Constrained Hamiltonian dynamics for electrons in magnetic field and additional forces besides the Lorentz force acting on electrons

Abstract

We consider the forces acting on electrons in magnetic field including the constraints and a condition arising from quantum mechanics. The force is calculated as the electron mass, $m_e$, multiplied by the total time-derivative of the velocity field evaluated using the quantum mechanical many-electron wave function. The velocity field includes a term of the Berry connection from the many-body wave function; thereby, quantum mechanical effects are included. It is shown that additional important forces besides the Lorentz force exist; they include the gradient of the electron velocity field kinetic energy, the gradient of the chemical potential, and the `force' for producing topologically protected loop currents. These additional forces are shown to be important in superconductivity, electric current in metallic wires, and charging of capacitors.

References in corpus (5)

• The Lorentz force and superconductivity
• The London moment: what a rotating superconductor reveals about superconductivity
• Theory of Supercurrent in Superconductors
• Schroedinger representation of quantum mechanics, Berry connection, and superconductivity
• Supercurrent and Electromotive force generations by the Berry connection from many-body wave functions

Cited by in corpus (3)

• The Meissner effect in superconductors: emergence versus reductionism
• Toward the detection of spin-vortex-induced loop currents in a single bilayer Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ thin film and their possible use as qubits: Model calculations for three nano-island architecture
• What holes in superconductors reveal about superconductivity