum Simulator ◽  
The One

An optical lattice quantum simulator is an ideal experimental platform to investigate nonequilibrium dynamics of a quantum many-body system, which is, in general, hard to simulate with classical computers. Here, we use our quantum simulator of the Bose-Hubbard model to study dynamics far from equilibrium after a quantum quench. We successfully confirm the energy conservation law in the one- and three-dimensional systems and extract the propagation velocity of the single-particle correlation in the one- and two-dimensional systems. We corroborate the validity of our quantum simulator through quantitative comparisons between the experiments and the exact numerical calculations in one dimension. In the computationally hard cases of two or three dimensions, by using the quantum-simulation results as references, we examine the performance of a numerical method, namely, the truncated Wigner approximation, revealing its usefulness and limitation. This work constitutes an exemplary case for the usage of analog quantum simulators.

scholarly journals Quantum critical dynamics in a spinor Hubbard model quantum simulator

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Jared O. Austin ◽  
Zihe Chen ◽  
Zachary N. Shaw ◽  
Khan W. Mahmud ◽  
Yingmei Liu
Keyword(s):  
Phase Transitions ◽  
Hubbard Model ◽  
Quantum Phase Transitions ◽  
Three Dimensional ◽  
Quantum Phase ◽  
Critical Dynamics ◽  
Scaling Effects ◽  
Many Body ◽  
Quantum Simulator ◽  
Quantum Critical

AbstractThree-dimensional (3D) strongly correlated many-body systems, especially their dynamics across quantum phase transitions, are prohibitively difficult to be numerically simulated. We experimentally demonstrate that such complex many-body dynamics can be efficiently studied in a 3D spinor Bose–Hubbard model quantum simulator, consisting of antiferromagnetic spinor Bose–Einstein condensates confined in cubic optical lattices. We find dynamics and scaling effects beyond the scope of existing theories at superfluid–insulator quantum phase transitions, and highlight spin populations as a good observable to probe the quantum critical dynamics. Our data indicate that the scaling exponents are independent of the nature of the quantum phase transitions. We also conduct numerical simulations in lower dimensions using time-dependent Gutzwiller approximations, which qualitatively describe our observations.

On the Recovery of 3D Spatial Statistics of Particles from 1D Measurements: Implications for Airborne Instruments

2014 ◽  
Vol 31 (10) ◽  
pp. 2078-2087 ◽  
Author(s):  
Michael L. Larsen ◽  
Clarissa A. Briner ◽  
Philip Boehner
Keyword(s):  
Point Processes ◽  
Pair Correlation ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional System ◽  
Cloud Droplets ◽  
Sampling Variability ◽  
One Dimensional ◽  
Natural Sampling ◽  
The One

Abstract The spatial positions of individual aerosol particles, cloud droplets, or raindrops can be modeled as a point processes in three dimensions. Characterization of three-dimensional point processes often involves the calculation or estimation of the radial distribution function (RDF) and/or the pair-correlation function (PCF) for the system. Sampling these three-dimensional systems is often impractical, however, and, consequently, these three-dimensional systems are directly measured by probing the system along a one-dimensional transect through the volume (e.g., an aircraft-mounted cloud probe measuring a thin horizontal “skewer” through a cloud). The measured RDF and PCF of these one-dimensional transects are related to (but not, in general, equal to) the RDF/PCF of the intrinsic three-dimensional systems from which the sample was taken. Previous work examined the formal mathematical relationship between the statistics of the intrinsic three-dimensional system and the one-dimensional transect; this study extends the previous work within the context of realistic sampling variability. Natural sampling variability is found to constrain substantially the usefulness of applying previous theoretical relationships. Implications for future sampling strategies are discussed.

scholarly journals SHOCK FORMATION IN THE COMPRESSIBLE EULER EQUATIONS AND RELATED SYSTEMS

2013 ◽  
Vol 10 (01) ◽  
pp. 149-172 ◽  
Author(s):  
GENG CHEN ◽  
ROBIN YOUNG ◽  
QINGTIAN ZHANG
Keyword(s):  
Euler Equations ◽  
Space Dimension ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Compressible Euler Equations ◽  
Shock Formation ◽  
Compressible Euler ◽  
Systems Of Conservation Laws ◽  
The One ◽  
Special Case

We prove shock formation results for the compressible Euler equations and related systems of conservation laws in one space dimension, or three dimensions with spherical symmetry. We establish an L∞ bound for C1 solutions of the one-dimensional (1D) Euler equations, and use this to improve recent shock formation results of the authors. We prove analogous shock formation results for 1D magnetohydrodynamics (MHD) with orthogonal magnetic field, and for compressible flow in a variable area duct, which has as a special case spherically symmetric three-dimensional (3D) flow on the exterior of a ball.

