45 research outputs found
Irreducible decompositions and stationary states of quantum channels
For a quantum channel (completely positive, trace-preserving map), we prove a
generalization to the infinite dimensional case of a result by Baumgartner and
Narnhofer. This result is, in a probabilistic language, a decomposition of a
general quantum channel into its irreducible positive recurrent components.
This decomposition is related with a communication relation on the reference
Hilbert space. This allows us to describe the full structure of invariant
states of a quantum channel, and of their supports
From n+1-level atom chains to n-dimensional noises
In quantum physics, the state space of a countable chain of (n+1)-level atoms
becomes, in the continuous field limit, a Fock space with multiplicity n. In a
more functional analytic language, the continuous tensor product space over R
of copies of the space C^{n+1} is the symmetric Fock space Gamma_s(L^2(R;C^n)).
In this article we focus on the probabilistic interpretations of these facts.
We show that they correspond to the approximation of the n-dimensional normal
martingales by means of obtuse random walks, that is, extremal random walks in
R^n whose jumps take exactly n+1 different values. We show that these
probabilistic approximations are carried by the convergence of the basic matrix
basis a^i_j(p) of \otimes_N \CC^{n+1} to the usual creation, annihilation and
gauge processes on the Fock space.Comment: 22 page
Landauer's Principle in Repeated Interaction Systems
We study Landauer's Principle for Repeated Interaction Systems (RIS)
consisting of a reference quantum system in contact with a
structured environment made of a chain of independent quantum
probes; interacts with each probe, for a fixed duration, in
sequence. We first adapt Landauer's lower bound, which relates the energy
variation of the environment to a decrease of entropy of the
system during the evolution, to the peculiar discrete time
dynamics of RIS. Then we consider RIS with a structured environment
displaying small variations of order between the
successive probes encountered by , after interactions,
in keeping with adiabatic scaling. We establish a discrete time non-unitary
adiabatic theorem to approximate the reduced dynamics of in this
regime, in order to tackle the adiabatic limit of Landauer's bound. We find
that saturation of Landauer's bound is equivalent to a detailed balance
condition on the repeated interaction system, reflecting the non-equilibrium
nature of the repeated interaction system dynamics. This is to be contrasted
with the generic saturation of Landauer's bound known to hold for continuous
time evolution of an open quantum system interacting with a single thermal
reservoir in the adiabatic regime.Comment: Linked entropy production to detailed balance relation, improved
presentation, and added concluding sectio
Entropic Fluctuations in Quantum Statistical Mechanics. An Introduction
These lecture notes provide an elementary introduction, within the framework
of finite quantum systems, to recent developments in the theory of entropic
fluctuations
Full statistics of energy conservation in two times measurement protocols
The first law of thermodynamics states that the average total energy current
between different reservoirs vanishes at large times. In this note we examine
this fact at the level of the full statistics of two times measurement
protocols also known as the Full Counting Statistics. Under very general
conditions, we establish a tight form of the first law asserting that the
fluctuations of the total energy current computed from the energy variation
distribution are exponentially suppressed in the large time limit. We
illustrate this general result using two examples: the Anderson impurity model
and a 2D spin lattice model.Comment: 5 pages, 1 figure. Accepted for publication in Phys. Rev.
A non-commutative Lévy-Cramér continuity theorem
International audienceIn classical probability, the Lévy-Cramér continuity theorem is a standard tool for proving convergence in distribution of a family of random variables. We prove a non-commutative analogues of this result