A deep understanding of the mechanisms underlying many-body quantum chaos is one of the big challenges in contemporary theoretical physics. We tackle this problem in the context of a set of perturbed quadratic Sachdev...
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A deep understanding of the mechanisms underlying many-body quantum chaos is one of the big challenges in contemporary theoretical physics. We tackle this problem in the context of a set of perturbed quadratic Sachdev-Ye-Kitaev (SYK) Hamiltonians defined on graphs. This allows us to disentangle the geometrical properties of the underlying single-particle problem and the importance of the interaction terms, showing that the former is the dominant feature ensuring the single-particle to many-body chaotic transition. Our results are verified numerically with state-of-the-art numerical techniques, capable of extracting eigenvalues in a desired energy window of very large Hamiltonians. Our approach essentially provides a new way of viewing many-body chaos from a single-particle perspective.
We propose a general framework of computing interfacial structures between two modulated *** we propose to use a computational box consisting of two half spaces,each occupied by a modulated phase with given position a...
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We propose a general framework of computing interfacial structures between two modulated *** we propose to use a computational box consisting of two half spaces,each occupied by a modulated phase with given position and *** boundary conditions and basis functions are chosen to be commensurate with the bulk *** observe that the ordered nature of modulated structures stabilizes the interface,which enables us to obtain optimal interfacial structures by searching local minima of the free energy *** framework is applied to the Landau-Brazovskii model to investigate interfaces between modulated phases with different relative positions and *** types of novel complex interfacial structures emerge from the calculations.
Using first-principles calculation, we propose an interface structure for single triple-layer FeSe on the SrTiO3(001) surface, a high-Tc superconductor found recently. The key component of this structure is the oxygen...
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Using first-principles calculation, we propose an interface structure for single triple-layer FeSe on the SrTiO3(001) surface, a high-Tc superconductor found recently. The key component of this structure is the oxygen deficiency on the top layer of the SrTiO3 substrate, as a result of Se etching used in preparing the high-Tc samples. The O vacancies strongly bind the FeSe triple layer to the substrate giving rise to a (2×1) reconstruction, as observed by scanning tunneling microscopy. The enhanced binding correlates to the significant increase of Tc observed in experiment. The O vacancies also serve as the source of electron doping, which modifies the Fermi surface of the first FeSe layer by filling the hole pocket near the center of the surface Brillouin zone, as suggested from angle-resolved photoemission spectroscopy measurement.
The statistical properties of decaying compressible turbulence are investigated by direct numerical simulations of flow in a periodic cube. Starting with fully developed turbulence for various microscale Reynolds numb...
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The dynamic behavior of RMSprop and Adam algorithms is studied through a combination of careful numerical experiments and theoretical explanations. Three types of qualitative features are observed in the training loss...
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The dynamics of velocity fluctuations, governed by the one-dimensional Burgers equation, driven by a white-in-time random force f with the spatial spectrum ‖f(k)‖2∝k−1, is considered. High-resolution numerical expe...
The dynamics of velocity fluctuations, governed by the one-dimensional Burgers equation, driven by a white-in-time random force f with the spatial spectrum ‖f(k)‖2∝k−1, is considered. High-resolution numerical experiments conducted in this work give the energy spectrum E(k)∝k−β with β=5/3±0.02. The observed two-point correlation function C(k,ω) reveals ω∝kz with the ‘‘dynamic exponent’’ z≊2/3. High-order moments of velocity differences show strong intermittency and are dominated by powerful large-scale shocks. The results are compared with predictions of the one-loop renormalized perturbation expansion.
This paper studies a class of probabilistic models on graphs, where edge variables depend on incident node variables through a fixed probability kernel. The class includes planted constraint satisfaction problems (CSP...
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We introduce a lattice Boltzmann model for simulating immiscible binary fluids in two dimensions. The model, based on the Boltzmann equation of lattice-gas hydrodynamics, incorporates features of a previously introduc...
We introduce a lattice Boltzmann model for simulating immiscible binary fluids in two dimensions. The model, based on the Boltzmann equation of lattice-gas hydrodynamics, incorporates features of a previously introduced discrete immiscible lattice-gas model. A theoretical value of the surface-tension coefficient is derived and found to be in excellent agreement with values obtained from simulations. The model serves as a numerical method for the simulation of immiscible two-phase flow; a preliminary application illustrates a simulation of flow in a two-dimensional microscopic model of a porous medium. Extension of the model to three dimensions appears straightforward.
Statistical properties of solutions of the random-force–driven Burgers equation are investigated by use of the dynamic renormalization group and direct numerical simulations. The agreement between computed and analyt...
Statistical properties of solutions of the random-force–driven Burgers equation are investigated by use of the dynamic renormalization group and direct numerical simulations. The agreement between computed and analytical results on both exponents and amplitudes of the correlation functions is good. It is shown that a small-scale noise dominates large-scale, long-time (k→0,ω→0) behavior of the system and, as a consequence, no microscopic system of interacting particles described by Burgers equation in the hydrodynamic limit (k→0,ω→0) exists.
The quantitative interpretation of the recent experiments on turbulent diffusivity in high‐Reynolds‐number Couette–Taylor flow by Tam and Swinney [Phys. Rev. A 36, 1374 (1987)], is presented.
The quantitative interpretation of the recent experiments on turbulent diffusivity in high‐Reynolds‐number Couette–Taylor flow by Tam and Swinney [Phys. Rev. A 36, 1374 (1987)], is presented.
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