scholarly journals Mobile impurities in integrable models

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
Andrew Campbell ◽  
Dimitri Gangardt
Keyword(s):  
Bethe Ansatz ◽  
Integrable Systems ◽  
Phonon Scattering ◽  
Integrable Models ◽  
Superfluid Phase ◽  
Leading Order ◽  
One Dimensional ◽  
Bethe Ansatz Solution ◽  
Gaudin Models ◽  
Inelastic Processes

We use a mobile impurity or depleton model to study elementary excitations in one-dimensional integrable systems. For Lieb-Liniger and bosonic Yang-Gaudin models we express two phenomenological parameters characterising renormalised interactions of mobile impurities with superfluid background: the number of depleted particles, NN and the superfluid phase drop \pi JπJ in terms of the corresponding Bethe Ansatz solution and demonstrate, in the leading order, the absence of two-phonon scattering resulting in vanishing rates of inelastic processes such as viscosity experienced by the mobile impurities.

scholarly journals QUASI-EXACTLY SOLVABLE DEFORMATIONS OF GAUDIN MODELS AND "QUASI-GAUDIN ALGEBRAS"

1998 ◽  
Vol 13 (04) ◽  
pp. 281-292 ◽  
Author(s):  
A. G. USHVERIDZE
Keyword(s):  
Bethe Ansatz ◽  
Complete Integrability ◽  
Integrable Models ◽  
Exact Solvability ◽  
New Class ◽  
Algebraic Bethe Ansatz ◽  
Exactly Solvable ◽  
Algebraic Deformation ◽  
Bethe Ansatz Solution ◽  
Gaudin Models

A new class of completely integrable models is constructed. These models are deformations of the famous integrable and exactly solvable Gaudin models. In contrast with the latter, they are quasi-exactly solvable, i.e. admit the algebraic Bethe ansatz solution only for some limited parts of the spectrum. An underlying algebra responsible for both the phenomena of complete integrability and quasi-exact solvability is constructed. We call it "quasi-Gaudin algebra" and demonstrate that it is a special non-Lie-algebraic deformation of the ordinary Gaudin algebra.

scholarly journals Yang-Baxter integrable Lindblad equations

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Aleksandra A. Ziolkowska ◽  
Fabian Essler
Keyword(s):  
Bethe Ansatz ◽  
Quantum Spin ◽  
Spin Chains ◽  
Integrable Models ◽  
Late Time ◽  
Quantum Spin Chains ◽  
Operator Formalism ◽  
One Dimensional ◽  
Time Dynamics

We consider Lindblad equations for one dimensional fermionic models and quantum spin chains. By employing a (graded) super-operator formalism we identify a number of Lindblad equations than can be mapped onto non-Hermitian interacting Yang-Baxter integrable models. Employing Bethe Ansatz techniques we show that the late-time dynamics of some of these models is diffusive.

PHASE SEPARATION AND FFLO PHASES IN ULTRACOLD GAS OF S = 5/2 ATOMS WITH ATTRACTIVE POTENTIAL IN A ONE-DIMENSIONAL TRAP

2012 ◽  
Vol 26 (16) ◽  
pp. 1230009 ◽  
Author(s):  
P. SCHLOTTMANN ◽  
A. A. ZVYAGIN
Keyword(s):  
Phase Separation ◽  
Bethe Ansatz ◽  
Bound States ◽  
Local Density ◽  
Attractive Potential ◽  
Fflo State ◽  
Effective Spin ◽  
One Dimensional ◽  
Bethe Ansatz Solution ◽  
The Rich

In the context of ultracold atoms with effective spin S = 5/2 confined to an elongated trap we study the one-dimensional Fermi gas interacting via an attractive δ-function potential using the Bethe ansatz solution. There are N = 2S + 1 = 6 fundamental states: The particles can either be unpaired or clustered in bound states of 2, 3, …, 2S and 2S + 1 fermions. The rich ground state phase diagram consists of these six states and various mixed phases in which combinations of the fundamental states coexist. Possible scenarios for phase separation due to the harmonic confinement along the tube are explored within the local density approximation. In an array of tubes with weak Josephson tunneling superfluid order may arise. The response functions determining the type of superfluid order are calculated using conformal field theory and the exact Bethe ansatz solution. They consist of a power law with distance times a sinusoidal term oscillating with distance. The wavelength of the oscillations is related to the periodicity of a generalized Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state.

scholarly journals BETHE ANSATZ SOLUTION OF THE CLOSED ANISOTROPIC SUPERSYMMETRIC U MODEL WITH QUANTUM SUPERSYMMETRY

2000 ◽  
Vol 15 (02) ◽  
pp. 133-143 ◽  
Author(s):  
KATRINA HIBBERD ◽  
ITZHAK RODITI ◽  
JON LINKS ◽  
ANGELA FOERSTER
Keyword(s):  
Bethe Ansatz ◽  
One Dimensional ◽  
Algebraic Bethe Ansatz ◽  
Bethe Ansatz Solution ◽  
Closed Lattice

The nested algebraic Bethe Ansatz is presented for the anisotropic supersymmetric U> model maintaining quantum supersymmetry. The Bethe Ansatz equations of the model are obtained on a one-dimensional closed lattice and an expression for the energy is given.

Thermodynamics of the Repulsive Lieb–Liniger Model

2019 ◽  
pp. 633-640
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Bethe Ansatz ◽  
Finite Temperature ◽  
Bose Gas ◽  
Main Ingredient ◽  
Ansatz Method ◽  
One Dimensional ◽  
Bethe Ansatz Solution ◽  
The One

This chapter discusses how the Bethe ansatz solution of the one-dimensional Bose gas with repulsive δ‎-function interaction is extended to finite temperatures, the thermody- namic Bethe ansatz. The excitations of this system consist of particle and hole excitations, which can be described by the corresponding densities of Bethe ansatz roots. It shows how these Bethe ansatz root densities are used to define an appropriate expression for the entropy of the system of Bose particles, which is the main ingredient for the extension of the Bethe ansatz method to finite temperature.

The Bethe Ansatz Solution of a One-Dimensional Fermion Model with Boundary Impurity

1998 ◽  
Vol 12 (23) ◽  
pp. 2435-2446
Author(s):  
Shu Chen ◽  
Yupeng Wang ◽  
Fan Yang ◽  
Fu-Cho Pu
Keyword(s):  
Bethe Ansatz ◽  
Coupling Coefficients ◽  
Ansatz Method ◽  
Fermion Model ◽  
One Dimensional ◽  
Consistent Condition ◽  
Self Consistent ◽  
Special Relations ◽  
Bethe Ansatz Solution ◽  
Special Case

We investigate a 1D fermion model with boundary impurity. When the boundary impurity coupling coefficients fullfil some special relations, this model is integrable. The integrable condition can be determined by the self-consistent condition. Furthermore, the eigenvalue and the Bethe ansatz equation are also obtained by using the coordinate Bethe ansatz method, thus the ground state properties is discussed in some special case.

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