Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas
| Autor: | Andrea Colcelli, Giuseppe Mussardo, Andrea Trombettoni, Jacopo Viti |
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| Přispěvatelé: | Colcelli, Andrea, Viti, J., Mussardo, G., Trombettoni, A. |
| Rok vydání: | 2018 |
| Předmět: |
Density matrix
Bosonization Tonks-Girardeau gas Atomic and Molecular Physics and Optics FOS: Physical sciences Field (mathematics) Lambda 01 natural sciences 010305 fluids & plasmas Tonks–Girardeau gas 0103 physical sciences 010306 general physics Condensed Matter - Statistical Mechanics Mathematical physics Physics Statistical Mechanics (cond-mat.stat-mech) Order (ring theory) Atomic and Molecular Physics and Optics Settore FIS/02 - Fisica Teorica Modelli e Metodi Matematici Atomic and Molecular Physic Distribution (mathematics) Quantum Gases (cond-mat.quant-gas) Exponent Condensed Matter - Quantum Gases 1d systems |
| Zdroj: | Repositório Institucional da UFRN Universidade Federal do Rio Grande do Norte (UFRN) instacron:UFRN Physical review, A Print 98 (2018). doi:10.1103/PhysRevA.98.063633 info:cnr-pdr/source/autori:Colcelli, A.; Viti, J.; Mussardo, G.; Trombettoni, A./titolo:Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas/doi:10.1103%2FPhysRevA.98.063633/rivista:Physical review, A Print/anno:2018/pagina_da:/pagina_a:/intervallo_pagine:/volume:98 |
| ISSN: | 2469-9934 2469-9926 |
| DOI: | 10.1103/physreva.98.063633 |
| Popis: | The scaling of the largest eigenvalue $\lambda_0$ of the one-body density matrix of a system with respect to its particle number $N$ defines an exponent $\mathcal{C}$ and a coefficient $\mathcal{B}$ via the asymptotic relation $\lambda_0 \sim \mathcal{B}\,N^{\mathcal{C}}$. The case $\mathcal{C}=1$ corresponds to off-diagonal long-range order. For a one-dimensional homogeneous Tonks-Girardeau gas, a well known result also confirmed by bosonization gives instead $\mathcal{C}=1/2$. Here we investigate the inhomogeneous case, initially addressing the behaviour of $\mathcal{C}$ in presence of a general external trapping potential $V$. We argue that the value $\mathcal{C}= 1/2$ characterises the hard-core system independently of the nature of the potential $V$. We then define the exponents $\gamma$ and $\beta$ which describe the scaling with $N$ of the peak of the momentum distribution and the natural orbital corresponding to $\lambda_0$ respectively, and we derive the scaling relation $\gamma + 2\beta= \mathcal{C}$. Taking as a specific case the power-law potential $V(x)\propto x^{2n}$, we give analytical formulas for $\gamma$ and $\beta$ as functions of $n$. Analytical predictions for the coefficient $\mathcal{B}$ are also obtained. These formulas are derived exploiting a recent field theoretical formulation and checked against numerical results. The agreement is excellent. Comment: 14 pages, 5 figures |
| Databáze: | OpenAIRE |
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