Scattering of electrons from an interacting region

We address the problem of transmission of electrons between two noninteracting leads through a region where they interact (quantum dot). We use a model of spinless electrons hopping on a one-dimensional lattice and with an interaction on a single bond. We show that all two-particle scattering states can be found exactly. Comparisons are made with numerical results on the time evolution of a two-particle wave packet, and several interesting features are found. For N particles, the scattering state is obtained within a two-particle scattering approximation. For a dot connected to Fermi seas at different chemical potentials, we find an expression for the change in the Landauer current resulting from the interactions on the dot. We end with some comments on the case of spin-1/2 electrons.     

Many-times formalism and Coulomb interaction

We extend here the many-times formalism, formerly used mainly for particles moving in given classical fields, to interacting particles. In order to minimize the difficulties associated with an equal-time interaction, we limit ourselves to nonrelativistic quantum mechanics and a two-particle interaction, such as that corresponding to the Coulomb force between charged particles. We obtain a set of differential equations which are really not consistent, but they serve as a guide to a formulation in terms of integral equations that has the same perturbation expansion as the usual theory for the scattering of particles. The integral equation for two-particle amplitudes can be modified to give the correct theory for bound states, but this is not the case for more than two particles. We expect that this theory can be generalized to a formulation of relativistic quantum mechanics of interacting particles.     

Coherence and clock shifts in ultracold fermi gases with resonant interactions

Using arguments based on sum rules, we derive a general result for the average shifts of rf lines in Fermi gases in terms of interatomic interaction strengths and two-particle correlation functions. We show that near an interaction resonance shifts vary inversely with the atomic scattering length, rather than linearly as in dilute gases, thus accounting for the experimental observation that clock shifts remain finite at Feshbach resonances.     

Ladder approximation of the equation of state for degenerate fermi systems

The equation of state is discussed for a system of degenerate fermions. The formation of bound states is allowed for; the latter may exhibit the Bose-Einstein condensation. A complex representation is given which includes bound and scattering two-particle states as well. Different (generalized) representations in terms of scattering quantities are given for the continuum contribution.     

Scattering of a scalar wave from a two-dimensional randomly rough Neumann surface

We present a reciprocity and unitarity preserving formulation of the scattering of a scalar plane wave from a two-dimensional, randomly rough surface on which the Neumann boundary condition is satisfied. The theory is formulated on the basis of the Rayleigh hypothesis in terms of a single-particle Green's function G(q_‖|k_‖) for the surface electromagnetic waves that exist at the surface due to its roughness, where k_‖ and q_‖ are the projections on the mean scattering plane of the wave vectors of the incident and scattered waves, respectively. The specular scattering is expressed in terms of the average of this Green's function over the ensemble of realizations of the surface profile function (G(q_‖|k_‖)). The Dyson equation satisfied by (G(q_‖|k_‖)) is presented, and the properties of the solution are discussed, with particular attention to the proper self-energy in terms of which the averaged Green's function is expressed. The diffuse scattering is expressed in terms of the ensemble average of a two-particle Green's function, which is the product of two single-particle Green's functions. The Bethe-Salpeter equation satisfied by the averaged two-particle Green's function is presented, and properties of its solution are discussed. In the small roughness limit, and with the irreducible vertex function approximated by the sum of the contribution from the maximally-crossed diagrams, which represent the coherent interference between all time-reversed scattering sequences, the solution of the Bethe-Salpeter equation predicts the presence of enhanced backscattering in the angular dependence of the intensity of the waves scattered diffusely.     

Bose-Einstein condensation with an entangled order parameter

We propose a practically accessible non-mean-field ground state of Bose-Einstein condensation, which occurs in an interspecies two-particle entangled state, and is thus described by an entangled order parameter. A suitably defined entanglement entropy is used as the characterization of the non-mean-field nature, and is found to persist in a wide parameter regime. The interspecies entanglement leads to novel interference terms in the dynamical equations governing the single-particle orbital wave function. Experimental feasibility and several methods of probe are discussed. We urge the study of multichannel scattering between different species of atoms.     

自旋梯可积模型的研究

通过对自旋梯可积模型的研究,求出该模型的能量本征值和两体散射矩阵.用可积模型中的坐标Bethe Ansatz方法,首先由薛定谔方程求得能量的本征方程.设定波函数的具体形式,求出本征能量,然后利用能量本征方程和波函数的连续性求出两体散射矩阵.求出单粒子、双粒子和N₀个粒子的本征能量,同时求得粒子的两体散射矩阵.自旋梯可积模型的本征能量和两体散射矩阵可通过Bethe Ansatz的方法求得.     

Scattering of a scalar wave from a two-dimensional randomly rough Neumann surface

Abstract

We present a reciprocity and unitarity preserving formulation of the scattering of a scalar plane wave from a two-dimensional, randomly rough surface on which the Neumann boundary condition is satisfied. The theory is formulated on the basis of the Rayleigh hypothesis in terms of a single-particle Green's function G(q_‖|k_‖) for the surface electromagnetic waves that exist at the surface due to its roughness, where k_‖ and q_‖ are the projections on the mean scattering plane of the wave vectors of the incident and scattered waves, respectively. The specular scattering is expressed in terms of the average of this Green's function over the ensemble of realizations of the surface profile function (G(q_‖|k_‖)). The Dyson equation satisfied by (G(q_‖|k_‖)) is presented, and the properties of the solution are discussed, with particular attention to the proper self-energy in terms of which the averaged Green's function is expressed. The diffuse scattering is expressed in terms of the ensemble average of a two-particle Green's function, which is the product of two single-particle Green's functions. The Bethe-Salpeter equation satisfied by the averaged two-particle Green's function is presented, and properties of its solution are discussed. In the small roughness limit, and with the irreducible vertex function approximated by the sum of the contribution from the maximally-crossed diagrams, which represent the coherent interference between all time-reversed scattering sequences, the solution of the Bethe-Salpeter equation predicts the presence of enhanced backscattering in the angular dependence of the intensity of the waves scattered diffusely.     

