1,130 research outputs found
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
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
Obtaining pure steady states in nonequilibrium quantum systems with strong dissipative couplings
Dissipative preparation of a pure steady state usually involves a commutative
action of a coherent and a dissipative dynamics on the target state. Namely,
the target pure state is an eigenstate of both the coherent and dissipative
parts of the dynamics. We show that working in the Zeno regime, i.e. for
infinitely large dissipative coupling, one can generate a pure state by a non
commutative action, in the above sense, of the coherent and dissipative
dynamics. A corresponding Zeno regime pureness criterion is derived. We
illustrate the approach, looking at both its theoretical and applicative
aspects, in the example case of an open spin- chain, driven out of
equilibrium by boundary reservoirs targeting different spin orientations. Using
our criterion, we find two families of pure nonequilibrium steady states, in
the Zeno regime, and calculate the dissipative strengths effectively needed to
generate steady states which are almost indistinguishable from the target pure
states.Comment: 8 pages, 6 figure
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
A Selective Relaxation Method for Numerical Solution of Schr\"odinger Problems
We propose a numerical method for evaluating eigenvalues and eigenfunctions
of Schr\"odinger operators with general confining potentials. The method is
selective in the sense that only the eigenvalue closest to a chosen input
energy is found through an absolutely-stable relaxation algorithm which has
rate of convergence infinite. In the case of bistable potentials the method
allows one to evaluate the fundamental energy splitting for a wide range of
tunneling rates.Comment: 4 pages with figures, uuencoded Z-compressed ps fil
Spontaneous symmetry breaking and inversion-line spectroscopy in gas mixtures
According to quantum mechanics chiral molecules, that is molecules that
rotate the polarization of light, should not exist. The simplest molecules
which can be chiral have four or more atoms with two arrangements of minimal
potential energy that are equivalent up to a parity operation. Chiral molecules
correspond to states localized in one potential energy minimum and can not be
stationary states of the Schr\"odinger equation. A possible solution of the
paradox can be founded on the idea of spontaneous symmetry breaking. This idea
was behind work we did previously involving a localization phase transition: at
low pressure the molecules are delocalized between the two minima of the
potential energy while at higher pressure they become localized in one minimum
due to the intermolecular dipole-dipole interactions. Evidence for such a
transition is provided by measurements of the inversion spectrum of ammonia and
deuterated ammonia at different pressures. A previously proposed model gives a
satisfactory account of the empirical results without free parameters. In this
paper, we extend this model to gas mixtures. We find that also in these systems
a phase transition takes place at a critical pressure which depends on the
composition of the mixture. Moreover, we derive formulas giving the dependence
of the inversion frequencies on the pressure. These predictions are susceptible
to experimental test.Comment: 15 pages, 11 figure
Binary mixtures of chiral gases
A possible solution of the well known paradox of chiral molecules is based on
the idea of spontaneous symmetry breaking. At low pressure the molecules are
delocalized between the two minima of a given molecular potential while at
higher pressure they become localized in one minimum due to the intermolecular
dipole-dipole interactions. Evidence for such a phase transition is provided by
measurements of the inversion spectrum of ammonia and deuterated ammonia at
different pressures. In particular, at pressure greater than a critical value
no inversion line is observed. These data are well accounted for by a model
previously developed and recently extended to mixtures. In the present paper,
we discuss the variation of the critical pressure in binary mixtures as a
function of the fractions of the constituents.Comment: 5 pages, 1 figure, text substantially based on arXiv:1501.02099 to be
presented in Progress in Electromagnetics Research Symposium (PIERS) 201
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