Nearest-neighbour distance to a trap in a one-dimensional Smoluchowski model

1993 ◽  
Vol 192 (4) ◽  
pp. 617-627 ◽  
Author(s):  
George H. Weiss
Keyword(s):  
Nearest Neighbour ◽  
Neighbour Distance ◽  
One Dimensional ◽  
Smoluchowski Model

scholarly journals Undecidability in quantum thermalization

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Naoto Shiraishi ◽  
Keiji Matsumoto
Keyword(s):  
Turing Machine ◽  
Thermal Equilibrium ◽  
General Theorem ◽  
Nearest Neighbour ◽  
Many Body ◽  
Initial State ◽  
One Dimensional ◽  
Universal Turing Machine ◽  
Many Body Systems ◽  
Neighbour Interaction

AbstractThe investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some never achieve thermal equilibrium. The central problem is to clarify whether a given system thermalizes, which has been addressed previously, but not resolved. Here, we show that this problem is undecidable. The resulting undecidability even applies when the system is restricted to one-dimensional shift-invariant systems with nearest-neighbour interaction, and the initial state is a fixed product state. We construct a family of Hamiltonians encoding dynamics of a reversible universal Turing machine, where the fate of a relaxation process changes considerably depending on whether the Turing machine halts. Our result indicates that there is no general theorem, algorithm, or systematic procedure determining the presence or absence of thermalization in any given Hamiltonian.

ELASTIC PROPERTIES OF STRAINED FCC AND HCP IRON

1993 ◽  
Vol 07 (01n03) ◽  
pp. 207-211
Author(s):  
T. KRAFT ◽  
M. METHFESSEL ◽  
M. VAN SCHILFGAARDE ◽  
M. SCHEFFLER
Keyword(s):  
Energy Cost ◽  
Interplanar Distance ◽  
Orbital Method ◽  
Full Potential ◽  
Local Spin Density Approximation ◽  
Nearest Neighbour ◽  
Density Approximation ◽  
Neighbour Distance ◽  
Large Lattice ◽  
Fcc Phase

Using the full-potential linear muffin-tin orbital method within the local spin-density approximation we analyse the influence of the nearest neighbour distance on fcc(111) or hcp(0001) iron layers. The LDA-LSDA error in describing ferromagnetic phases is determined to be at least 15 mRy/atom. As a consequence of this error, our calculations favour paramagnetic ground states. In this sense, the reported results have some model character. However, our analysis of the elastic energy cost under distortions should hold for transition metals in general. Allowing relaxations of the interplanar distance the fcc phase can become energetically favourable over the hcp phase at large lattice mismatches. The main reason for this behaviour is the enhanced stiffness of the hcp interplanar bonds due to the shortening of the axial c/a ratio.

scholarly journals A computationally efficient estimator for mutual information

2008 ◽  
Vol 464 (2093) ◽  
pp. 1203-1215 ◽  
Author(s):  
Dafydd Evans
Keyword(s):  
Data Analysis ◽  
Mutual Information ◽  
Time Complexity ◽  
Exploratory Data Analysis ◽  
Nearest Neighbour ◽  
Computationally Efficient ◽  
One Dimensional ◽  
Exploratory Data ◽  
Efficient Alternative ◽  
Computationally Expensive

Mutual information quantifies the determinism that exists in a relationship between random variables, and thus plays an important role in exploratory data analysis. We investigate a class of non-parametric estimators for mutual information, based on the nearest neighbour structure of observations in both the joint and marginal spaces. Unless both marginal spaces are one-dimensional, we demonstrate that a well-known estimator of this type can be computationally expensive under certain conditions, and propose a computationally efficient alternative that has a time complexity of order ( N  log  N ) as the number of observations N →∞.

The almost sure central limit theorem for one-dimensional nearest-neighbour random walks in a space-time random environment

2004 ◽  
Vol 41 (01) ◽  
pp. 83-92 ◽  
Author(s):  
Jean Bérard
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Walks ◽  
Central Limit ◽  
Random Environment ◽  
Space Time ◽  
Nearest Neighbour ◽  
One Dimensional ◽  
The Central Limit Theorem ◽  
Almost All

The central limit theorem for random walks on ℤ in an i.i.d. space-time random environment was proved by Bernabeiet al.for almost all realization of the environment, under a small randomness assumption. In this paper, we prove that, in the nearest-neighbour case, when the averaged random walk is symmetric, the almost sure central limit theorem holds for anarbitrarylevel of randomness.

scholarly journals Bulk-edge correspondence and long-range hopping in the topological plasmonic chain

Nanophotonics ◽  
2019 ◽  
Vol 8 (8) ◽  
pp. 1337-1347 ◽  
Author(s):  
Simon R. Pocock ◽  
Paloma A. Huidobro ◽  
Vincenzo Giannini
Keyword(s):  
Long Range ◽  
Metallic Nanoparticles ◽  
Nearest Neighbour ◽  
Edge States ◽  
Physical Treatment ◽  
Bulk Properties ◽  
One Dimensional ◽  
Measure Of Symmetry ◽  
Dipolar System ◽  
Desirable Trait

AbstractThe existence of topologically protected edge modes is often cited as a highly desirable trait of topological insulators. However, these edge states are not always present. A realistic physical treatment of long-range hopping in a one-dimensional dipolar system can break the symmetry that protects the edge modes without affecting the bulk topological number, leading to a breakdown in bulk-edge correspondence (BEC). Hence, it is important to gain a better understanding of where and how this occurs, as well as how to measure it. Here we examine the behaviour of the bulk and edge modes in a dimerised chain of metallic nanoparticles and in a simpler non-Hermitian next-nearest-neighbour model to provide some insights into the phenomena of bulk-edge breakdown. We construct BEC phase diagrams for the simpler case and use these ideas to devise a measure of symmetry-breaking for the plasmonic system based on its bulk properties. This provides a parameter regime in which BEC is preserved in the topological plasmonic chain, as well as a framework for assessing this phenomenon in other systems.

Simulation of Dynamics of Solid-Liquid Transition

1995 ◽  
Vol 407 ◽  
Author(s):  
Y. Kogure ◽  
H. Masuyama ◽  
M. Doyama
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Nearest Neighbour ◽  
Neighbour Distance ◽  
Liquid Transition ◽  
Dynamics Simulations ◽  
Solid Liquid ◽  
Copper Crystals

ABSTRACTMolecular dynamics simulations on the solid-liquid transition of copper crystals have been performed. The configulation and the motion of atoms are monitored by RDF. It is seen that the height of the first peak in the RDF, which located at the nearest neighbour distance, decreased drastically as the temperature is increased.

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