629 research outputs found
Statistical solutions and Kolmogorov entropy for the lattice long-wave-short-wave resonance equations in weighted space
This article studies the lattice long-wave-short-wave resonance equations in weighted spaces.
The authors first prove the global well-posedness of the initial value problem and the existence of
the pullback attractor for the process generated by the solution mappings in the weighted space.
Then they establish that the process possesses a family of invariant Borel probability measures
supported by the pullback attractor. Afterwards, they verify that this family of Borel probability
measures satisfies the Liouville theorem and is a statistical solution of the lattice long-wave-shortwave resonance equations. Finally, they prove an upper bound of the Kolmogorov entropy of the
statistical solutio
Schrödinger operators in the twentieth century
This paper reviews the past fifty years of work on spectral theory and related issues in nonrelativistic quantum mechanics
Mathematical Theory of the Wigner-Weisskopf Atom
These notes provide an introduction to the spectral theory of the Friedrichs model. This model is used in quantum physics to describe the coupling of a discrete set of energy levels to a continuum of states. We restrict ourselves to the simplest possible case of a single energy level coupled to a continuum, the so-called Wigner-Weisskopf atom. We discuss both, perturbative and non-perturbative aspects. We also consider the fermionic second quantization of this model and discuss its nonequilibrium thermodynamics: steady states, steady currents and entropy production
Covariant Mappings for the Description of Measurement, Dissipation and Decoherence in Quantum Mechanics
The general formalism of quantum mechanics for the description of statistical
experiments is briefly reviewed, introducing in particular position and
momentum observables as POVM characterized by their covariance properties with
respect to the isochronous Galilei group. Mappings describing state
transformations both as a consequence of measurement and of dynamical evolution
for a closed or open system are considered with respect to the general
constraints they have to obey and their covariance properties with respect to
symmetry groups. In particular different master equations are analyzed in view
of the related symmetry group, recalling the general structure of mappings
covariant under the same group. This is done for damped harmonic oscillator,
two-level system and quantum Brownian motion. Special attention is devoted to
the general structure of translation-covariant master equations. Within this
framework a recently obtained quantum counterpart of the classical linear
Boltzmann equation is considered, as well as a general theoretical framework
for the description of different decoherence experiments, pointing to a
connection between different possible behaviours in the description of
decoherence and the characteristic functions of classical L\'evy processes.Comment: Comments: 38 pages, to appear in Lecture Notes in Physics,
Springer-Verla
QCD Sum Rules and Applications to Nuclear Physics
Applications of QCD sum-rule methods to the physics of nuclei are reviewed,
with an emphasis on calculations of baryon self-energies in infinite nuclear
matter. The sum-rule approach relates spectral properties of hadrons
propagating in the finite-density medium, such as optical potentials for
quasinucleons, to matrix elements of QCD composite operators (condensates). The
vacuum formalism for QCD sum rules is generalized to finite density, and the
strategy and implementation of the approach is discussed. Predictions for
baryon self-energies are compared to those suggested by relativistic nuclear
physics phenomenology. Sum rules for vector mesons in dense nuclear matter are
also considered.Comment: 92 pages, ReVTeX, 9 figures can be obtained upon request (to Xuemin
Jin
Topics in Modern Quantum Optics
This is the written version of lectures presented at "The 17th Symposium on
Theoretical Physics - Applied Field Theory", 29 June - 1 July, 1998, the
Sangsan Mathematical Science Building, Seoul National University, Seoul, Korea.Comment: 97 pages, 23 figures, 187 references. Misprints corrected, most
figures redrawn and references update
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