Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userExcitations in the Yang-Gaudin Bose gas
117
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang-Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at $2k_F$ and a finite-momentum roton minimum. Such features occur at energies far above the finite volume excitation gap, vanish slowly as $1/L$ for fixed spinon number, and can persist to the thermodynamic limit at fixed spinon density. Features such as the $2k_F$ gap also persist to multi-particle excitation continua. Our results show that excitations in the finite system can behave in a qualitatively different manner to analogous excitations in the thermodynamic limit. The Yang-Gaudin Bose gas is also host to multi-spinon bound states, known as $Lambda$-strings. We study these excitations both in the thermodynamic limit under the string hypothesis and in finite size systems where string deviations are taken into account. In the zero-temperature limit we present a simple relation between the length $n$ $Lambda$-string dressed energies $epsilon_n(lambda)$ and the dressed energy $epsilon(k)$. We solve the Yang-Yang-Takahashi equations numerically and compare to the analytical solution obtained under the strong couple expansion, revealing that the length $n$ $Lambda$-string dressed energy is Lorentzian over a wide range of real string centers $lambda$ in the vicinity of $lambda = 0$. We then examine the finite size effects present in the dispersion of the two-spinon bound states by numerically solving the Bethe ansatz equations with string deviations.
rate research
Read More
Pseudogap is a ubiquitous phenomenon in strongly correlated systems such as high-$T_{rm c}$ superconductors, ultracold atoms and nuclear physics. While pairing fluctuations inducing the pseudogap are known to be enhanced in low-dimensional systems, such effects have not been explored well in one of the most fundamental 1D models, that is, Gaudin-Yang model. In this work, we show that the pseudogap effect can be visible in the single-particle excitation in this system using a diagrammatic approach. Fermionic single-particle spectra exhibit a unique crossover from the double-particle dispersion to pseudogap state with increasing the attractive interaction and the number density at finite temperature. Surprisingly, our results of thermodynamic quantities in unpolarized and polarized gases show an excellent agreement with the recent quantum Monte Carlo and complex Langevin results, even in the region where the pseudogap appears.
We study the quench dynamics of one dimensional bosons or fermion quantum gases with either attractive or repulsive contact interactions. Such systems are well described by the Gaudin-Yang model which turns out to be quantum integrable. We use a contour integral approach, the Yudson approach, to expand initial states in terms of Bethe Ansatz eigenstates of the Hamiltonian. Making use of the contour, we obtain a complete set of eigenstates, including both free states and bound states. These states constitute a larger Hilbert space than described by the standard String hypothesis. We calculate the density and noise correlations of several quenched systems such as a static or kinetic impurity evolving in an array of particles.
The dynamic spin structure factor $mathcal{S}(k,omega)$ of a system of spin-1/2 bosons is investigated at arbitrary strength of interparticle repulsion. As a function of $omega$ it is shown to exhibit a power-law singularity at the threshold frequency defined by the energy of a magnon at given $k.$ The power-law exponent is found exactly using a combination of the Bethe Ansatz solution and an effective field theory approach.
For a decade the fate of a one-dimensional gas of interacting bosons in an external trapping potential remained mysterious. We here show that whenever the underlying integrability of the gas is broken by the presence of the external potential, the inevitable diffusive rearrangements between the quasiparticles, quantified by the diffusion constants of the gas, eventually lead the system to thermalise at late times. We show that the full thermalising dynamics can be described by the generalised hydrodynamics with diffusion and force terms, and we compare these predictions with numerical simulations. Finally, we provide an explanation for the slow thermalisation rates observed in numerical and experimental settings: the hydrodynamics of integrable models is characterised by a continuity of modes, which can have arbitrarily small diffusion coefficients. As a consequence, the approach to thermalisation can display pre-thermal plateau and relaxation dynamics with long polynomial finite-time corrections.
We describe the use of the exact Yang-Yang solutions for the one-dimensional Bose gas to enable accurate kinetic-energy thermometry based on the root-mean-square width of an experimentally measured momentum distribution. Furthermore, we use the stochastic projected Gross-Pitaevskii theory to provide the first quantitative description of the full momentum distribution measurements of Van Amerongen et al., Phys. Rev. Lett. 100, 090402 (2008). We find the fitted temperatures from the stochastic projected Gross-Pitaevskii approach are in excellent agreement with those determined by Yang-Yang kinetic-energy thermometry.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
