Thermodynamic properties of a finite one-dimensional system of bosons with repulsive delta-function interaction

1995 ◽  
Vol 73 (3-4) ◽  
pp. 245-247
Author(s):  
K. L. Poon ◽  
K. Young ◽  
D. Kiang
Keyword(s):  
Thermodynamic Properties ◽  
Thermodynamic Limit ◽  
General Model ◽  
Finite Size ◽  
Delta Function ◽  
One Dimension ◽  
Dimensional System ◽  
One Dimensional ◽  
Finite Size Corrections

The thermodynamics of N bosons in a length L in one dimension, with repulsive delta-function interaction, is studied numerically for finite N, L. The results show the nature of finite-size corrections and how the thermodynamic limit is approached, and hopefully will be of some guidance in seeking the solution of a more general model.

Mixture of interacting supersymmetric spinless fermions and bosons in a one-dimensional trap

2016 ◽  
Vol 30 (25) ◽  
pp. 1630007 ◽  
Author(s):  
P. Schlottmann
Keyword(s):  
Gas Phase ◽  
Ground State ◽  
State Energy ◽  
Optical Trap ◽  
Interaction Strength ◽  
Finite Size ◽  
One Dimension ◽  
One Dimensional ◽  
Bethe Ansatz Solution ◽  
Finite Size Corrections

We consider a gas mixture consisting of spinless fermions and bosons in one dimension interacting via a repulsive [Formula: see text]-function potential. Bosons and fermions are assumed to have equal masses and the interaction strength between bosons and among bosons and fermions is the same. Using the Bethe ansatz solution of the model, we study the ground state properties, the dressed energy potentials for the two bands of rapidities, the elementary particle and hole excitations, the thermodynamics, the finite size corrections to the ground state energy leading to the conformal towers, and the asymptotic behavior at large distances of some relevant correlation functions. The low-energy excitations of the system form a two-component Luttinger liquid. In an elongated optical trap the gas phase separates as a function of the distance from the center of the trap.

scholarly journals Kirkwood-Buff Integrals Using Molecular Simulation: Estimation of Surface Effects

Nanomaterials ◽  
2020 ◽  
Vol 10 (4) ◽  
pp. 771 ◽  
Author(s):  
Noura Dawass ◽  
Peter Krüger ◽  
Sondre K. Schnell ◽  
Othonas A. Moultos ◽  
Ioannis G. Economou ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
Thermodynamic Limit ◽  
Finite Size ◽  
Surface Effects ◽  
System Size ◽  
Distribution Functions ◽  
Finite Systems ◽  
System Method ◽  
The One ◽  
The Relationship

Kirkwood-Buff (KB) integrals provide a connection between microscopic properties and thermodynamic properties of multicomponent fluids. The estimation of KB integrals using molecular simulations of finite systems requires accounting for finite size effects. In the small system method, properties of finite subvolumes with different sizes embedded in a larger volume can be used to extrapolate to macroscopic thermodynamic properties. KB integrals computed from small subvolumes scale with the inverse size of the system. This scaling was used to find KB integrals in the thermodynamic limit. To reduce numerical inaccuracies that arise from this extrapolation, alternative approaches were considered in this work. Three methods for computing KB integrals in the thermodynamic limit from information of radial distribution functions (RDFs) of finite systems were compared. These methods allowed for the computation of surface effects. KB integrals and surface terms in the thermodynamic limit were computed for Lennard–Jones (LJ) and Weeks–Chandler–Andersen (WCA) fluids. It was found that all three methods converge to the same value. The main differentiating factor was the speed of convergence with system size L. The method that required the smallest size was the one which exploited the scaling of the finite volume KB integral multiplied by L. The relationship between KB integrals and surface effects was studied for a range of densities.

Thermodynamic properties of a one-dimensional system of charged bosons

1993 ◽  
Vol 48 (5) ◽  
pp. 3352-3360
Author(s):  
T. W. Craig ◽  
D. Kiang ◽  
A. Niégawa
Keyword(s):  
Thermodynamic Properties ◽  
Dimensional System ◽  
One Dimensional

Thermodynamic Properties of a q-Boson Gas Trapped in an n-Dimensional Harmonic Potential

2003 ◽  
Vol 10 (02) ◽  
pp. 135-145 ◽  
Author(s):  
Guozhen Su ◽  
Lixuan Chen ◽  
Jincan Chen
Keyword(s):  
Heat Capacity ◽  
Distribution Function ◽  
Critical Temperature ◽  
Thermodynamic Properties ◽  
Harmonic Potential ◽  
Einstein Condensation ◽  
Dimensional System ◽  
One Dimensional ◽  
Bose Einstein Condensation ◽  
Bose Einstein

The thermodynamic properties of an ideal q-boson gas trapped in an n-dimensional harmonic potential are studied, based on the distribution function of q-bosons. The critical temperature Tc,q of Bose-Einstein condensation (BEC) and the heat capacity C of the system are derived analytically. It is shown that for the q-boson gas trapped in a harmonic potential, BEC may occur in any dimension when q ≠ 1, the critical temperature is always higher than that of an ordinary Bose gas (q = 1), and the heat capacity is continuous at Tc,q for a one-dimensional system but discontinuous at Tc,q for a two- or multi-dimensional system.

Finite Size Corrections for One Dimensional Interacting Fermions

1992 ◽  
Vol 9 (8) ◽  
pp. 393-396
Author(s):  
Liu Yimin ◽  
Pu Fuque (Fu-Cho Pu) ◽  
Su Hang
Keyword(s):  
Finite Size ◽  
One Dimensional ◽  
Finite Size Corrections

scholarly journals Aspects of the kinetic equations for a special one-dimensional system

1979 ◽  
Vol 21 (2) ◽  
pp. 145-175
Author(s):  
J. W. Evans
Keyword(s):  
Initial Conditions ◽  
Asymptotic Properties ◽  
Kinetic Equations ◽  
Continuous Distribution ◽  
Hard Core ◽  
Delta Function ◽  
Distribution Functions ◽  
Periodic Case ◽  
Dimensional System ◽  
One Dimensional

AbstractSome initial value problems are considered which arise in the treatment of a one-dimensional gas of point particles interacting with a “hard-core” potential.Two basic types of initial conditions are considered. For the first, one particle is specified to be at the origin with a given velocity. The positions in phase space of the remaining background of particles are represented by continuous distribution functions. The second problem is a periodic analogue of the first.Exact equations for the delta-function part of the single particle distribution functions are derived for the non-periodic case and approximate equations for the periodic case. These take the form of differential operator equations. The spectral and asymptotic properties of the operators associated with the two cases are examined and compared. The behaviour of the solutions is also considered.

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