18 research outputs found
Do We Understand Quantum Mechanics - Finally?
After some historical remarks concerning Schroedinger's discovery of wave
mechanics, we present a unified formalism for the mathematical description of
classical and quantum-mechanical systems, utilizing elements of the theory of
operator algebras. We then review some basic aspects of quantum mechanics and,
in particular, of its interpretation. We attempt to clarify what Quantum
Mechanics tells us about Nature when appropriate experiments are made. We
discuss the importance of the mechanisms of "dephasing" and "decoherence" in
associating "facts" with possible events and rendering complementary possible
events mutually exclusive.Comment: 42 pages, contribution to the Proceedings of a conference in memory
of Erwin Schroedinger, Vienna, January 201
Analyticity of the self-energy in total momentum of an atom coupled to the quantized radiation field
We study a neutral atom with a non-vanishing electric dipole moment coupled
to the quantized electromagnetic field. For a sufficiently small dipole moment
and small momentum, the one-particle (self-) energy of an atom is proven to be
a real-analytic function of its momentum. The main ingredient of our proof is a
suitable form of the Feshbach-Schur spectral renormalization group.Comment: Small typos and inconsistencies corrected. Accepted for publication
in J. Funct. Ana
A "Garden of Forking Paths" - the Quantum Mechanics of Histories of Events
We present a short survey of a novel approach, called "ETH approach", to the
quantum theory of events happening in isolated physical systems and to the
effective time evolution of states of systems featuring events. In particular,
we attempt to present a clear explanation of what is meant by an "event" in
quantum mechanics and of the significance of this notion. We then outline a
theory of direct (projective) and indirect observations or recordings of
physical quantities and events. Some key ideas underlying our general theory
are illustrated by studying a simple quantum-mechanical model of a mesoscopic
system.Comment: 26 pages, 3 figure
Spectral Analysis of a Model for Quantum Friction
An otherwise free classical particle moving through an extended spatially
homogeneous medium with which it may exchange energy and momentum will undergo
a frictional drag force in the direction opposite to its velocity with a
magnitude which is typically proportional to a power of its speed. We study
here the quantum equivalent of a classical Hamiltonian model for this friction
phenomenon that was proposed in [11]. More precisely, we study the spectral
properties of the quantum Hamiltonian and compare the quantum and classical
situations. Under suitable conditions on the infrared behaviour of the model,
we prove that the Hamiltonian at fixed total momentum has no ground state
except when the total momentum vanishes, and that its spectrum is otherwise
absolutely continuous.Comment: 40 page
Scattering theory for Lindblad master equations
International audienceWe study scattering theory for a quantum-mechanical system consisting of a particle scattered off a dynamical target that occupies a compact region in position space. After taking a trace over the degrees of freedom of the target, the dynamics of the particle is generated by a Lindbladian acting on the space of trace-class operators. We study scattering theory for a general class of Lindbladians with bounded interaction terms. First, we consider models where a particle approaching the target is always re-emitted by the target. Then we study models where the particle may be captured by the target. An important ingredient of our analysis is a scattering theory for dissipative operators on Hilbert space
Uncertainty-aware Flexibility Envelope Prediction in Buildings with Controller-agnostic Battery Models
Buildings are a promising source of flexibility for the application of demand
response. In this work, we introduce a novel battery model formulation to
capture the state evolution of a single building. Being fully data-driven, the
battery model identification requires one dataset from a period of nominal
controller operation, and one from a period with flexibility requests, without
making any assumptions on the underlying controller structure. We consider
parameter uncertainty in the model formulation and show how to use risk
measures to encode risk preferences of the user in robust uncertainty sets.
Finally, we demonstrate the uncertainty-aware prediction of flexibility
envelopes for a building simulation model from the Python library Energym.Comment: 7 pages, 3 figures. Submitted to the 2023 American Control Conference
(ACC