56 research outputs found
Dissipative Continuous Spontaneous Localization (CSL) model
Collapse models explain the absence of quantum superpositions at the
macroscopic scale, while giving practically the same predictions as quantum
mechanics for microscopic systems. The Continuous Spontaneous Localization
(CSL) model is the most refined and studied among collapse models. A well-known
problem of this model, and of similar ones, is the steady and unlimited
increase of the energy induced by the collapse noise. Here we present the
dissipative version of the CSL model, which guarantees a finite energy during
the entire system's evolution, thus making a crucial step toward a realistic
energy-conserving collapse model. This is achieved by introducing a non-linear
stochastic modification of the Schr\"odinger equation, which represents the
action of a dissipative finite-temperature collapse noise. The possibility to
introduce dissipation within collapse models in a consistent way will have
relevant impact on the experimental investigations of the CSL model, and
therefore also on the testability of the quantum superposition principle.Comment: 11 pages, 1 figure; v2 title changed, closer to published versio
Momentum coupling in non-Markovian Quantum Brownian motion
We consider a model of non-Markovian Quantum Brownian motion that consists of
an harmonic oscillator bilinearly coupled to a thermal bath, both via its
position and momentum operators. We derive the master equation for such a model
and we solve the equations of motion for a generic Gaussian system state. We
then investigate the resulting evolution of the first and second moments for
both an Ohmic and a super-Ohmic spectral density. In particular, we show that,
irrespective of the specific form of the spectral density, the coupling with
the momentum enhances the dissipation experienced by the system, accelerating
its relaxation to the equilibrium, as well as modifying the asymptotic state of
the dynamics. Eventually, we characterize explicitly the non-Markovianity of
the evolution, using a general criterion which relies on the positivity of the
master equation coefficients
Quantum master equation for collisional dynamics of massive particles with internal degrees of freedom
We address the microscopic derivation of a quantum master equation in
Lindblad form for the dynamics of a massive test particle with internal degrees
of freedom interacting through collisions with a background ideal gas. When
either internal or centre of mass degrees of freedom can be treated
classically, previously established equations are obtained as special cases. If
in an interferometric setup the internal degrees of freedom are not detected at
the output, the equation can be recast in the form of a generalized Lindblad
structure, which describes non-Markovian effects. The effect of internal
degrees of freedom on centre of mass decoherence is considered in this
framework.Comment: 18 pages, 2 figures; v2: corresponds to published versio
Dissipative extension of the Ghirardi-Rimini-Weber model
In this paper we present an extension of the Ghirardi-Rimini-Weber model for
the spontaneous collapse of the wavefunction. Through the inclusion of
dissipation, we avoid the divergence of the energy on the long time scale,
which affects the original model. In particular, we define new jump operators,
which depend on the momentum of the system and lead to an exponential
relaxation of the energy to a finite value. The finite asymptotic energy is
naturally associated to a collapse noise with a finite temperature, which is a
basic realistic feature of our extended model. Remarkably, even in the presence
of a low temperature noise, the collapse model is effective. The action of the
new jump operators still localizes the wavefunction and the relevance of the
localization increases with the size of the system, according to the so-called
amplification mechanism, which guarantees a unified description of the
evolution of microscopic and macroscopic systems. We study in detail the
features of our model, both at the level of the trajectories in the Hilbert
space and at the level of the master equation for the average state of the
system. In addition, we show that the dissipative Ghirardi-Rimini-Weber model,
as well as the original one, can be fully characterized in a compact way by
means of a proper stochastic differential equation.Comment: 25 pages, 2 figures; v2: close to the published versio
Quantum regression theorem and non-Markovianity of quantum dynamics
We explore the connection between two recently introduced notions of
non-Markovian quantum dynamics and the validity of the so-called quantum
regression theorem. While non-Markovianity of a quantum dynamics has been
defined looking at the behaviour in time of the statistical operator, which
determines the evolution of mean values, the quantum regression theorem makes
statements about the behaviour of system correlation functions of order two and
higher. The comparison relies on an estimate of the validity of the quantum
regression hypothesis, which can be obtained exactly evaluating two points
correlation functions. To this aim we consider a qubit undergoing dephasing due
to interaction with a bosonic bath, comparing the exact evaluation of the
non-Markovianity measures with the violation of the quantum regression theorem
for a class of spectral densities. We further study a photonic dephasing model,
recently exploited for the experimental measurement of non-Markovianity. It
appears that while a non-Markovian dynamics according to either definition
brings with itself violation of the regression hypothesis, even Markovian
dynamics can lead to a failure of the regression relation.Comment: 11 pages, 4 figure
Gravity and the Collapse of the Wave Function: a Probe into Di\'osi-Penrose model
We investigate the Di\'osi-Penrose (DP) proposal for connecting the collapse
of the wave function to gravity. The DP model needs a free parameter, acting as
a cut-off to regularize the dynamics, and the predictions of the model highly
depend on the value of this cut-off. The Compton wavelength of a nucleon seems
to be the most reasonable cut-off value since it justifies the non-relativistic
approach. However, with this value, the DP model predicts an unrealistic high
rate of energy increase. Thus, one either is forced to choose a much larger
cut-off, which is not physically justified and totally arbitrary, or one needs
to include dissipative effects in order to tame the energy increase. Taking the
analogy with dissipative collisional decoherence seriously, we develop a
dissipative generalization of the DP model. We show that even with dissipative
effects, the DP model contradicts known physical facts, unless either the
cut-off is kept artificially large, or one limits the applicability of the
model to massive systems. We also provide an estimation for the mass range of
this applicability.Comment: 15 pages, 1 figure; v2 updated references and fixed minor mistakes in
Eqs.(18) and (31)-(34), thanks to Marko Toros for pointing them ou
Rate operator unravelling for open quantum system dynamics
Stochastic methods with quantum jumps are often used to solve open quantum
system dynamics. Moreover, they provide insight into fundamental topics, as the
role of measurements in quantum mechanics and the description of non-Markovian
memory effects. However, there is no unified framework to use quantum jumps to
describe open system dynamics in any regime. We solve this issue by developing
the Rate Operator Quantum Jump (ROQJ) approach. The method not only applies to
both Markovian and non-Markovian evolutions, but also allows us to unravel
master equations for which previous methods do not work. In addition, ROQJ
yields a rigorous measurement-scheme interpretation for a wide class of
dynamics, including a set of master equations with negative decay rates, and
sheds light on different types of memory effects which arise when using
stochastic quantum jump methods.Comment: 6 + 6 pages, 1 figure, accepted in Phys. Rev. Let
Open systems with error bounds: spin boson model with spectral density variations
In the study of open quantum systems, one of the most common ways to describe
environmental effects on the reduced dynamics is through the spectral density.
However, in many models this object cannot be computed from first principles
and needs to be inferred on phenomenological grounds or fitted to experimental
data. Consequently, some uncertainty regarding its form and parameters is
unavoidable; this in turn calls into question the accuracy of any theoretical
predictions based on a given spectral density. Here, we focus on the spin-boson
model as a prototypical open quantum system, and find two error bounds on
predicted expectation values in terms of the spectral density variation
considered, and state a sufficient condition for the strongest one to apply. We
further demonstrate an application of our result, by bounding the error brought
about by the approximations involved in the Hierarchical Equations of Motion
resolution method for spin-boson dynamics.Comment: 5+5 pages, minor edits since last unpublished versio
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