9 research outputs found
A new non-perturbative approach to Quantum Brownian Motion
Starting from the Caldeira-Leggett (CL) model, we derive the equation
describing the Quantum Brownian motion, which has been originally proposed by
Dekker purely from phenomenological basis containing extra anomalous diffusion
terms. Explicit analytical expressions for the temperature dependence of the
diffusion constants are derived. At high temperatures, additional momentum
diffusion terms are suppressed and classical Langivin equation can be recovered
and at the same time positivity of the density matrix(DM) is satisfied. At low
temperatures, the diffusion constants have a finite positive value, however,
below a certain critical temperature, the Master Equation(ME) does not satisfy
the positivity condition as proposed by Dekker.Comment: 5 page
Bang-Bang control of a qubit coupled to a quantum critical spin bath
We analytically and numerically study the effects of pulsed control on the
decoherence of a qubit coupled to a quantum spin bath. When the environment is
critical, decoherence is faster and we show that the control is relatively more
effective. Two coupling models are investigated, namely a qubit coupled to a
bath via a single link and a spin star model, yielding results that are similar
and consistent.Comment: 10 pages, 4 figures, replaced with published versio
Derivation of exact master equation with stochastic description: Dissipative harmonic oscillator
A systematic procedure for deriving the master equation of a dissipative
system is reported in the framework of stochastic description. For the
Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and
elementary derivation of the bath-induced stochastic field is presented. The
dynamics of the system is thereby fully described by a stochastic differential
equation and the desired master equation would be acquired with statistical
averaging. It is shown that the existence of a closed-form master equation
depends on the specificity of the system as well as the feature of the
dissipation characterized by the spectral density function. For a dissipative
harmonic oscillator it is observed that the correlation between the stochastic
field due to the bath and the system can be decoupled and the master equation
naturally comes out. Such an equation possesses the Lindblad form in which time
dependent coefficients are determined by a set of integral equations. It is
proved that the obtained master equation is equivalent to the well-known
Hu-Paz-Zhang equation based on the path integral technique. The procedure is
also used to obtain the master equation of a dissipative harmonic oscillator in
time-dependent fields.Comment: 24page
On the quantum langevin equation
The quantum Langevin equation is the Heisenberg equation of motion for the (operator) coordinate of a Brownian particle coupled to a heat bath. We give an elementary derivation of this equation for a simple coupled-oscillator model of the heat bath.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45153/1/10955_2005_Article_BF01011142.pd
Thermal Properties of an Inflationary Universe
An energetic justification of a thermal component during inflation is given.
The thermal component can act as a heat reservoir which induces thermal
fluctuations on the inflaton field system. We showed previously that such
thermal fluctuations could dominate quantum fluctuations in producing the
initial seeds of density perturbations. A Langevin-like rate equation is
derived from quantum field theory which describes the production of
fluctuations in the inflaton field when acted upon by a simple modeled heat
reservoir. In a certain limit this equation is shown to reduce to the standard
Langevin equation, which we used to construct "Warm Inflation" scenarios in
previous work. A particle physics interpretation of our system-reservoir model
is offered.Comment: 28 pages, 0 figures, In Press Physical Review D 199
Independent oscillator model of a heat bath: Exact diagonalization of the Hamiltonian
The problem of a quantum oscillator coupled to an independent-oscillator model of a heat bath is discussed. The transformation to normal coordinates is explicitly constructed using the method of Ullersma. With this transformation an alternative derivation of an exact formula for the oscillator free energy is constructed. The various contributions to the oscillator energy are calculated, with the aim of further understanding this formula. Finally, the limitations of linear coupling models, such as that used by Ullersma, are discussed in the form of some critical remarks.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45154/1/10955_2005_Article_BF01011565.pd