12 research outputs found
Quantum Thermodynamics and Canonical Typicality
We present here a set of lecture notes on quantum thermodynamics and
canonical typicality. Entanglement can be constructively used in the
foundations of statistical mechanics. An alternative version of the postulate
of equal a priori probability is derived making use of some techniques of
convex geometr
Quantum cavities with alternating boundary conditions
We consider the quantum dynamics of a free nonrelativistic particle moving in
a cavity and we analyze the effect of a rapid switching between two different
boundary conditions. We show that this procedure induces, in the limit of
infinitely frequent switchings, a new effective dynamics in the cavity related
to a novel boundary condition. We obtain a dynamical composition law for
boundary conditions which gives the emerging boundary condition in terms of the
two initial ones
Self-adjoint extensions and unitary operators on the boundary
We establish a bijection between the self-adjoint extensions of the Laplace
operator on a bounded regular domain and the unitary operators on the boundary.
Each unitary encodes a specific relation between the boundary value of the
function and its normal derivative. This bijection sets up a characterization
of all physically admissible dynamics of a nonrelativistic quantum particle
confined in a cavity. More- over, this correspondence is discussed also at the
level of quadratic forms. Finally, the connection between this parametrization
of the extensions and the classical one, in terms of boundary self-adjoint
operators on closed subspaces, is shown.Comment: 16 page
Moving Walls and Geometric Phases
We unveil the existence of a non-trivial Berry phase associated to the
dynamics of a quantum particle in a one dimensional box with moving walls. It
is shown that a suitable choice of boundary conditions has to be made in order
to preserve unitarity. For these boundary conditions we compute explicitly the
geometric phase two-form on the parameter space. The unboundedness of the
Hamiltonian describing the system leads to a natural prescription of
renormalization for divergent contributions arising from the boundary.Comment: 16 pages, 5 figure
Boundaries without boundaries
Starting with a quantum particle on a closed manifold without boundary, we
consider the process of generating boundaries by modding out by a group action
with fixed points, and we study the emergent quantum dynamics on the quotient
manifold. As an illustrative example, we consider a free nonrelativistic
quantum particle on the circle and generate the interval via parity reduction.
A free particle with Neumann and Dirichlet boundary conditions on the interval
is obtained, and, by changing the metric near the boundary, Robin boundary
conditions can also be accommodated. We also indicate a possible method of
generating non-local boundary conditions. Then, we explore an alternative
generation mechanism which makes use of a folding procedure and is applicable
to a generic Hamiltonian through the emergence of an ancillary spin degree of
freedom.Comment: 19 pages, 4 figure
Can Decay Be Ascribed to Classical Noise?
No.Comment: 11 page
Quantum fluctuation relations
We present here a set of lecture notes on exact fluctuation relations. We prove the Jarzynski equality and the Crooks fluctuation theorem, two paradigmatic examples of classical fluctuation relations. Finally, we consider their quantum versions, and analyze analogies and differences with the classical case