Ground state

The ground state of a quantum mechanical or quantum field theoretical system is the state with the lowest possible energy (see energy level ).

Description

The ground state of a system is always stable, since there is no lower energy state in which it could move. Systems in states of higher energy (excited state) can proceed in accordance with the conservation of energy while releasing energy in the ground state, if it is allowed by certain laws, such as other conservation laws ( selection rules ), is prohibited.

Since the temperature is a monotonically increasing function of the energy systems is usually located in a "cold" area in their ground state; for most systems, such as atoms, the room temperature is already a cold environment.

Quantum mechanical system

A quantum- mechanical system is in its ground state, it can still contain a surprising amount of energy. This can be seen by the example of the Fermi distribution of the conduction electrons in a metal: the Fermi temperature of the highest energy electrons in the vicinity of the Fermi level is located at some 10,000 K - even if the metal is sufficiently cooled below room temperature. This energy can be the metal but do not remove and use, because the electron gas can not take a still lower energy state.

The ground state of a quantum system need not be unique. If there are a plurality of states with the same lowest energy, this is referred to as a degenerate ground state. An example in which this occurs is the spontaneous breaking of symmetry, where the symmetry of the system is effectively reduced due to the degeneracy of the ground state.

In quantum field theory, the ground state is often referred to as a vacuum state, vacuum or quantum vacuum. The ground state on the flat Minkowski space-time is defined by its invariance under Poincaré transformations, especially under the time translation. As for curved space- times, the Poincaré group is not a symmetry group, quantum fields in curved space-times have i.Allg. not have a unique ground state. More specifically, there is only a unique ground state if there is a one-parameter isometry group of time translations of spacetime.