Roberto Quezada

Two-photon absorption and emission process

We analyze the two-photon absorption and emission process and characterize the stationary states at zero and positive temperature. We show that entangled stationary states exist only at zero temperature and, at positive temperature, there exists infinitely many commuting invariant states satisfying the detailed balance condition.

A CYCLE DECOMPOSITION AND ENTROPY PRODUCTION FOR CIRCULANT QUANTUM MARKOV SEMIGROUPS

We propose a definition of cycle representation for Quantum Markov Semigroups (QMS) and of Quantum Entropy Production Rate (QEPR) in terms of the ρ-adjoint. We introduce the class of circulant QMS, which admit non-equilibrium steady states but exhibit symmetries that allow us to compute explicitly the QEPR, gain a deeper insight into the notion of cycle decomposition and prove that quantum detailed balance holds if and only if the QEPR equals zero.

On three new principles in non-equilibrium statistical mechanics and Markov semigroups of weak coupling limit type

We introduce three new principles: the nonlinear Boltzmann–Gibbs prescription, the local KMS condition and the generalized detailed balance (GDB) condition. We prove the equivalence of the first two under general conditions and we discuss a master equation formulation of the third one.

Spectral properties of the two-photon absorption and emission process

The quantum Markov semigroup of the two-photon absorption and emission process has two extremal normal invariant states. Starting from an arbitrary initial state it converges toward some convex combination of these states as time goes to infinity (approach to equilibrium). We compute the exact exponential rate of this convergence showing that it depends only on the emission rates. Moreover, we show that off-diagonal matrix elements of any initial state go to zero with an exponential rate which is smaller than the exponential rate of convergence of the diagonal part. In other words quantum features of a state survive longer than the relaxation time of its classical part.

THE ASYMMETRIC EXCLUSION QUANTUM MARKOV SEMIGROUP

In this paper we study a class of quantum Markov semigroups whose restriction to an abelian sub-algebra coincides, on the configurations with finite support, with the exclusion type semigroups introduced in Liggetts book14 of exchange rates

Interaction Representation Method for Markov Master Equations in Quantum Optics

a_{rs}^{\pm}

The Θ-KMS adjoint and time reversed quantum Markov semigroups

not symmetric in the index site r, s. We find a sufficient condition for the existence of infinitely many faithful diagonal (or classical) invariant states for the semigroup, that satisfy a quantum detailed balance condition. This class of semigroups arises naturally in the stochastic limit of quantum interacting particles in the sense of Accardi and Kozyrev.1 We call these semigroups asymmetric exclusion quantum Markov semigroups and the associated processes asymmetric exclusion quantum processes.

SUFFICIENT CONDITION FOR THE EXISTENCE OF INVARIANT STATES FOR THE ASYMMETRIC EXCLUSION QMS

Sufficient conditions for a quantum dynamical semigroup (QDS) to be unital are proved for a class of problems in quantum optics with Hamiltonians which are self-adjoint polynomials of any finite order in creation and annihilation operators. The order of the Hamiltonian may be higher than the order of completely positive part of the formal generator of a QDS.

Non-equilibrium steady states of a Markov generator of weak coupling limit type modeling absorption-emission of m and n photons

We introduce the notion of Θ-KMS adjoint of a quantum Markov semigroup, which is identified with the time reversed semigroup. The break of Θ-KMS symmetry, or Θ-standard quantum detailed balance in the sense of Fagnola–Umanita,11 is measured by means of the von Neumann relative entropy of states associated with the semigroup and its Θ-KMS adjoint.

Quantum Markov Semi-Groups of Quasi-Generic Spin Systems

We improve the sufficient condition for existence of invariant states for the Asymmetric Exclusion Quantum Markov Semigroup given in Ref. 5.