Damping @ Granada abstracts:
Hugh Jones (Imperial College, London)
Title: The remarkable optical properties of materials with coordinated gain and loss.
Abstract: In recent years a great deal of work has been done on understanding quantum theories
which have a non-Hermitian Hamiltonian, but which nevertheless possess a real energy
spectrum, due in many cases to an underlying PT symmetry. In some
circumstances, however, this symmetry may be broken, in which case some
or all of the eigenvalues coalesce into complex conjugate pairs.These
ideas have now found practical application in the field of classical
optics, where the paraxial equation of propagation is formally
identical to the Schroedinger equation, with the role of the quantum
potential being played by the variations in the refractive index. Wave
guides and optical lattices with the carefully coordinated regions of
loss and gain implied by PT symmetry have many remarkable properties,
some of which may prove useful in optical devices needed for optical
computers. We review both the original concepts of PT symmetry in
quantum mechanics and their application in classical optics.
Dieter Schuch (Institut für Theoretische Physik, Frankfurt)
Title: Dissipation, Irreversibility and their Interrelations in Classical and Quantum Physics
Abstract: In the classical theory of open systems, two aspects must be considered: (1) the dissipation of
energy and (2) the irreversible time-evolution. The first can be
described by a modified Newtonian equation with an additional friction
force (Langevin equation), the latter in a probabilistic description
via a Fokker-Planck equation with diffusion terms. In conventional
quantum mechanics, similar equations are obtained in Madelung’s
hydrodynamic version using a modified Hamilton-Jacobi equation for the
phase of the wavefunction and a (reversible) continuity equation for
its amplitude. Important is that both these quantities are not
independent of each other but coupled via some invariants. This
coupling can be traced back to a complex nonlinear Riccati equation
that occurs in
time-dependent as well as time-independent quantum mechanics and also
has (at the least, formal) similarities with the quantum Arnold
transformation. It also becomes important for open quantum systems
since the dissipative aspect is essentially reflected by the behaviour
of the phase, whereas the irreversibility is related to a kind of
Fokker-Planck equation for the amplitude, leading to a non-unitary
time-evolution. In this context, different effective descriptions of
open quantum systems leading to nonlinear Schrödinger equations with
(possibly complex) friction terms, (linear) time-dependent Hamiltonians
(e.g. Caldirola-Kanai approach) etc. and their interrelations (e.g. via
non-unitary transformations) will be discussed. Also for open quantum
systems, relations can be drawn to complex nonlinear Riccati equations.
Similar equations also occur in other fields of physics, like classical
and quantum optics, Bose-Einstein condensates or cosmological models,
and the modifications in the case of open quantum systems can provide
clues for similar modifications in these fields.
Julio Guerrero (Departamento de Matematica Aplicada, Murcia and IAA-CSIC, Granada)
Title: The Quantum Arnold Transformation and its Applications
Abstract: The Quantum Arnold Transformation relating system with
quadratic, time-dependent Hamiltonians with the free particle is
revised, and some of its applications to dissipative systems,
inflationary cosmological models, and
Bose-Einstein Condensates, are shown.
Beppe Marmo (INFN Napoli)
Title: The observables of a dissipative quantum system
Abstract: A time-dependent product is introduced between the observables of a dissipative quantum
system, that accounts for the effects of dissipation on observables and commutators. In the $t \to \infty$
limit this yields a contracted algebra. The general ideas are corroborated by a few explicit examples.
Francisco Lopez-Ruiz (IAA-CSIC, Granada)
Title: Symmetries of the Bateman's dual system
Abstract: For the Caldirola-Kanai (C-K) system, describing a quantum damped harmonic oscillator, a couple of
constant-of-motion operators generating the Heisenberg algebra can be
found making use of the Quantum Arnold Transformation. The inclusion of
the standard time evolution symmetry in this algebra for the C-K
non-conservative system, in a unitary manner, requires a non-trivial
extension of this basic algebra and hence the physical system itself.
