Particle Creation

Yasunari Kurita, Michikazu Kobayashi, Hideki Ishihara +1 more

We formulate particle-creation phenomena in Bose-Einstein condensates in terms of conserving gapless mean-field theory for weakly interacting Bose gases. The particle-creation spectrum is calculated by rediagonalizing the Bogoliubov--de Gennes (BdG) Hamiltonian in mean-field theory. The conservation implies that quasiparticle creation is accompanied by quantum back reaction to the condensates. Particle creation in this mean-field theory is found to be equivalent to that in quantum field theory (QFT) in curved space-time. An expression is obtained for an effective metric affected by quantum back reaction. The formula for the particle-creation spectrum obtained in terms of QFT in curved space-time is shown to be the same as that given by rediagonalizing the BdG Hamiltonian.

Serghey V. Vonsovsky, Mikhail I. Katsnelson

Leo P. Kadanoff, Gordon Baym

The properties of a quantum mechanical system composed of many identical particles are most conveniently described in terms of the second-quantized, Heisenberg representation, particle-creation, and annihilation operators. The creation operator, ψ †( r , t), when acting to the right on a state of the system, adds a particle to the state at the space-time point r , t; the annihilation operator ψ ( r , t), the adjoint of the creation operator, acting to the right, removes a particle from the state at the point r , t.

Malcolm H. MacGregor

Alessandro Teta

Joscha Henheik, Roderich Tumulka

Abstract Only recently has it been possible to construct a self-adjoint Hamiltonian that involves the creation of Dirac particles at a point source in 3d space. Its definition makes use of an interior-boundary condition. Here, we develop for this Hamiltonian a corresponding theory of the Bohmian configuration. That is, we (non-rigorously) construct a Markov jump process ( Q t ) t ∈ R in the configuration space of a variable number of particles that is | ψ t | 2 -distributed at every time t and follows Bohmian trajectories between the jumps. The jumps correspond to particle creation or annihilation events and occur either to or from a configuration with a particle located at the source. The process is the natural analog of Bell’s jump process, and a central piece in its construction is the determination of the rate of particle creation. The construction requires an analysis of the asymptotic behavior of the Bohmian trajectories near the source. We find that the particle reaches the source with radial speed 0, but orbits around the source infinitely many times in finite time before absorption (or after emission).