Ground-state and quenched-state properties of a one-dimensional interacting lattice gas in a random potential

1987 ◽  
Vol 49 (5-6) ◽  
pp. 1235-1254 ◽  
Author(s):  
Y. Fonk ◽  
H. J. Hilhorst
Keyword(s):  
Ground State ◽  
Lattice Gas ◽  
Random Potential ◽  
One Dimensional

scholarly journals Distribution of Cracks in a Chain of Atoms at Low Temperature

2021 ◽  
Author(s):  
Sabine Jansen ◽  
Wolfgang König ◽  
Bernd Schmidt ◽  
Florian Theil
Keyword(s):  
Low Temperature ◽  
Ground State ◽  
Lattice Gas ◽  
Nearest Neighbor ◽  
Periodic Lattice ◽  
Many Body ◽  
One Dimensional ◽  
Uniform Estimates ◽  
A Chain ◽  
Crystalline Domains

AbstractWe consider a one-dimensional classical many-body system with interaction potential of Lennard–Jones type in the thermodynamic limit at low temperature $$1/\beta \in (0,\infty )$$ 1 / β ∈ ( 0 , ∞ ) . The ground state is a periodic lattice. We show that when the density is strictly smaller than the density of the ground state lattice, the system with N particles fills space by alternating approximately crystalline domains (clusters) with empty domains (voids) due to cracked bonds. The number of domains is of the order of $$N\exp (- \beta e_\mathrm {surf}/2)$$ N exp ( - β e surf / 2 ) with $$e_\mathrm {surf}>0$$ e surf > 0 a surface energy. For the proof, the system is mapped to an effective model, which is a low-density lattice gas of defects. The results require conditions on the interactions between defects. We succeed in verifying these conditions for next-nearest neighbor interactions, applying recently derived uniform estimates of correlations.

scholarly journals Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Przemysław Kościk ◽  
Arkadiusz Kuroś ◽  
Adam Pieprzycki ◽  
Tomasz Sowiński
Keyword(s):  
Boundary Conditions ◽  
Ground State ◽  
Pair Correlation ◽  
Contact Interactions ◽  
One Dimensional ◽  
Particle Correlations ◽  
Variational Scheme ◽  
Full Control ◽  
Arbitrary Shapes

AbstractWe derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. It is based on assumption that all inter-particle correlations have two-body nature. By construction, the proposed ansatz is exact in the noninteracting limit, exactly encodes boundary conditions forced by contact interactions, and gives full control on accuracy in the limit of infinite repulsions. We show its efficiency in a whole range of intermediate interactions for different external potentials. Our results manifest that for generic non-parabolic potentials mutual correlations forced by interactions cannot be captured by distance-dependent functions.

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