Quantum Hamiltonians and stochastic jumps

TY - JOUR

T1 - Quantum Hamiltonians and stochastic jumps

AU - Dürr, Detlef

AU - Goldstein, Sheldon

AU - Tumulka, Roderich

AU - Zanghì, Nino

PY - 2005/2

Y1 - 2005/2

N2 - With many Hamiltonians one can naturally associate a |Ψ| 2-distributed Markov process. For nonrelativistic quantum mechanics, this process is in fact deterministic, and is known as Bohmian mechanics. For the Hamiltonian of a quantum field theory, it is typically a jump process on the configuration space of a variable number of particles. We define these processes for regularized quantum field theories, thereby generalizing previous work of John S. Bell [3] and of ourselves [11]. We introduce a formula expressing the jump rates in terms of the interaction Hamiltonian, and establish a condition for finiteness of the rates.

AB - With many Hamiltonians one can naturally associate a |Ψ| 2-distributed Markov process. For nonrelativistic quantum mechanics, this process is in fact deterministic, and is known as Bohmian mechanics. For the Hamiltonian of a quantum field theory, it is typically a jump process on the configuration space of a variable number of particles. We define these processes for regularized quantum field theories, thereby generalizing previous work of John S. Bell [3] and of ourselves [11]. We introduce a formula expressing the jump rates in terms of the interaction Hamiltonian, and establish a condition for finiteness of the rates.

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U2 - https://doi.org/10.1007/s00220-004-1242-0

DO - https://doi.org/10.1007/s00220-004-1242-0

M3 - Review article

SN - 0010-3616

VL - 254

SP - 129

EP - 166

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 1

ER -