3,516 research outputs found
Bounds on Decoherence and Error
When a confined system interacts with its walls (treated quantum
mechanically), there is an intertwining of degrees of freedom. We show that
this need not lead to entanglement, hence decoherence. It will generally lead
to error. The wave function optimization required to avoid decoherence is also
examined.Comment: 10 pages, plain TeX, no figure
Opposite Thermodynamic Arrows of Time
A model in which two weakly coupled systems maintain opposite running
thermodynamic arrows of time is exhibited. Each experiences its own retarded
electromagnetic interaction and can be seen by the other. The possibility of
opposite-arrow systems at stellar distances is explored and a relation to dark
matter suggested.Comment: To appear in Phys. Rev. Let
Imaging geometry through dynamics: the observable representation
For many stochastic processes there is an underlying coordinate space, ,
with the process moving from point to point in or on variables (such as
spin configurations) defined with respect to . There is a matrix of
transition probabilities (whether between points in or between variables
defined on ) and we focus on its ``slow'' eigenvectors, those with
eigenvalues closest to that of the stationary eigenvector. These eigenvectors
are the ``observables,'' and they can be used to recover geometrical features
of
A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems
The hierarchical equations of motion technique has found widespread success
as a tool to generate the numerically exact dynamics of non-Markovian open
quantum systems. However, its application to low temperature environments
remains a serious challenge due to the need for a deep hierarchy that arises
from the Matsubara expansion of the bath correlation function. Here we present
a hybrid stochastic hierarchical equation of motion (sHEOM) approach that
alleviates this bottleneck and leads to a numerical cost that is nearly
independent of temperature. Additionally, the sHEOM method generally converges
with fewer hierarchy tiers allowing for the treatment of larger systems.
Benchmark calculations are presented on the dynamics of two level systems at
both high and low temperatures to demonstrate the efficacy of the approach.
Then the hybrid method is used to generate the exact dynamics of systems that
are nearly impossible to treat by the standard hierarchy. First, exact energy
transfer rates are calculated across a broad range of temperatures revealing
the deviations from the Forster rates. This is followed by computations of the
entanglement dynamics in a system of two qubits at low temperature spanning the
weak to strong system-bath coupling regimes.Comment: 20 pages, 6 figure
Path integral in a magnetic field using the Trotter product formula
The derivation of the Feynman path integral based on the Trotter product
formula is extended to the case where the system is in a magnetic field.Comment: To appear in the American Journal of Physics, 200
Stability of quantum breathers
Using two methods we show that a quantized discrete breather in a 1-D lattice
is stable. One method uses path integrals and compares correlations for a
(linear) local mode with those of the quantum breather. The other takes a local
mode as the zeroth order system relative to which numerical, cutoff-insensitive
diagonalization of the Hamiltonian is performed.Comment: 4 pages, 3 figure
Statistical comparison of ensemble implementations of Grover's search algorithm to classical sequential searches
We compare pseudopure state ensemble implementations, quantified by their
initial polarization and ensemble size, of Grover's search algorithm to
probabilistic classical sequential search algorithms in terms of their success
and failure probabilities. We propose a criterion for quantifying the resources
used by the ensemble implementation via the aggregate number of oracle
invocations across the entire ensemble and use this as a basis for comparison
with classical search algorithms. We determine bounds for a critical
polarization such that the ensemble algorithm succeeds with a greater
probability than the probabilistic classical sequential search. Our results
indicate that the critical polarization scales as N^(-1/4) where N is the
database size and that for typical room temperature solution state NMR, the
polarization is such that the ensemble implementation of Grover's algorithm
would be advantageous for N > 10^2
Closed Path Integrals and Renormalisation in Quantum Mechanics
We suggest a closed form expression for the path integral of quantum
transition amplitudes. We introduce a quantum action with renormalized
parameters. We present numerical results for the potential. The
renormalized action is relevant for quantum chaos and quantum instantons.Comment: Revised text, 1 figure added; Text (LaTeX file), 1 Figure (ps file
Observing trajectories with weak measurements in quantum systems in the semiclassical regime
We propose a scheme allowing to observe the evolution of a quantum system in
the semiclassical regime along the paths generated by the propagator. The
scheme relies on performing consecutive weak measurements of the position. We
show how weak trajectories" can be extracted from the pointers of a series of
measurement devices having weakly interacted with the system. The properties of
these "weak trajectories" are investigated and illustrated in the case of a
time-dependent model system.Comment: v2: Several minor corrections were made. Added Appendix (that will
appear as Suppl. Material). To be published in Phys Rev Let
Extended self-energy functional approach for strongly-correlated lattice bosons in the superfluid phase
Among the various numerical techniques to study the physics of strongly
correlated quantum many-body systems, the self-energy functional approach (SFA)
has become increasingly important. In its previous form, however, SFA is not
applicable to Bose-Einstein condensation or superfluidity. In this paper we
show how to overcome this shortcoming. To this end we identify an appropriate
quantity, which we term , that represents the correlation correction of the
condensate order parameter, as it does the self-energy for the Green's
function. An appropriate functional is derived, which is stationary at the
exact physical realizations of and of the self-energy. Its derivation is
based on a functional-integral representation of the grand potential followed
by an appropriate sequence of Legendre transformations. The approach is not
perturbative and therefore applicable to a wide range of models with local
interactions. We show that the variational cluster approach based on the
extended self-energy functional is equivalent to the "pseudoparticle" approach
introduced in Phys. Rev. B, 83, 134507 (2011). We present results for the
superfluid density in the two-dimensional Bose-Hubbard model, which show a
remarkable agreement with those of Quantum-Monte-Carlo calculations.Comment: 1 additional figure showing the region close to the tip of the Mott
lobe, minor changes in the tex
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