Julio C. García

Interaction Representation Method for Markov Master Equations in Quantum Optics

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.

On the Lindblad Equation with Unbounded Time-Dependent Coefficients

We prove newa priori estimates for the resolvent of a minimal quantum dynamical semigroup. These estimates simplify well-known conditions sufficient for conservativity and impose continuity conditions on the time-dependent operator coefficients ensuring the existence of conservative solutions of the Markov evolution equations.

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

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

On the structure of a cone of normal unbounded completely positive maps

The paper suggests a constructive characterization of unbounded completely positive maps introduced earlier by Chebotarev for the theory of quantum dynamical semigroups. We prove that such cones are generated by a positive self-adjoint “reference” operator ΛεB(H) as follows: for any completely positive unbounded map Ф(·)εCPn*(F) these exists a completely positive normal bounded mapR(·)εCPn(H) such that ϕ(·)=ΛR(·)Λ. The class contains mappings that are unclosable sesquilinear forms.

Some non-equilibrium invariant states for the asymmetric exclusion QMS at level one

We review the Asymmetric Exclusion QMS in the light of new results, taking as a starting point the dynamics in the one particle space. We give a condition for the Asymmetric Exclusion QMS to be conservative, prove that an invariant state is necessarily diagonal and give conditions on eigenvalues of such an invariant state. We also give, a necessary condition to annul the generator of the predual semigroup; with this and the weighted detailed balance condition, we propose a method to construct some non-equilibrium invariant states.

Conservativity of Quantum Dynamical Evolution Systems

The main aim of this work is to provide a criterion for conservativity of minimal solutions of time-dependent master equations with unbounded coefficients (Quantum Dynamical Evolution System, QDES). In Section 2 we prove a criterion for conservativity of a QDES without using resolvents and in Section 3 we give sufficient conditions for conservativity of the class of QDES whose completely positive part is a time-dependent bounded sesquilinear form on a Hilbert space K t densely and continuously embedded in H and satisfies an extension property.