Exact Results for the Boundary Energy of One-Dimensional Bosons
arXiv:1908.08172 · doi:10.1103/PhysRevLett.123.250602
Abstract
We study bosons in a one-dimensional hard-wall box potential. In the case of contact interaction, the system is exactly solvable by the Bethe ansatz, as first shown by Gaudin in 1971. Although contained in the exact solution, the boundary energy in the thermodynamic limit for this problem is only approximately calculated by Gaudin, who found the leading order result at weak repulsion. Here we derive an exact integral equation that enables one to calculate the boundary energy in the thermodynamic limit at an arbitrary interaction. We then solve such an equation and find the asymptotic results for the boundary energy at weak and strong interactions. The analytical results obtained from the Bethe ansatz are in agreement with the ones found by other complementary methods, including quantum Monte Carlo simulations. We study the universality of the boundary energy in the regime of a small gas parameter by making a comparison with the exact solution for the hard rod gas.
arXiv commentsix pages main text and three pages supplemental material; to appear in Physical Review Letters
References in corpus (34)
- Non-equilibrium coherence dynamics in one-dimensional Bose gases
- Bose-Einstein condensation of atoms in a uniform potential
- Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
- Realization of an Excited, Strongly-Correlated Quantum Gas Phase
- Evidence for a critical velocity in a Bose-Einstein condensed gas
- Ultradilute low-dimensional liquids
- Emergence of coherence in a uniform quasi-two-dimensional Bose gas
- Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction
- Beyond Tonks-Girardeau: strongly correlated regime in quasi-one-dimensional Bose gases
- Fermi-Bose mapping for one-dimensional Bose gases
- Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong Coupling
- Dynamical structure factor of one-dimensional Bose gases: experimental signatures of beyond-Luttinger liquid physics
- Recurrences in an isolated quantum many-body system
- Probing three-body correlations in a quantum gas using the measurement of the third moment of density fluctuations
- Correlation functions and momentum distribution of one-dimensional Bose systems
- The liquid state of one-dimensional Bose mixtures: a quantum Monte-Carlo study
- Evidence of Luttinger liquid behavior in one-dimensional dipolar quantum gases
- Weakly interacting Bose gas in the one-dimensional limit
- Ground-state properties of a one-dimensional system of dipoles
- Dynamics of excitations in a one-dimensional Bose liquid
- The 1D interacting Bose gas in a hard wall box
- Excitation spectrum of the Lieb-Liniger model
- One-dimensional liquid He: dynamical properties beyond Luttinger liquid theory
- Super Tonks-Girardeau state in an attractive one-dimensional dipolar gas
- From single-particle excitations to sound waves in a box-trapped atomic Bose-Einstein condensate
- The fermionic limit of the delta-function Bose gas: a pseudopotential approach
- Spin dynamics and Andreev-Bashkin effect in mixtures of one-dimensional Bose gases
- Low-dimensional weakly interacting Bose gases: non-universal equations of state
- Low-energy excitations of a one-dimensional Bose gas with weak contact repulsion
- Luttinger liquid behavior of one-dimensional 3He
- Beyond-Luttinger-Liquid thermodynamics of a one-dimensional contact repulsive Bose gas
- Phase diagram of Rydberg atoms with repulsive van der Waals interaction
- Fluctuation-induced potential for an impurity in a semi-infinite one-dimensional Bose gas
- Spectrum of elementary excitations in Galilean-invariant integrable models
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- Mediated interaction between polarons in a one-dimensional Bose gas
- Exactly-solvable system of one-dimensional trapped bosons with short and long-range interactions
- Fluctuation-induced potential for an impurity in a semi-infinite one-dimensional Bose gas
- Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
- Quantum dark solitons in ultracold one-dimensional Bose and Fermi gases
- Variational optimization of continuous matrix product states
- Dark solitons revealed in Lieb-Liniger eigenstates
- Classical and quantum metrology of the Lieb-Liniger model
- Exact result for the polaron mass in a one-dimensional Bose gas
- Density profile of a semi-infinite one-dimensional Bose gas and bound states of the impurity
- Dispersion relation of a polaron in the Yang-Gaudin Bose gas
- Quantum Borderlines -- Fluctuation Energies in Ultracold Bose Gases
- Love--Lieb integral equations: applications, theory, approximations, and computation
- Hole-induced anomaly in the thermodynamic behavior of a one-dimensional Bose gas
- Reflection phase shifts of bouncing Bogoliubov waves