Bloch electrons in a magnetic field: why does chaos send electrons the hard Way?

A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on any other moving charge or current that is present in the field. Like an electric field, the magnetic field is also a vector field. At any position, the direction of the magnetic field is defined as the direction in which the north pole of a compass needle points.
A magnetic field is defined by the force that a charged particle experiences...

A charged particle experiences a force when moving through a magnetic field. Consider the field to be uniform and the charged particle to move perpendicular to it. If the field is in a vacuum, the magnetic field is the dominant factor determining the motion. Since the magnetic force is perpendicular to the direction of motion, a charged particle follows a curved path. The particle continues to follow this curved path until it forms a complete circle. Another way to look at this is that the...

Moving charges experience a force in a magnetic field. Since the magnetic fields produced by moving charges are proportional to the current, a conductor carrying a current creates a magnetic field around it.
Consider a compass placed near a current-carrying wire. The wire experiences a force that aligns the needle of the compass tangentially around the wire. Thus, the current-carrying wire produces concentric circular loops of magnetic field. The magnetic field generated by a wire can be...

Electrons revolving around a nucleus are analogous to a circular current carrying loop. This current produces a magnetic dipole moment proportional to the electron's orbital angular momentum. Since the orbital angular momentum is quantized in terms of the reduced Planck's constant, the dipole moment is quantized in the Bohr Magneton. The value of the Bohr magneton is 9.27 x 10-24 Am2. Electrons also have an intrinsic spin angular momentum, and the associated spin magnetic moment is...

A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving with a constant velocity. Like the electric field, the magnetic field at any point is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the source point and the field point. However, unlike the electric field, the magnetic field is always perpendicular to the plane containing the line...

In addition to the electric forces between electric charges, moving electric charges exert magnetic forces on each other. A magnetic field is created by a moving charge or a group of moving charges known as the electric current. A magnetic force is experienced by a second current or moving charge in response to this magnetic field. Fundamentally, interactions between moving electrons in the atoms of two bodies produce magnetic forces between them.
The magnetic force acting on a moving charge...