dimensional many - body problem with contact interaction : Including a tunable impurity
نویسندگان
چکیده
The one-dimensional problem of N particles with contact interaction in the presence of a tunable transmitting and reflecting impurity is investigated along the lines of the coordinate Bethe ansatz. As a result, the system is shown to be exactly solvable by determining the eigenfunctions and the energy spectrum. The latter is given by the solutions of the Bethe ansatz equations which we establish for different boundary conditions in the presence of the impurity. These impurity Bethe equations contain as special cases well-known Bethe equations for systems on the half-line. We briefly study them on their own through the toy-examples of one and two particles. It turns out that the impurity can be tuned to lift degeneracies in the energies and can create bound states when it is sufficiently attractive. The example of an impurity sitting at the center of a box and breaking parity invariance shows that such an impurity can be used to confine asymmetrically a stationary state. This could have interesting applications in condensed matter physics.
منابع مشابه
one - dimensional many - body problem with contact interaction : Including a tunable impurity
The one-dimensional problem of N particles with contact interaction in the presence of a tunable transmitting and reflecting impurity is investigated along the lines of the coordinate Bethe ansatz. As a result, the system is shown to be exactly solvable by determining the eigenfunctions and the energy spectrum. The latter is given by the solutions of the Bethe ansatz equations which we establis...
متن کاملFour-dimensional Kondo Problem
In 1934, de Haas, de Boer, and van den Berg observed that a small concentration of magnetic impurities in a metal leads to a minimum in the temperature dependence of the resistance. Thirty years later, this effect was explained by Jun Kondo, who used perturbation theory to study the exchange interaction of a localized magnetic impurity with the conduction electrons of the host metal. Further de...
متن کاملFrom few to many: observing the formation of a Fermi sea one atom at a time.
Knowing when a physical system has reached sufficient size for its macroscopic properties to be well described by many-body theory is difficult. We investigated the crossover from few- to many-body physics by studying quasi-one-dimensional systems of ultracold atoms consisting of a single impurity interacting with an increasing number of identical fermions. We measured the interaction energy of...
متن کاملQuantum entanglement in the two-impurity Kondo model
In order to quantify quantum entanglement in two-impurity Kondo systems, we calculate the concurrence, negativity, and von Neumann entropy. The entanglement of the two Kondo impurities is shown to be determined by two competing many-body effects, namely the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida RKKY interaction, I. Due to the spin-rotational invariance of the ground state, the conc...
متن کاملMesoscopic Kondo problem
– We study the effect of mesoscopic fluctuations on a magnetic impurity coupled to a spatially confined electron gas with a temperature in the mesoscopic range (i.e. between the mean level spacing ∆ and the Thouless energy ETh). Comparing “poor-man’s scaling” with exact Quantum Monte Carlo, we find that for temperatures larger than the Kondo temperature, many aspects of the fluctuations can be ...
متن کامل