44 research outputs found
Thermalization of noninteracting quantum systems coupled to blackbody radiation: A Lindblad-based analysis
We study the thermalization of an ensemble of elementary,
arbitrarily-complex, quantum systems, mutually noninteracting but coupled as
electric or magnetic dipoles to a blackbody radiation. The elementary systems
can be all the same or belong to different species, distinguishable or
indistinguishable, located at fixed positions or having translational degrees
of freedom. Even if the energy spectra of the constituent systems are
nondegenerate, as we suppose, the ensemble unavoidably presents degeneracies of
the energy levels and/or of the energy gaps. We show that, due to these
degeneracies, a thermalization analysis performed by the popular quantum
optical master equation reveals a number of serious pathologies, possibly
including a lack of ergodicity. On the other hand, a consistent thermalization
scenario is obtained by introducing a Lindblad-based approach, in which the
Lindblad operators, instead of being derived from a microscopic calculation,
are established as the elements of an operatorial basis with squared amplitudes
fixed by imposing a detailed balance condition and requiring their
correspondence with the dipole transition rates evaluated under the first-order
perturbation theory. Due to the above-mentioned degeneracies, this procedure
suffers a basis arbitrariness which, however, can be removed by exploiting the
fact that the thermalization of an ensemble of noninteracting systems cannot
depend on the ensemble size. As a result, we provide a clear-cut partitioning
of the thermalization time into dissipation and decoherence times, for which we
derive formulas giving the dependence on the energy levels of the elementary
systems, the size of the ensemble, and the temperature of the blackbody
radiation.Comment: 9 pages, 1 figur
Ground state of many-body lattice systems via a central limit theorem
We review a novel approach to evaluate the ground-state properties of
many-body lattice systems based on an exact probabilistic representation of the
dynamics and its long time approximation via a central limit theorem. The
choice of the asymptotic density probability used in the calculation is
discussed in detail.Comment: 9 pages, contribution to the proceedings of 12th International
Conference on Recent Progress in Many-Body Theories, Santa Fe, New Mexico,
August 23-27, 200
Phase transitions and gaps in quantum random energy models
By using a previously established exact characterization of the ground state
of random potential systems in the thermodynamic limit, we determine the ground
and first excited energy levels of quantum random energy models, discrete and
continuous. We rigorously establish the existence of a universal first order
quantum phase transition, obeyed by both the ground and the first excited
states. The presence of an exponentially vanishing minimal gap at the
transition is general but, quite interestingly, the gap averaged over the
realizations of the random potential is finite. This fact leaves still open the
chance for some effective quantum annealing algorithm, not necessarily based on
a quantum adiabatic scheme.Comment: 8 pages, 4 figure