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of three ways by double clicking it, by clicking it once and then clicking Apply Study, or by dragging-and-dropping the study into the pane of your choice 2 My Study Sets tab The content here is identical to the My Study Sets module You can choose this tab by clicking on the tab, and by clicking on any of the study sets, you can examine or edit the components of that study set You will learn later in this chapter exactly how to make and name a study set 3 Panes Most of the right side of this dialog box is devoted to the placement of the panes that make up the entire chart Each small rectangle represents a pane, and they are in the same order as they would be displayed on the chart itself.

the superfluid, which tends to restore uniformity. This is because any nonun!' formity in density will obviously cause the energy to rise above its absolute minimum. A nonuniform phase cp will also make the energy rise, because, while the system is invariant under a global gauge transformation (i.e., constant CP), it 1not invariant under a local one (i.e., space-dependent cp.) If the number of particles in a cell changes by !::.N during the time inter\ai !::.t, then the energy of the cell is uncertain by an amount !::.E ::::: Ii/!::.t. Thus

(13.57 1

(13.581

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where JL is the chemical potential. Another way to derive these equations is to note that the energy E( cp, N) of a cell is an effective classical Hamiltonian, where licp and N are canonically conjugate coordinates. The equations above are the Hamiltonian equations of motion. These are Anderson's equations* governing superfluid flow. Although we have derived them at absolute zero, they continue to apply at finite temperatures, with the partial derivatives taken to be adiabatic derivatives.

To view the appointment details or make changes, you can doubleclick the appointment to reopen the Appointment window.

The superfluid order parameter (o/(x) > must be a continuous function of x. In particular, its phase cp(x) must change by at most an integer multiple of 27T when we traverse a closed loop in the superfluid. This means that the vorticity in

P. W. Anderson, Rev. Mod. Phys. 38, 298 (1966). This paper contains applications of these equations.

superfluid flow must be quantized:

(13.59)

You can grab the upper portion of any of these panes and drag it up or down in order to rearrange the order of the panes You can also drag a study from the Studies tab into any of the panes in order to apply that study to that pane For example, if you dragged Simple Moving Average into the Volume pane, it would apply that study to the volume 4 Buttons There are eight other elements to this editor, seven of which are buttons and one of which is a checkbox These are each described below The buttons in the studies editor perform the following functions: About Study This provides an instant link to a glossary entry and graphic description of the study, so if you want to get some quick information about a study, click on the study of interest and then the About Study button.

(n=0,1,2, ... )

Obviously n = 0 if the closed loop can be continuously shrunken to a point. The values n 4= 0 occur if the superfluid flows in a multiply connected region, for example, between two cylinders. The multiply connected region may also be created by the liquid itself: The superfluid can be expelled from a self-formed tube filled with normal fluid, and will flow around this tube with nonzero vorticity, i.e., n 4= 0 in (13.59). The tube, called the vortex core, could be a line whose ends terminate on boundary surfaces or it could form a ring. The excitation is called a vortex line in the first case, and a vortex ring in the second. Both types of vortex motion have been observed experimentally. * The coarse-grained description of the superfluid obviously breaks down in the vicinity of the vortex core. The core diameter is a phenomenological parameter that can be calculated only by considering the microscopic dynamics. In the approximation of incompressible superfluid flow in the presence of vorticity, the equations for the superfluid velocity are

(13.60)

where j is the vorticity density, the vorticity per unit cross-sectional area of the vortex core. Note that Vs in this case is mathematically analogous to the magnetic field set up by a current density distribution j. The energy associated with superfluid flow is just the kinetic energy of the fluid elements:

(13.61)

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