Second and third virial coefficient of a quantum gas from two-particle scattering amplitude

Starting from the cluster expansion of the partition function the second and third virial coefficient of a quantum gas is expressed in terms of the two-particle scattering amplitude. In the case of spherically symmetric interaction the result forB(T) agrees with the well known expression ofBeth andUhlenbeck, but the method given here is also valid for non-spherically symmetric and even for non-local potentials. For the third virial coefficientC(T) an expression is derived in lowest order in the two-particle scattering amplitude which is suitable for numerical calculations.     

Scattering tightly bound dimers off a scattering potential

The motion of two attractively interacting atoms in an optical lattice is investigated in the presence of a scattering potential. The initial wavefunction can be prepared by using tightly bound exact two-particle eigenfunction for vanishing scattering potential. This allows to numerically simulate the dynamics in the generation of two-particle Schrödinger cat states using a scheme recently proposed for scattering of quantum matter wave solitons.     

Three-body treatment of Coulomb effects in the problem of long-range effective interactions

The problem of Coulomb scattering of a charged particle by a two-particle bound system, consisting of a charged and a neutral particle, is investigated in the integral-equation approach of rigorous three-body theory. The bound state of the two particles is provided by a short-range interaction chosen in the simplest form using anS-wave separable potential. The integral equation defining the effective potential of the interaction of the charged particle with the two-particle bound system is formulated. It is shown that the multiple Coulomb scattering of the involved charged particles generates a sequence of long-range terms in the effective potential. It turns out that the long-range effects of Coulomb scattering are partly cancelled. As a result the polarization potential does not contain the longest-ranged terms which decrease at large distances as ^–2 and ^–3.     

Coulomb scattering in a 2D interacting electron gas and production of EPR pairs

We propose a setup to generate nonlocal spin Einstein-Podolsky-Rosen pairs via pair collisions in a 2D interacting electron gas, based on constructive two-particle interference in the spin-singlet channel at the pi/2 scattering angle. We calculate the scattering amplitude via the Bethe-Salpeter equation in the ladder approximation and small r(s) limit and find that the Fermi sea leads to a substantial renormalization of the bare scattering process. From the scattering length, we estimate the current of spin-entangled electrons and show that it is within experimental reach.     

Ward identities for interacting electronic systems

A Ward-Takahashi identity, as a consequence of gauge invariance and in a form that relates self-energy to the two-particle Bethe-Salpeter scattering kernel, was first derived by Vollhardt and Wölfle for a system of independent particles moving in a random medium. This is generalized to a class of interacting electronic systems in materials with or without random impurities, following a procedure previously used for classical wave transport in disordered media. This class of systems also possesses other symmetry properties such as invariance under time translations and local spin rotations, which imply local conservation laws for energy and spin current. They imply additional Vollhardt-Wölfle type identities. We present non-perturbative derivations of these identities, and consider the constraints they impose on the relationship between the self-energy and the two-particle scattering kernel.     

Multiple-Scattering Contributions to the Electrical Conductivity of Non-Ideal Plasmas. I. Two Particle Scattering

On the basis of the Green's function formalism multiple scattering effects due to two-particle scattering are investigated with respect to their influence on the electrical conductivity of dense, non-ideal hydrogen plasmas. Both the linear response formalism and the rigorous kinetic treatment via the Kadanoff-Baym equation yield equivalent results for this case. A local lowering of the conductance isotherms for is found to be a consequence of the disappearence of the last bound state of the shielded electron-proton complex. Influences due to lowest order dynamical shielding effects are found to cause considerable lowering of the conductivity in this region due to photon polarization. We also discuss effects of multiple two-particle scattering on the photon-polarization itself.     

Confinement induced molecules in a 1D Fermi gas

We have observed two-particle bound states of atoms confined in a one-dimensional matter waveguide. These bound states exist irrespective of the sign of the scattering length, contrary to the situation in free space. Using radio-frequency spectroscopy we have measured the binding energy of these dimers as a function of the scattering length and confinement and find good agreement with theory. The strongly interacting one-dimensional Fermi gas which we create in an optical lattice represents a realization of a tunable Luttinger liquid.     

The three-boson stimulated scattering behaviour

We show the resonance behaviour of three-boson “stimulated scattering” (TBSS) which was observed recently. In a sufficiently cold boson gas the zero momentum particles accumulation should take place as a result of TBSS alone without any collective effects and for any non-bonding two-particle interaction potential.     

Threshold behaviour of the three-particle scattering amplitude and gas approximation in the many-body problem

It is established by investigation of the gas approximation for the ground state energy in many-body problem how the low energy parameters of the two-particle and essentially three-particle scattering amplitude determine the dominant terms of the energy expansion in series of gas parameter. The correspondence to the gas approximation in the Faddeev integral equations in the form of the three-particle amplitude low energy behaviour near the threshold E → 0 is obtained.     

Theory of fluctuations in non-equilibrium Fermi gas

We present the equations for the equal-time two-particle correlation functions in degenerate electron gas. In association with the Onsager-type equation for the time-displaced correlation function, the equations constitute the basis of the theory of fluctuations in non-equilibrium degenerate electron gas. Thanks to the prevalence of the small-angle inter-electron scattering, the theory takes a rather simple form.     

Elasticity,factorization and S-matrices in (1+1)-dimensions

The hypothesis of vanishing particle-production, non-vanishing backward scattering and a factorisation condition on the S-matrix allow an infinite arbitrariness in the two-particle scattering amplitudes. The general form is explicitly obtained.