765 research outputs found
A transverse Hamiltonian variational technique for open quantum stochastic systems and its application to coherent quantum control
This paper is concerned with variational methods for nonlinear open quantum
systems with Markovian dynamics governed by Hudson-Parthasarathy quantum
stochastic differential equations. The latter are driven by quantum Wiener
processes of the external boson fields and are specified by the system
Hamiltonian and system-field coupling operators. We consider the system
response to perturbations of these energy operators and introduce a transverse
Hamiltonian which encodes the propagation of the perturbations through the
unitary system-field evolution. This provides a tool for the infinitesimal
perturbation analysis and development of optimality conditions for coherent
quantum control problems. We apply the transverse Hamiltonian variational
technique to a mean square optimal coherent quantum filtering problem for a
measurement-free cascade connection of quantum systems.Comment: 12 pages, 1 figure. A brief version of this paper will appear in the
proceedings of the IEEE Multi-Conference on Systems and Control, 21-23
September 2015, Sydney, Australi
Stochastic semiclassical gravity
In the first part of this paper, we show that the semiclassical
Einstein-Langevin equation, introduced in the framework of a stochastic
generalization of semiclassical gravity to describe the back reaction of matter
stress-energy fluctuations, can be formally derived from a functional method
based on the influence functional of Feynman and Vernon. In the second part, we
derive a number of results for background solutions of semiclassical gravity
consisting of stationary and conformally stationary spacetimes and scalar
fields in thermal equilibrium states. For these cases, fluctuation-dissipation
relations are derived. We also show that particle creation is related to the
vacuum stress-energy fluctuations and that it is enhanced by the presence of
stochastic metric fluctuations.Comment: 26 pages, RevTeX, no figure
Cosmological consequences of Quantum Gravity proposals
In this thesis, we study the implications of Quantum Gravity models for the
dynamics of spacetime and the ensuing departures from classical General
Relativity. The main focus is on cosmological applications, particularly the
impact of quantum gravitational effects on the dynamics of a homogenous and
isotropic cosmological background. Our interest lies in the consequences for
the evolution of the early universe and singularity resolution, as well as in
the possibility of providing an alternative explanation for dark matter and
dark energy in the late universe.
The thesis is divided into two main parts, dedicated to alternative (and
complementary) ways of tackling the problem of Quantum Gravity. The first part
is concerned with cosmological applications of background independent
approaches to Quantum Gravity, both in the context of loop quantisation and in
quantum geometrodynamics. Particularly relevant in this work is the Group Field
Theory approach, which we use to study the effective dynamics of the emergent
universe from a full theory of Quantum Gravity (i.e. without symmetry
reduction).
In the second part, modified gravity theories are introduced as tools to
provide an effective description of quantum gravitational effects, e.g. by
introducing new degrees of freedom and symmetries. Particularly relevant in
this respect is local conformal invariance, which finds a natural realisation
in the framework of Weyl geometry. We build a modified theory of gravity based
on such symmetry principle, and argue that new fields in the extended
gravitational sector may play the role of dark matter. New degrees of freedom
are also natural in models with varying fundamental `constants', which we
examine critically.
Finally, we discuss prospects for future work and point at directions for the
derivation of realistic cosmological models from Quantum Gravity candidates.Comment: PhD thesis, King's College London (supervisor: Mairi Sakellariadou),
282 pages, 20 figures; submitted in September 201
Covariance Dynamics and Entanglement in Translation Invariant Linear Quantum Stochastic Networks
This paper is concerned with a translation invariant network of identical
quantum stochastic systems subjected to external quantum noise. Each node of
the network is directly coupled to a finite number of its neighbours. This
network is modelled as an open quantum harmonic oscillator and is governed by a
set of linear quantum stochastic differential equations. The dynamic variables
of the network satisfy the canonical commutation relations. Similar large-scale
networks can be found, for example, in quantum metamaterials and optical
lattices. Using spatial Fourier transform techniques, we obtain a sufficient
condition for stability of the network in the case of finite interaction range,
and consider a mean square performance index for the stable network in the
thermodynamic limit. The Peres-Horodecki-Simon separability criterion is
employed in order to obtain sufficient and necessary conditions for quantum
entanglement of bipartite systems of nodes of the network in the Gaussian
invariant state. The results on stability and entanglement are extended to the
infinite chain of the linear quantum systems by letting the number of nodes go
to infinity. A numerical example is provided to illustrate the results.Comment: 11 pages, 3 figures, submitted to the 54th IEEE Conference on
Decision and Control, December 15-18, 2015, Osaka, Japa
Covariant Quantum Dynamical Semigroups: Unbounded generators
A survey of the probabilistic approaches to quantum dynamical semigroups with
unbounded generators is given. An emphasis is made upon recent advances in the
structural theory of covariant Markovian master equations. The relations with
the classical Levy-Khinchin formula are elucidated. As an example, a complete
characterizations of the Galilean covariant irreversible quantum Markovian
evolutions is given in terms of the corresponding quantum master and Langevin
equations. Important topics for future investigation are outlined.Comment: 14 pages,Latex, no figures, submitted to the Semigroup Volume, Group
21, Goslar 199
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