Surprisingly, this extension leads directly to the so-called Bateman's
dual system, which now includes a new particle acting as an energy
reservoir. The group of symmetries of the dual system will be
presented, as well as a quantization
that implies, in particular, a first-order Schrödinger equation. Some
comments on its physical solutions as well as on its resonant states
will be made in order to clarify a frequent misunderstanding spread
through the literature.
Mikel Fernández-Méndez (Instituto de Estructura de la Materia IEM-CSIC, Madrid)
Title: Unitarity and uniqueness in the quantization of cosmological perturbations
Abstract: We study the Fock quantization of the scalar perturbations
about the FLRW model in the 3-sphere with a scalar massive field as
matter content. After expanding the perturbations in modes using the
eigenstates of the Laplace-Beltrami operator, a perturbative analysis
is performed up to terms quadratic in these modes. We fix the gauge
almost completely and introduce a canonical transformation in order to
obtain a convenient formulation of the system. We consider Fock
quantizations of the perturbations with the following properties: i) an
SO(4)-invariant vacuum state
and ii) unitarily implementable perturbations dynamics. All such representations are proven to be unitarily equivalent.
Jose Luis Jaramillo (Albert Einstein Institut, Potsdam)
Title: Probing spacetime dynamics through horizon geometry dissipation
Abstract: The qualitative and quantitative understanding of
near-horizon gravitational dynamics in the strong-field regime
represents a challenge both at a fundamental level and in astrophysical
applications. We discuss a research methodology in which spacetime
dynamics is probed through the cross-correlation of geometric
quantities constructed on the black hole horizon and on null infinity.
These two hypersurfaces respond to evolving gravitational fields in the
bulk, providing canonical "test screens" in a "scattering"-like
perspective onto spacetime dynamics. Aiming at fitting the general
theme of the workshop, we will underline here the link between some of
the elements in this analysis framework and the dissipation of the
"test screen" geometry from the perspective of a viscous-fluid analogy
of black hole horizons.
Guillermo A. Mena Marugán (Instituto de Estructura de la Materia IEM-CSIC, Madrid)
Title: Uniqueness of the Fock quantization in nonstationary spacetimes
Abstract: A fundamental problem in quantum field theory in curved spacetimes is the ambiguity in the choice of a
Fock representation for the canonical commutation relations. There exists an infinite number of
choices that lead to inequivalent physical predictions. In stationary scenarios, a common strategy
consists in demanding the invariance of the vacuum under the background spacetime symmetries. When
stationarity is lost, a possible generalization is to replace time invariance by the requirement of a
unitary evolution. In fact, when the spatial sections are compact, the criterion of a unitary
dynamics, together with the invariance under the symmetries of the field equation, turn out to select
a unique family of Fock quantizations for scalar fields with a time dependent mass. We study in detail
the case of the three-sphere, and discuss the applications in cosmology.
Jaime Julve (Instituto de Fisica Fundamental, IFF-CSIC, Madrid)
Título: Some properties of Gamow states.
Abstract: The resonant solutions (Gamow states) to the Schrödinger
equation, corresponding to complex energies and momenta, lie outside
the familiar realm of Hermitian operators in Hilbert spaces. Some
results on the norm, inner products, expansions, and contribution to
completeness relations of these states are worked out for 1-dimensional
systems with quantum barriers.
Enrico Celeghini - University of Florence, Italy
Title: BROKEN SYMMETRIES
ABSTRACT: Two objects we classify together cannot be identical as we have to distinguish
between them. Thus they can only be almost equal: every symmetry is -by
itself- broken. To describe a broken symmetries, up to few decades ago,
the unique possibility was to start from an exact mathematical symmetry
and to introduce the breaking at the physical level or in the states
(as in spontaneous symmetry
breaking) or in the operators (as in mass formulas for hadrons).
Recently a possibility has appeared to consider the breaking directly
in the mathematics. This talk is devoted to discuss this new approach
where
deformations of Lie algebras, called quantum algebras, are introduced.
Unfortunately these objects are infinite dimensional: indeed they are
properly called by mathematicians Quantum Universal Enveloping
Algebras. They are
infinite dimensional deformations of the infinite dimensional algebra
of the polynomials constructed on the Lie algebras generators. We have
thus to came back and individuate, among the infinitely many possible
bases, the relevant one. In Lie algebras this work has been done by
Cartan and Dinkin one century ago but, for quantum algebras, the choice
has been up to now arbitrarily done.
