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Collapse models with non-white noises: II. Particle-density coupled noises

Stephen L Adler, Angelo Bassi

We continue the analysis of models of spontaneous wave function collapse with stochastic dynamics driven by non-white Gaussian noise. We specialize to a model in which a classical "noise" field, with specified autocorrelator, is coupled to a local nonrelativistic particle density. We derive general results in this model for the rates of density matrix diagonalization and of state vector reduction, and show that (in the absence of decoherence) both processes are governed by essentially the same rate parameters. As an alternative route to our reduction results, we also derive the Fokker-Planck equations that correspond to the initial stochastic Schrödinger equation. For specific models of the noise autocorrelator, including ones motivated by the structure of thermal Green's functions, we discuss the qualitative and qantitative dependence on model parameters, with particular emphasis on possible cosmological sources of the noise field.We continue the analysis of models of spontaneous wave function collapse with stochastic dynamics driven by non-white Gaussian noise. We specialize to a model in which a classical "noise" field, with specified autocorrelator, is coupled to a local nonrelativistic particle density. We derive general results in this model for the rates of density matrix diagonalization and of state vector reduction, and show that (in the absence of decoherence) both processes are governed by essentially the same rate parameters. As an alternative route to our reduction results, we also derive the Fokker-Planck equations that correspond to the initial stochastic Schrödinger equation. For specific models of the noise autocorrelator, including ones motivated by the structure of thermal Green's functions, we discuss the qualitative and qantitative dependence on model parameters, with particular emphasis on possible cosmological sources of the noise field.

arXiv:0807.2846Journal of Physics A Mathematical and TheoreticalSep 8, 200846 citations

On the quantum time autocorrelation functions

Juan A. White, Santiago Velasco, Antonio Calvo Hernández +1 more

Physics Letters AJul 1, 198814 citations

AUTOCORRELATION OF QUANTUM-MECHANICAL WAVE FUNCTIONS

Richard Bourret

Canadian Journal of PhysicsSep 1, 19590 citations

Time-dependent transition rates for a multilevel quantum system stochastically coupled to a thermal bath

Santiago Velasco, Juan A. White, Antonio Calvo Hernández

Two different approaches (quantum and semiclassical) used to calculate time-dependent transition rates for a multilevel molecular system stochastically interacting with a thermal bath are presented. While the former is based on the use of a relationship between the real and the imaginary parts of the time autocorrelation function (TAF) associated with the interaction Hamiltonian, the latter relies on the replacement of a quantum TAF by the corresponding anticommutator. Two well-known examples for a stochastic interaction Hamiltonian, an Ornstein-Uhlenbeck process and a white-noise process, have been considered. In both cases, explicit expressions for the transition rates in terms of a reduced set of parameters characterizing the bath are obtained. In the Gaussian regime both quantum and semiclassical transition rates show a time-damped oscillatory behavior towards the same steady value. In the white-noise (\ensuremath{\delta}-correlated) regime, while the quantum transition rates are time dependent, the semiclassical rates are not. The high- and the low-temperature limits for the quantum and the semiclassical transition rates are also reported. The semiclassical results reduce to the quantum results only in the high-temperature limit.Two different approaches (quantum and semiclassical) used to calculate time-dependent transition rates for a multilevel molecular system stochastically interacting with a thermal bath are presented. While the former is based on the use of a relationship between the real and the imaginary parts of the time autocorrelation function (TAF) associated with the interaction Hamiltonian, the latter relies on the replacement of a quantum TAF by the corresponding anticommutator. Two well-known examples for a stochastic interaction Hamiltonian, an Ornstein-Uhlenbeck process and a white-noise process, have been considered. In both cases, explicit expressions for the transition rates in terms of a reduced set of parameters characterizing the bath are obtained. In the Gaussian regime both quantum and semiclassical transition rates show a time-damped oscillatory behavior towards the same steady value. In the white-noise (\ensuremath{\delta}-correlated) regime, while the quantum transition rates are time dependent, the semiclassical rates are not. The high- and the low-temperature limits for the quantum and the semiclassical transition rates are also reported. The semiclassical results reduce to the quantum results only in the high-temperature limit.

Physical Review AApr 1, 198911 citations

WHITE NOISE ANALYSIS AND ITS APPLICATIONS TO QUANTUM DYNAMICS

Takeyuki Hida

WORLD SCIENTIFIC eBooksApr 1, 20010 citations

Quantum white noise with singular non-linear interaction

Luigi Accardi, I. V. Volovich

A model of a system driven by quantum white noise with singular quadratic self--interaction is considered and an exact solution for the evolution operator is found. It is shown that the renormalized square of the squeezed classical white noise is equivalent to the quantum Poisson process. We describe how equations driven by nonlinear functionals of white noise can be derived in nonlinear quantum optics by using the stochastic approximation.

arXiv:quant-ph/9704029Apr 16, 19973 citations

Derivation of a quantum time autocorrelation function from a classical white-noise process

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