Ballistic deposition on surfaces

Meakin, Paul; Ramanlal, P.; Sander, Leonard M.; Ball, Robin C.

doi:10.1103/physreva.34.5091

Cited by 629 publications

(431 citation statements)

References 32 publications

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“…This model is almost identical to standard models for surface growth [71,72]. It is in the KPZ universality class (it is straightforward to simulate the model and confirm the expected KPZ exponents), and some nonuniversal properties can also be determined exactly (see below).…”

Section: Properties Of the Solvable Modelmentioning

confidence: 74%

“…At late times the model therefore becomes equivalent to the well-known "single step" surface growth model [71], in which ΔS ¼ AE1 only. An appealing feature of this model is that, for a certain choice of boundary conditions (BCs), the late-time probability distribution of the growing interface can be determined exactly [71]. [The solvable case corresponds to choosing periodic BCs in the classical problem.…”

Section: Entanglement Speed In the Solvable Modelmentioning

confidence: 99%

“…This confirms the expected KPZ exponent α ¼ 1=2. It also allows the mean growth rate of the surface to be calculated [71]: the mean height increase in a given time step can be calculated by averaging over the four possible initial configurations for a bond and its two neighbors. After rescaling time so that one unit of time corresponds to an average of one unitary per bond, this gives an entanglement growth rate [Eq.…”

Section: Entanglement Speed In the Solvable Modelmentioning

confidence: 99%

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Quantum Entanglement Growth under Random Unitary Dynamics

et al. 2017

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Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the "entanglement tsunami" in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated KardarParisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like ðtimeÞ 1=3 and are spatially correlated over a distance ∝ ðtimeÞ 2=3 . We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a "minimal cut" picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the "velocity" of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the wellstudied problem of pinning of a membrane or domain wall by disorder.

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Section: Properties Of the Solvable Modelmentioning

confidence: 74%

Section: Entanglement Speed In the Solvable Modelmentioning

confidence: 99%

Section: Entanglement Speed In the Solvable Modelmentioning

confidence: 99%

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Quantum Entanglement Growth under Random Unitary Dynamics

et al. 2017

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“…From this basis the physics literature seeks to describe finer properties of the deposition process. The reader is referred to the survey article [18], and to articles [16], [17], and [20].…”

Section: Statistical Mechanicsmentioning

confidence: 99%

Strong law of large numbers for the interface in ballistic deposition

Seppäläinen

2000

Annales De l'Institut Henri Poincare (B) Probability and Statistics

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Summary. We prove a hydrodynamic limit for ballistic deposition on a multidimensional lattice. In this growth model particles rain down at random and stick to the growing cluster at the first point of contact. The theorem is that if the initial random interface converges to a deterministic macroscopic function, then at later times the height of the scaled interface converges to the viscosity solution of a Hamilton-Jacobi equation. The proof idea is to decompose the interface into the shapes that grow from individual seeds of the initial interface. This decomposition converges to a variational formula that defines viscosity solutions of the macrosopic equation. The technical side of the proof involves subadditive methods and large deviation bounds for related first-passage percolation processes.

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“…(1) is usually put forward to determine both ζ and z in a jointly way by simulating the growth dynamics over different substrate sizes. With the aim of obtaining an independent (separate) evaluation of these exponents, in addition to this standard procedure we will also exploit the known equivalence between BCSOS models and interacting gases of hard-core particles [14]. Following the thread of ideas given in [15], we will recast the Metropolis operator that rules our growth simulations in terms of a quantum spin representation.…”

Section: Introductionmentioning

confidence: 99%

Nonuniversal dynamics of dimer growing interfaces

Grynberg

2007

Phys. Rev. E

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A finite temperature version of body-centered solid-on-solid growth models involving attachment and detachment of dimers is discussed in 1+1 dimensions. The dynamic exponent of the growing interface is studied numerically via the spectrum gap of the underlying evolution operator. The finite size scaling of the latter is found to be affected by a standard surface tension term on which the growth rates depend. This non-universal aspect is also corroborated by the growth behavior observed in large scale simulations. By contrast, the roughening exponent remains robust over wide temperature ranges.

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Ballistic deposition on surfaces

Cited by 629 publications

References 32 publications

Quantum Entanglement Growth under Random Unitary Dynamics

Quantum Entanglement Growth under Random Unitary Dynamics

Strong law of large numbers for the interface in ballistic deposition

Nonuniversal dynamics of dimer growing interfaces

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