On electric fields created by quantized vortices

Abstract

It is shown that in a magnetic field quantized vortices in a superfluid obtain a real quantized electric charge concentrated in the vortex core. This charge is compensated by an opposite surface charge located at a macroscopic distance from the vortex axis. It is determined that the polarization caused by the vortex velocity field does not give rise to electric fields outside an infinite cylinder. Observation of electric fields created by the vortices is possible only near the end surfaces of the cylinder which must be closed with dielectric covers to prevent superfluid leaking. Influence of cover properties on the potential created by the vortex is researched. Potential created by the vortices on point and ring electrodes are calculated. were undertaken to understand the nature of the observed phenomena, but they are unsuccessful up to date. However, several interesting results were obtained which concern the mechanisms of polarization of both superfluid and normal systems. For example, in Melnikovskiy's article [4] it is shown that accelerated motion of a dielectric medium leads to its polarization proportional to the acceleration. Natsik [5] - [7] has studied the peculiarities of polarization of superfluid systems and, developing Melnikovskiy's ideas, has found that vortex motion of atoms in a superfluid must lead to their polarization caused by centrifugal force acting on them. In this case the polarization vector is directed normally to the velocity of the fluid moving around the vortex line, so the polarization vectors form a "hedgehog". Unfortunately, observation of electric fields caused by this "hedgehog" is rather difficult due to their rapid decrease with distance from the vortex line (reverse proportional to the cube of the distance). The authors [14] - [16] found that in a magnetic field the vortex line acquires a real electric charge whose magnitude is proportional to the vortex circulation and is quantized in the same way as the circulation. The compensating charge of the opposite sign appears on the surface of the system. Macroscopic spatial separation of the vortex charge and the compensating one allows to measure the electric field caused by these charges and to observe the motion of vortices in the superfluid. In this message we discuss the significant aspects of measuring the electric fields generated by the vortices.First we recall the arguments of the articles [14] -[16]. In a magnetic field H a rarefied medium moving with velocity v acquires polarizationHere α is the atom polarizability, n is the medium den- * Electronic address: shevchenko@ilt.kharkov.ua sity, c is the velocity of light. It follows from the common expression for the electric induction of the moving mediumwhere µ is the magnetic permeability, that the expression (1) for the dipole moment P is valid when µ = 1 and ǫ = 1 + 4πnα. In a superfluid there exists a "characteristic configuration" of the velocity field v caused by a vortex,Here φ is the phase of the order parameter. In the case of a rectilinear vortex in a uniform m...

Two approaches to the description of dilute superfluid Bose systems

“…We see a fundamental difference of the expressions (28) and (29) from the similar expressions (21) in the previous section. Because of this difference, in this case the system energy E ¼ h0jĤj0i is a functional in the form of an infinite series in powers of U and U þ .…”

“…2 and 17) and in terms of the two-particle order parameter U(r 1 , r 2 ). [18][19][20][21] It is found that there are fundamental differences between these two approaches. In applying the first method to composite bosons the effects related to the exchange interaction are completely lost, which in some cases, particularly in the case of the Coulomb interaction between the particles, leads to qualitatively incorrect results.…”

“…It is easy to see that the operatorsb þ k andb k satisfy the commutation relations different from Bose ones. They satisfy the Bose statistics for k 6 ¼ k 0 and the Pauli principlê 26 The authors in a number of works, [18][19][20][21] developing the approach of Keldysh, studied properties of dilute electronhole systems, caused by their internal structure. In this section we generalize the theory from Refs.…”

“…17 in several works of the authors, [18][19][20][21] there was developed fundamentally different approach to description of the effects associated with the internal motion of complex bosons. The authors simulated the Bose system with a dilute electron-hole gas, particles of which interact with each other following the Coulomb law.…”