1,352,417 research outputs found
Effects of Noise, Correlations and errors in the preparation of initial states in Quantum Simulations
In principle a quantum system could be used to simulate another quantum
system. The purpose of such a simulation would be to obtain information about
problems which cannot be simulated with a classical computer due to the
exponential increase of the Hilbert space with the size of the system and which
cannot be measured or controlled in an actual experiment. The system will
interact with the surrounding environment, with the other particles in the
system and be implemented using imperfect controls making it subject to noise.
It has been suggested that noise does not need to be controlled to the same
extent as it must be for general quantum computing. However the effects of
noise in quantum simulations and how to treat them are not completely
understood. In this paper we study an existing quantum algorithm for the
one-dimensional Fano-Anderson model to be simulated using a liquid-state NMR
device. We calculate the evolution of different initial states in the original
model, and then we add interacting spins to simulate a more realistic
situation. We find that states which are entangled with their environment, and
sometimes correlated but not necessarily entangled have an evolution which is
described by maps which are not completely positive. We discuss the conditions
for this to occur and also the implications.Comment: Revtex 4-1, 14 pages, 21 figures, version 2 has typos corrected and
acknowledgement adde
The TRAPPIST-1 system: Orbital evolution, tidal dissipation, formation and habitability
We study the dynamical evolution of the TRAPPIST-1 system under the influence
of orbital circularization through tidal interaction with the central star. We
find that systems with parameters close to the observed one evolve into a state
where consecutive planets are linked by first order resonances and consecutive
triples, apart from planets c, d and e, by connected three body Laplace
resonances. The system expands with period ratios increasing and mean
eccentricities decreasing with time. This evolution is largely driven by tides
acting on the innermost planets which then influence the outer ones. In order
that deviations from commensurability become significant only on time
scales or longer, we require that the tidal parameter associated with the
planets has to be such that At the same time, if we start
with two subsystems, with the inner three planets comprising the inner one,
associated with the planets has to be on the order (and not significantly
exceeding) for the two subsystems to interact and end up in the
observed configuration. This scenario is also supported by modelling of the
evolution through disk migration which indicates that the whole system cannot
have migrated inwards together. Also in order to avoid large departures from
commensurabilities, the system cannot have stalled at a disk inner edge for
significant time periods. We discuss the habitability consequences of the tidal
dissipation implied by our modelling, concluding that planets d, e and f are
potentially in habitable zones.Comment: 27 pages, 15 figures, accepted for publication in MNRA
Tensor Self Energy in a Vector-Tensor Model
The tensor self energy is computed at one loop order in a model in which a
vector and tensor interact in a way that eliminates all tensor degrees of
freedom. Divergencies arise which cannot be eliminated without introducing a
kinetic term for the tensor field which does not appear in the classical
action. We comment on a possible resolution of this puzzle.Comment: 7 pages, LaTeX, additional analysis and comment
Classical phase transitions in a one-dimensional short-range spin model
Ising's solution of a classical spin model famously demonstrated the absence
of a positive-temperature phase transition in one-dimensional equilibrium
systems with short-range interactions. No-go arguments established that the
energy cost to insert domain walls in such systems is outweighed by entropy
excess so that symmetry cannot be spontaneously broken. An archetypal way
around the no-go theorems is to augment interaction energy by increasing the
range of interaction. Here we introduce new ways around the no-go theorems by
investigating entropy depletion instead. We implement this for the Potts model
with invisible states.Because spins in such a state do not interact with their
surroundings, they contribute to the entropy but not the interaction energy of
the system. Reducing the number of invisible states to a negative value
decreases the entropy by an amount sufficient to induce a positive-temperature
classical phase transition. This approach is complementary to the long-range
interaction mechanism. Alternatively, subjecting positive numbers of invisible
states to imaginary or complex fields can trigger such a phase transition. We
also discuss potential physical realisability of such systems.Comment: 29 pages, 11 figure
Competition between spin-induced charge instabilities in underdoped cuprates
We study the static charge correlation function in a one-band model on a square lattice. The Hamiltonian consists of effective hoppings of the electrons between the lattice sites and the Heisenberg Hamiltonian. Approximating the irreducible charge correlation function by a single bubble yields the ladder approximation for the charge correlation function. In this approximation, one finds, in general, three charge instabilities - two of them are due to nesting, the third one is the flux phase instability. Since these instabilities cannot explain the experiments in hole-doped cuprates, we have included in the irreducible charge correlation function also Aslamasov-Larkin (AL) diagrams where charge fluctuations interact with products of spin fluctuations. We then find at high temperatures a nematic or d-wave Pomeranchuk instability with a very small momentum. Its transition temperature decreases roughly linearly with doping in the underdoped region and vanishes near optimal doping. Decreasing the temperature further, a secondary axial charge-density wave (CDW) instability appears with mainly d-wave symmetry and a wave vector somewhat larger than the distance between nearest-neighbor hot spots. At still lower temperatures, the diagonal flux phase instability emerges. A closer look shows that the AL diagrams enhance mainly axial and not diagonal charge fluctuations in our one-band model. This is the main reason why axial and not diagonal instabilities are the leading ones in agreement with experiment. The two instabilities due to nesting vanish already at very low temperatures and do not play any major role in the phase diagram. Remarkable is that the nematic and the axial CDW instabilities show a large reentrant behavior.Fil: Zeyher, Roland. Max Planck Institute For Solid State Research; AlemaniaFil: Greco, Andres Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; Argentin
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