This paper continues the work Y. Suhov, M. Kelbert. FK-DLR states of a quantum bose-gas, arXiv:1304.0782 [math-ph], and focuses on infinite-volume bosonic states for a quantum system (a quantum gas) in a plane. We work under similar assumptions upon the form of local Hamiltonians and the type of the (pair) interaction potential as in the reference above. The result of the paper is that any infinite-volume FK-DLR functional corresponding to the Hamiltonians is shift-invariant, regardless of whether this functional is unique or not.This paper continues the work Y. Suhov, M. Kelbert. FK-DLR states of a quantum bose-gas, arXiv:1304.0782 [math-ph], and focuses on infinite-volume bosonic states for a quantum system (a quantum gas) in a plane. We work under similar assumptions upon the form of local Hamiltonians and the type of the (pair) interaction potential as in the reference above. The result of the paper is that any infinite-volume FK-DLR functional corresponding to the Hamiltonians is shift-invariant, regardless of whether this functional is unique or not.

arXiv:1304.4177Apr 15, 20133 citations

Integral functions of the Bose gas

Maxine Pitter Lunn

Letters in Mathematical PhysicsJan 1, 19830 citations

A study of correlation functions for the delta-function Bose gas

Dennis B. Creamer, H. B. Thacker, David Wilkinson

Physica D Nonlinear PhenomenaJun 1, 198628 citations

Continuous Matrix Product Ansatz for the One-Dimensional Bose Gas with Point Interaction

Isao Maruyama, Hosho Katsura

We study a matrix product representation of the Bethe ansatz state for the Lieb-Linger model describing the one-dimensional Bose gas with delta-function interaction. We first construct eigenstates of the discretized model in the form of matrix product states using the algebraic Bethe ansatz. Continuous matrix product states are then exactly obtained in the continuum limit with a finite number of particles. The factorizing $F$ -matrices in the lattice model are indispensable for the continuous matrix product states and lead to a marked reduction from the original bosonic system with infinite degrees of freedom to the five-vertex model.We study a matrix product representation of the Bethe ansatz state for the Lieb-Linger model describing the one-dimensional Bose gas with delta-function interaction. We first construct eigenstates of the discretized model in the form of matrix product states using the algebraic Bethe ansatz. Continuous matrix product states are then exactly obtained in the continuum limit with a finite number of particles. The factorizing $F$-matrices in the lattice model are indispensable for the continuous matrix product states and lead to a marked reduction from the original bosonic system with infinite degrees of freedom to the five-vertex model.

arXiv:1003.5463Journal of the Physical Society of JapanJul 15, 201023 citations

Simplified Approach to the Ground-State Energy of an Imperfect Bose Gas. III. Application to the One-Dimensional Model

Élliott H. Lieb, Werner Liniger

We continue the study of the integrodifferential equation proposed previously for the evaluation of the ground-state energy of an imperfect Bose gas. We apply it here to the one-dimensional delta-function gas where the exact result is known for all values of the coupling constant $\ensuremath{\gamma}$. The results are: (i) For small $\ensuremath{\gamma}$, the equation gives the correct first two terms in an asymptotic series; (ii) a numerical solution of the equation shows that the maximum relative error occurs for $\ensuremath{\gamma}=\ensuremath{\infty}$ in which case it is 19%; (iii) for $\ensuremath{\gamma}=\ensuremath{\infty}$ we are able to compare the exact two-particle distribution function with that given by the equation. The agreement is quite good.We continue the study of the integrodifferential equation proposed previously for the evaluation of the ground-state energy of an imperfect Bose gas. We apply it here to the one-dimensional delta-function gas where the exact result is known for all values of the coupling constant $\ensuremath{\gamma}$. The results are: (i) For small $\ensuremath{\gamma}$, the equation gives the correct first two terms in an asymptotic series; (ii) a numerical solution of the equation shows that the maximum relative error occurs for $\ensuremath{\gamma}=\ensuremath{\infty}$ in which case it is 19%; (iii) for $\ensuremath{\gamma}=\ensuremath{\infty}$ we are able to compare the exact two-particle distribution function with that given by the equation. The agreement is quite good.

Physical ReviewApr 20, 196418 citations

Field correlation functions in a one-dimensional Bose gas

Anatoli G. Izergin, V. E. Korepin, Nicolai Reshetikhin

Journal of Mathematical SciencesJul 1, 19892 citations

F

-matrices in the lattice model are indispensable for the continuous matrix product states and lead to a marked reduction from the original bosonic system with infinite degrees of freedom to the five-vertex model.