Momentum Distribution in the Ground State of the One‐Dimensional System of Impenetrable Bosons

1964 ◽  
Vol 5 (7) ◽  
pp. 930-943 ◽  
Author(s):  
A. Lenard
Keyword(s):  
Momentum Distribution ◽  
Ground State ◽  
Dimensional System ◽  
One Dimensional ◽  
The One

Quantum mechanics of the damped harmonic oscillator

2002 ◽  
Vol 80 (6) ◽  
pp. 645-660 ◽  
Author(s):  
M Blasone ◽  
P Jizba
Keyword(s):  
Harmonic Oscillator ◽  
Ground State ◽  
Geometric Phase ◽  
State Energy ◽  
Dimensional System ◽  
One Dimensional ◽  
Damped Harmonic Oscillator ◽  
Linear Harmonic Oscillator ◽  
Two Dimensional System ◽  
The One

We quantize the system of a damped harmonic oscillator coupled to its time-reversed image, known as Bateman's dual system. By using the Feynman–Hibbs method, the time-dependent quantum states of such a system are constructed entirely in the framework of the classical theory. The geometric phase is calculated and found to be proportional to the ground-state energy of the one-dimensional linear harmonic oscillator to which the two-dimensional system reduces under appropriate constraint. PACS Nos.: 03.65Ta, 03.65Vf, 03.65Ca, 03.65Fd

scholarly journals Dimerization in Quantum Spin Chains with O(n) Symmetry

2021 ◽  
Author(s):  
Jakob E. Björnberg ◽  
Peter Mühlbacher ◽  
Bruno Nachtergaele ◽  
Daniel Ueltschi
Keyword(s):  
Phase Diagram ◽  
Ground State ◽  
Quantum Spin ◽  
Spin Chains ◽  
Dimensional System ◽  
Quantum Spin Chains ◽  
One Dimensional ◽  
Open Region ◽  
Quantum Spins ◽  
The One

AbstractWe consider quantum spins with $$S\ge 1$$ S ≥ 1 , and two-body interactions with $$O(2S+1)$$ O ( 2 S + 1 ) symmetry. We discuss the ground state phase diagram of the one-dimensional system. We give a rigorous proof of dimerization for an open region of the phase diagram, for S sufficiently large. We also prove the existence of a gap for excitations.

Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster
Keyword(s):  
Reaction Diffusion ◽  
Dominant Mode ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Perturbation ◽  
Dimensional System ◽  
One Dimensional ◽  
Brusselator Model ◽  
The One ◽  
Dominant Structure

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.

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.

REACTION-FRONT DYNAMICS IN A+B→C WITH INITIALLY-SEPARATED REACTANTS

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 405-415 ◽  
Author(s):  
S. HAVLIN ◽  
M. ARAUJO ◽  
H. LARRALDE ◽  
A. SHEHTER ◽  
H.E. STANLEY
Keyword(s):  
Reaction Front ◽  
Reaction Rate ◽  
Reaction System ◽  
Diffusion Reaction ◽  
Dimensional System ◽  
Scaling Exponent ◽  
One Dimensional ◽  
Recent Developments ◽  
The One ◽  
Front Dynamics

We review recent developments in the study of the diffusion reaction system of the type A+B→C in which the reactants are initially separated. We consider the case where the A and B particles are initially placed uniformly in Euclidean space at x>0 and x<0 respectively. We find that whereas for d≥2 a single scaling exponent characterizes the width of the reaction zone, a multiscaling approach is needed to describe the one-dimensional system. We also present analytical and numerical results for the reaction rate on fractals and percolation systems.

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