Brownian motion of a quantum harmonic oscillator

The problem of describing the Brownian motion of a quantum harmonic oscillator or free particle is treated in the formalism of quantum dynamical semigroups. Certain inequalities involving the friction and diffusion coefficients and Planck's constant are derived. The nature of the quantum Langevin equation is discussed.     

Decoherence of quantum Brownian motion in noncommutative space

The decoherence of a harmonic oscillator under two-dimensional quantum Brownian motion on a noncommutative plane is investigated. The interaction with the environment is considered by two separate models so-called coupled and uncoupled. The two-dimensional master equation and its noncommutative counterpart are derived for both employed models. The rate of the linear entropy (predictability sieve) is chosen as a criterion to investigate the purity in the presence of the space noncommutativity. Besides, a two-dimensional charged harmonic oscillator on a plane which is imposed by a perpendicular magnetic field is introduced as a realization of our model. Therefore, our approach provides a formalism to investigate the influence of the magnetic field on the decoherence of the pure states. We show that in the high magnetic field limit the rate of the decoherence will be decreased.     

The underlying Brownian motion of nonrelativistic quantum mechanics

Nonrelativistic quantum mechanics can be derived from real Markov diffusion processes by extending the concept of probability measure to the complex domain. This appears as the only natural way of introducing formally classical probabilistic concepts into quantum mechanics. To every quantum state there is a corresponding complex Fokker-Planck equation. The particle drift is conditioned by an auxiliary equation which is obtained through stochastic energy conservation; the logarithmic transform of this equation is the Schrödinger equation. To every quantum mechanical operator there is a stochastic process; the replacement of operators by processes leads to all the well-known results of quantum mechanics, using stochastic calculus instead of formal quantum rules. Comparison is made with the classical stochastic approaches and the Feynman path integral formulation.     

Path sums for Brownian motion and quantum mechanics

A treatment is given of classical Brownian motion in phase space based on path summation. It treats efficiently the usual exactly solvable cases when the external force is linear in momentum or position. The method might be useful for generating approximations for more complicated external forces. A path sum formalism is given to generate the Wigner propagator in the Wigner-Weyl phase space formulation of quantum mechanics. The short-time Brownian and Wigner propagators bear a generic similarity.     

Zeno and anti-Zeno effects for quantum Brownian motion

In this Letter, we investigate the occurrence of the Zeno and anti-Zeno effects for quantum Brownian motion. We single out the parameters of both the system and the reservoir governing the crossover between Zeno and anti-Zeno dynamics. We demonstrate that, for high reservoir temperatures, the short time behavior of environment induced decoherence is ultimately responsible for the occurrence of either the Zeno or the anti-Zeno effect. Finally, we suggest a way to manipulate the decay rate of the system and to observe a controlled continuous passage from decay suppression to decay acceleration using engineered reservoirs in the trapped ion context.     

Quantum and classical correlations in quantum Brownian motion

We investigate the entanglement properties of the joint state of a distinguished quantum system and its environment in the quantum Brownian motion model. This model is a frequent starting point for investigations of environment-induced superselection. Using recent methods from quantum information theory, we show that there exists a large class of initial states for which no entanglement will be created at all times between the system of salient interest and the environment. If the distinguished system has been initially prepared in a pure Gaussian state, then entanglement is created immediately, regardless of the temperature of the environment and the nonvanishing coupling.     

Brownian motion of a classical particle in quantum environment

The Klein–Kramers equation, governing the Brownian motion of a classical particle in a quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large friction the corresponding Smoluchowski equation is obtained. Introducing the Bohm quantum potential, this Smoluchowski equation is extended to describe the Brownian motion of a quantum particle in quantum environment.     

Dilations of quantum dynamical semigroups with classical Brownian motion

We show that any quantum dynamical semigroup can be written with the help of the solution of a vector-valued classical stochastic differential equation. Moreover this equation leads to a natural construction of a unitary dilation in term of Wiener spaces.On leave of absence from Institute of Theoretical Physics and Astrophysics, Gdansk, PolandBevoegdverklaard navorser N.F.W.O., Belgium     

Decoherence induced by zero-point fluctuations in quantum Brownian motion

We show a completely analytical approach to the decoherence induced by a zero temperature environment on a Brownian test particle. We consider an Ohmic environment bilinearly coupled to an oscillator and compute the master equation. From diffusive coefficients, we evaluate the decoherence time for the usual quantum Brownian motion and also for an upside-down oscillator, as a toy model of a quantum phase transition.     

Kubo-Einstein relation for quantum Brownian motion in a periodic potential

Using a previously derived general formalism for a dissipative quantum particle in a boson bath, we prove that when the damping is Ohmic, the Kubo-Einstein relation between the diffusion constant and the linear mobilityD=kTM holds to all orders in V₀ for a periodic potentialV(x)=V ₀ cos(k)₀ x).     

Thermodynamic suppression of Brownian motion

We have used helium-3 nuclear reaction analysis to measure the Brownian motion (intradiffusion coefficient) of polystyrene in a partially miscible blend with poly(alpha-methylstyrene). In the one-phase region, when the correlation length is close to the polystyrene chain size, the intradiffusion coefficient falls to half of its thermal value. For larger and smaller values of the correlation length, diffusion is normal. These results show that the correlation length of a polymer blend constrains polymer diffusion, as suggested from previous neutron scattering measurements, and mean-field theory.     

Theory of rotational Brownian motion

The correlation function for the angular velocity of a Brownian particle suspended in a liquid is analyzed with an account of the viscous aftereffect. The main term in the asymptotic exression for this function is equal to the eddy correlation function for the translational velocity of a liquid found from the Navier-Stokes equations.Translated from Izvestiya VUZ. Fizika, No. 10, pp. 13–17, October, 1969.In conclusion the author thanks Professor I. Z. Fisher for guidance and for constant interest in his study.