Here we mimic the Cartan-Dinkin approach to individuate the finite
dimensional quantum algebra canonical basis. Resorting to analyticity but also
to the underlying Hopf algebra a self-consistent perturbative approach has been
thus developed and the quantum algebra canonical generators, deformation of the
Lie ones, obtained.
The approach is general and consistent extensions to quantum superalgebras as
well as to quantum Poisson algebras has been developed.
Juan Calvo (Departamento de Matematica Aplicada, Universidad de Granada)
Title: Dynamic and dispersion properties in relativistic kinetic systems
Manuel Calixto (Departamento de Matematica Aplicada, Universidad de Granada and IAA-CSIC, Granada)
Title: Damping Dicke's Maser Model
Abstract: We consider a system of spins coupled to a single mode of the
electromagnetic radiation and study the loss effect in the quantum
phase transition from ``normal'' to ``superradiant'' through a coupling
to phonons.
Fernando Barbero (Instituto de Estructura de la Materia IEM-CSIC, Madrid)
Title: Black hole entropy and the thermodynamic limit
Abstract: The stastistical entropy in thermodynamics is usually a
staircase function of the energy that cannot be used directly to derive
other quantities by differentiation. The standard remedy to this
problem is to define a suitable
thermodynamic limit in which the entropy is smooth and well behaved. I
will discuss in the talk how this can be explicitly done in the case of
black holes in loop quantum gravity and show in several examples how
the subdominant corrections to the asymptotic behavior of the entropy
as a function of the area change in the large area limit.
Daniel Martín-de Blas (Instituto de Estructura de la Materia IEM-CSIC, Madrid)
Title: The hybrid Gowdy model: Solvable Hamiltonian constraint and inhomogeneous quantum cosmologies
Mercedes Martín-Benito (Instituto de Estructura de la Materia IEM-CSIC, Madrid)
Title: First steps to bring spin foams closer to statistical physics
Javier Olmedo (Instituto de Estructura de la Materia IEM-CSIC, Madrid)
Title: Inhomogeneities and inflation in LQC: A hybrid approach
Abstrac: We quantize to completion a homogeneous and isotropic spacetime with positive
spatial curvature coupled to a massive scalar field in the framework of Loop Quantum Cosmology.
We provide the physical Hilbert space constructed out of the space of initial data on the
minimum volume section. By means of a perturbative treatment we introduce inhomogeneities
adopting a hybrid quantum approach, i.e., assuming that these degrees
of freedom can be suitably described by astandard Fock quantization.
For the considered case of compact spatial topology, the requirements
of: i) invariance of the vacuum state under the spatial isometries, and
ii) unitary implementation of the quantum dynamics, pick up a
privileged set of gauge invariant potentials and a unique Fock
representation (up to unitary equivalence).
Carlos Barcelo (IAA-CSIC, Granada)
Title: In search of a solution for the trans-Planckian catastrophe
Abstract: We use the avoidance of the trans-Planckian problem of Hawking radiation
as a guiding principle in searching for a compelling scenario for the evaporation of
black holes or black-hole-like objects. We argue that there exist only three possible
scenarios, depending on whether the classical notion of long-lived horizon is preserved
by high-energy physics and on whether the dark and compact astrophysical objects that
we observe have long-lived horizons in the first place. Along the way, we find that i)
a theory with high-energy superluminal signaling and a long-lived trapping horizon would
be extremely unstable in astrophysical terms and that ii) stellar pulsations of objects
hovering right outside but extremely close to their gravitational radius can result in
a mechanism for Hawking emission.
Victor Aldaya (IAA-CSIC, Granada)
Title: Where are all singularities gone?
Abstract: In order to clarify the nature of the solution manifold of static and isitropic
solutions of Einstein equations in the vacuum, and particularly, the symplectic structure
and dynamical symmetries, we investigate the analogous problem in the simpler case of
massless Klein-Gordon equation.