Three-dimensional effects in low-strain integrity testing of piles: analytical solution

2016 ◽  
Vol 53 (2) ◽  
pp. 225-235 ◽  
Author(s):  
Changjie Zheng ◽  
George P. Kouretzis ◽  
Xuanming Ding ◽  
Hanlong Liu ◽  
Harry G. Poulos
Keyword(s):  
Impact Load ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Integrity Testing ◽  
Integrity Tests ◽  
The One ◽  
Propagation Of Waves ◽  
The Impact ◽  
Pile Integrity ◽  
Elastic Soil

The interpretation of low-strain integrity tests of piles is commonly based on methods developed around the one-dimensional wave propagation theory. In reality, waves resulting from the impact of a hammer on a pile head propagate in three dimensions, and the validity of the plane-front assumption is rather questionable for cases where the size of the hammer is small relative to that of the pile. This paper presents an analytical model of the dynamic response of a pile to an impact load on its head, considering propagation of waves in both vertical and radial directions. The proposed formulation applies to a pile of finite length embedded in multilayered elastic soil, and allows for considering both shape and material pile defects, by reducing locally the radius of the pile cross section or the Young’s modulus of its material. Arithmetic examples are used to depict the effect of high-frequency interferences on the interpretation of pile integrity tests, which can only be accounted for in the three-dimensional formulation of the problem, and lead to practical suggestions for the interpretation of such tests.

Diffraction of Electrons by Two and Three Mutually Orthogonal Standing Light Waves

1975 ◽  
Vol 53 (2) ◽  
pp. 157-164 ◽  
Author(s):  
F. Ehlotzky
Keyword(s):  
Electron Scattering ◽  
Light Wave ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Standing Light Wave ◽  
Light Waves ◽  
The One ◽  
Rectangular Lattices

The one-dimensional problem of electron scattering by a standing light wave, known as the Kapitza–Dirac effect, is shown to be easily extendable to two and three dimensions, thus showing all characteristics of diffraction of electrons by simple two- and three-dimensional rectangular lattices.

scholarly journals Disorder-controlled relaxation in a three-dimensional Hubbard model quantum simulator

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
W. Morong ◽  
S. R. Muleady ◽  
I. Kimchi ◽  
W. Xu ◽  
R. M. Nandkishore ◽  
...  
Keyword(s):  
Hubbard Model ◽  
Three Dimensional ◽  
Quantum Simulator

scholarly journals Cooling and instabilities in colliding flows

2021 ◽  
Author(s):  
R N Markwick ◽  
A Frank ◽  
J Carroll-Nellenback ◽  
B Liu ◽  
E G Blackman ◽  
...  
Keyword(s):  
Thermal Instability ◽  
Three Dimensional ◽  
Oscillation Period ◽  
Three Dimensions ◽  
Temperature Dependent ◽  
Radiative Shock ◽  
Hydrodynamic Simulations ◽  
Protostellar Jets ◽  
The One ◽  
Cooling Function

Abstract Collisional self-interactions occurring in protostellar jets give rise to strong shocks, the structure of which can be affected by radiative cooling within the flow. To study such colliding flows, we use the AstroBEAR AMR code to conduct hydrodynamic simulations in both one and three dimensions with a power law cooling function. The characteristic length and time scales for cooling are temperature dependent and thus may vary as shocked gas cools. When the cooling length decreases sufficiently rapidly the system becomes unstable to the radiative shock instability, which produces oscillations in the position of the shock front; these oscillations can be seen in both the one and three dimensional cases. Our simulations show no evidence of the density clumping characteristic of a thermal instability, even when the cooling function meets the expected criteria. In the three-dimensional case, the nonlinear thin shell instability (NTSI) is found to dominate when the cooling length is sufficiently small. When the flows are subjected to the radiative shock instability, oscillations in the size of the cooling region allow NTSI to occur at larger cooling lengths, though larger cooling lengths delay the onset of NTSI by increasing the oscillation period.

