QUANTUM HAMILTONIANS AND SELF-ORGANISED CRITICALITY

1994 ◽  
Vol 08 (25n26) ◽  
pp. 3463-3471 ◽  
Author(s):  
JOHN CARDY
Keyword(s):  
Master Equation ◽  
Quantum System ◽  
Critical Behavior ◽  
Classical Limit ◽  
Particle Model ◽  
Hydrodynamic Behavior ◽  
One Dimensional ◽  
Self Organised Criticality ◽  
Stochastic Particle

We consider a stochastic particle model which has been proposed to exhibit the essential features of self-organised criticality. The master equation is reformulated as a one-dimensional quantum system of interacting bosons. The hydrodynamic behavior of the system is recovered as the classical limit of the quantum system, and the problem of fluctuations, important for the critical behavior, is discussed.

Quantum Boxes, Stringed Instruments

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Energy Level ◽  
Schrödinger Equation ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Probability Distributions ◽  
Wave Functions ◽  
Energy Level Diagram ◽  
One Dimensional ◽  
Stringed Instruments ◽  
Symmetry Properties

Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.

Critical behavior and anisotropic magnetocaloric effect of the quasi-one-dimensional hexagonal ferromagnet PrCrGe3

2021 ◽  
Vol 103 (10) ◽  
Author(s):  
Xiaojun Yang ◽  
Junxiao Pan ◽  
Shijiang Liu ◽  
Mao Yang ◽  
Leiming Cao ◽  
...  
Keyword(s):  
Magnetocaloric Effect ◽  
Critical Behavior ◽  
One Dimensional

scholarly journals Circuit Simulates One-Dimensional Quantum System

Physics ◽  
2018 ◽  
Vol 11 ◽  
Author(s):  
Emanuele Dalla Torre ◽  
Eran Sela
Keyword(s):  
Quantum System ◽  
One Dimensional

scholarly journals Equivalence between Redfield- and master-equation approaches for a time-dependent quantum system and coherence control

2011 ◽  
Vol 83 (6) ◽  
Author(s):  
D. O. Soares-Pinto ◽  
M. H. Y. Moussa ◽  
J. Maziero ◽  
E. R. deAzevedo ◽  
T. J. Bonagamba ◽  
...  
Keyword(s):  
Master Equation ◽  
Quantum System ◽  
Time Dependent

Characterization of Biosensor Detection Process at Ultra-Low Concentration Through a Stochastic Particle Model

2010 ◽  
Author(s):  
Samar Shah ◽  
Yaling Liu ◽  
Walter Hu
Keyword(s):  
Liquid Solution ◽  
Particle Model ◽  
Low Concentration ◽  
Detection Process ◽  
Nanoparticle Detection ◽  
Early Disease Detection ◽  
Cost Efficient ◽  
New Applications ◽  
Stochastic Particle

Biosensor detection process involves binding between biomolecules in a solution and a functionalized sensor surface. These sensors are time and cost efficient, sensitive, and enable new applications in medicine, drug design, and environmental monitoring. In literatures, various biosensor designs have been proposed, such as planar electrodes, nanowire, and nanospheres for different applications. However, to fully realize the potentials of these biosensors for biomarker/nanoparticle detection, several challenges must be addressed. In particular, ultra-sensitive biosensors are needed for detection of ultra-low concentration biomarkers such as cancer markers for early disease detection. The goal of this paper is to understand the diffusion process of biomarkers in a liquid solution and the binding with nanosensor surface through a stochastic particle model.

Surfaces with pores: hydrodynamic lubrication

2017 ◽  
Vol 69 (4) ◽  
pp. 471-483 ◽  
Author(s):  
Leonid Burstein
Keyword(s):  
Design Methodology ◽  
Hydrodynamic Lubrication ◽  
Dimensional Model ◽  
Hydrodynamic Behavior ◽  
Content Type ◽  
One Dimensional ◽  
Lubricating Film ◽  
Cell Dimensions ◽  
Practical Implications ◽  
Pore Cell

Purpose This paper aims to assess the hydrodynamic lubrication of two opposing surfaces with identical pores having a semicircular profile. The surfaces are treated with more than one pore that allows clarification of whether there exists interaction between the pores. Design/methodology/approach A transient, spatial, one-dimensional model of surfaces with regular pores was developed and applied in the context of fluid lubrication. MATLAB software has been used. Findings Calculations show that a lubricating film between two surfaces with pores provides better hydrodynamic conditions in comparison to that on one surface with pores. It was also shown that the pores of one surface act as separate objects and can take into account only the interaction between the pores of the opposite surfaces. In addition, it was found that there are optimum values of the pore radii, gap and pore cell dimensions at which the bearing capacity of the film is maximal. Practical implications The computer program used for the pore parameter calculations provided the optimal lubrication. Originality/value This is the first study of the lubricating film hydrodynamic behavior of two opposite surfaces with pores having a semicircular profile.

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