We consider a two-dimensional particle of charge e interacting with a homogeneous magnetic eld perpendicular to the plane and a potential well which is transported along a closed loop in the plane. We show that a bound state corresponding to a simple isolated eigenvalue acquires at that Berry's phase equal to 2 sgne times the number of ux quanta through the oriented area encircled by the loop. We also argue that this is a purely quantum e ect since the corresponding Hannay angle is zero.

We discuss formulations of boundary conditions in a quantum graph vertex and demonstrate that the so-called ST-form can be further reduced up to a form more effective in certain applications: In particular, in identifying the number of independent parameters for given ranks of two connection matrices, or in calculating the scattering matrix when both matrices are singular. The new form of boundary conditions, called the P Q R S-form, also gives a natural scheme to design generalized low and high pass quantum filters.

No abstract uploaded!

In this letter we discuss a new physical effect: we show that the BoseEinstein condensate can be created in quasi-one-dimensional systems in a purely geometrical way, namely by bending or other suitable deformation of a tube. We demonstrate this for the perfect Bose gas as well as for the case of mean-field particle interactions.

No abstract uploaded!