GENERALIZED FIRST-FIT ALGORITHMS IN TWO AND THREE DIMENSIONS

1990 ◽  
Vol 01 (02) ◽  
pp. 131-150 ◽  
Author(s):  
KEQIN LI ◽  
KAM-HOI CHENG
Keyword(s):  
Bin Packing ◽  
Three Dimensional ◽  
Packing Problem ◽  
Three Dimensions ◽  
Performance Ratio ◽  
Dimensional Case ◽  
Performance Bound ◽  
Worst Case ◽  
Packing Problems ◽  
The One

We investigate the two and three dimensional bin packing problems, i.e., packing a list of rectangles (boxes) into unit square (cube) bins so that the number of bins used is a minimum. A simple on-line packing algorithm for the one dimensional bin packing problem, the First-Fit algorithm, is generalized to two and three dimensions. We first give an algorithm for the two dimensional case and show that its asymptotic worse case performance ratio is [Formula: see text]. The algorithm is then generalized to the three dimensional case and its performance ratio [Formula: see text]. The second algorithm takes a parameter and we prove that by choosing the parameter properly, it has an asymptotic worst case performance bound which can be made as close as desired to 1.72=2.89 and 1.73=4.913 respectively in two and three dimensions.

On the Interpretation of Vowel “Quality”: The Dimension of Rounding

1989 ◽  
Vol 19 (1) ◽  
pp. 24-30 ◽  
Author(s):  
Leigh Lisker
Keyword(s):  
Vocal Tract ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Vowel Space ◽  
Tongue Position ◽  
Two Measures ◽  
The One ◽  
Jaw Position ◽  
Three Dimensional Space

The usual description of vowels in respect to their “phonetic quality” requires the linguist to locate them within a so-called “vowel space,” apparently articulatory in nature, and having three dimensions labeled high-low (or close-open), front-back, and unrounded-rounded. The first two are coordinates of tongue with associated jaw position, while the third specifies the posture of the lips. It is recognized that vowels can vary qualitatively in ways that this three-dimensional space does not account for. So, for example, vowels may differ in degree of nasalization, and they may be rhotacized or r-colored. Moreover, it is recognized that while this vowel space serves important functions within the community of linguists, both the two measures of tongue position and the one for the lips inadequately identify those aspects of vocal tract shapes that are primarily responsible for the distinctive phonetic qualities of vowels (Ladefoged 1971). With all this said, it remains true enough that almost any vowel pair of different qualities can be described as occupying different positions with the space. Someone hearing two vowels in sequence and detecting a quality difference will presumably also be able to diagnose the nature of the articulatory shift executed in going from one vowel to the other.

Thermoacoustic Modeling of a Graphene-Based Actuator

2014 ◽  
Author(s):  
Jonghoon Bin ◽  
William S. Oates ◽  
Kunihiko Taira
Keyword(s):  
Three Dimensional ◽  
Three Dimensions ◽  
Model Parameters ◽  
Three Dimensional Model ◽  
Mcmc Algorithms ◽  
Flux Boundary Conditions ◽  
Model Parameter Uncertainty ◽  
The One ◽  
Different Characteristics ◽  
Surface Temperature Variation

A model for two-dimensional graphene-based thermoacoutic membranes is investigated analytically and validated numerically in this study. In one-dimension, the temperature and the pressure variables are analytically determined by decoupling the two variables in the governing equations due to the large disparity between length scales. We further extend the one-dimensional findings to three dimensions. The three-dimensional pressure fluctuation produced by the surface temperature variation is determined with the aid of the acoustic piston model. Through the one and three-dimensional model analysis, the dependence of acoustic pressure as a function of frequency is studied and the acoustic response with respect to the frequency shows different characteristics when assuming Dirichlet (temperature) or Neumann (heat flux) boundary conditions. The general thermoacoustic model is then applied to a graphene-on-paper sound device. Probabilistic Bayesian method coupled with Monte Carlo Markov Chain (MCMC) algorithms is used to optimize model parameters and to analyze model parameter uncertainty. Excellent correlations of thermoacoustic behavior is predicted by the model which provides insight into heat transport mechanisms associated with generating sound from thermally cycling graphene at high frequencies.

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