3,425 research outputs found
Memory effect on the formation of drying cracks
We propose a model for the formation of drying cracks in a viscoplastic
material. In this model, we observe that when an external force is applied to a
viscoplastic material before drying, the material memorizes the effect of the
force as a plastic deformation. The formation of the drying cracks is
influenced by this plastic deformation. This outcome clarifies the result of a
recent experiments which demonstrated that a drying fracture pattern on a
powder-water mixture depends on the manner in which an external force is
applied before drying. We analytically express the position of the first crack
as a function of the strength of an external force applied before drying. From
the expression, we predict that there exists a threshold on the strength of the
force. When the force applied is smaller than the threshold, the first crack is
formed at the center of the mixture; however, when the force applied exceeds
the threshold, the position of the first crack deviates from the center. The
extent of the deviation increases as a linear function of the difference
between the strength of the force and the threshold.Comment: 9 pages, 9 figure
Designing Robust Unitary Gates: Application to Concatenated Composite Pulse
We propose a simple formalism to design unitary gates robust against given
systematic errors. This formalism generalizes our previous observation [Y.
Kondo and M. Bando, J. Phys. Soc. Jpn. 80, 054002 (2011)] that vanishing
dynamical phase in some composite gates is essential to suppress amplitude
errors. By employing our formalism, we naturally derive a new composite unitary
gate which can be seen as a concatenation of two known composite unitary
operations. The obtained unitary gate has high fidelity over a wider range of
the error strengths compared to existing composite gates.Comment: 7 pages, 4 figures. Major revision: improved presentation in Sec. 3,
references and appendix adde
Non-perturbative proton stability
Proton decay is a generic prediction of GUT models and is therefore an
important channel to detect the existence of unification or to set limits on
GUT models. Current bounds on the proton lifetime are around 10^33 years, which
sets stringent limits on the GUT scale. These limits are obtained under
`reasonable' assumptions about the size of the hadronic matrix elements. In
this paper we present a non-perturbative calculation of the hadronic matrix
elements within the chiral bag model of the proton. We argue that there is an
exponential suppression of the matrix elements, due to non-perturbative QCD,
that stifles proton decay by orders of magnitude -- potentially O(10^-10). This
suppression is present for small quark masses and is due to the chiral symmetry
breaking of QCD. Such a suppression has clear implications for GUT models and
could resuscitate several scenarios
Dual Formulation of the Lie Algebra S-expansion Procedure
The expansion of a Lie algebra entails finding a new, bigger algebra G,
through a series of well-defined steps, from an original Lie algebra g. One
incarnation of the method, the so-called S-expansion, involves the use of a
finite abelian semigroup S to accomplish this task. In this paper we put
forward a dual formulation of the S-expansion method which is based on the dual
picture of a Lie algebra given by the Maurer-Cartan forms. The dual version of
the method is useful in finding a generalization to the case of a gauge free
differential algebra, which in turn is relevant for physical applications in,
e.g., Supergravity. It also sheds new light on the puzzling relation between
two Chern-Simons Lagrangians for gravity in 2+1 dimensions, namely the
Einstein-Hilbert Lagrangian and the one for the so-called "exotic gravity".Comment: 12 pages, no figure
Dynamical invariants for quantum control of four-level systems
We present a Lie-algebraic classification and detailed construction of the
dynamical invariants, also known as Lewis-Riesenfeld invariants, of the
four-level systems including two-qubit systems which are most relevant and
sufficiently general for quantum control and computation. These invariants not
only solve the time-dependent Schr\"odinger equation of four-level systems
exactly but also enable the control, and hence quantum computation based on
which, of four-level systems fast and beyond adiabatic regimes.Comment: 11 pages, 5 table
Minimal and Robust Composite Two-Qubit Gates with Ising-Type Interaction
We construct a minimal robust controlled-NOT gate with an Ising-type
interaction by which elementary two-qubit gates are implemented. It is robust
against inaccuracy of the coupling strength and the obtained quantum circuits
are constructed with the minimal number (N=3) of elementary two-qubit gates and
several one-qubit gates. It is noteworthy that all the robust circuits can be
mapped to one-qubit circuits robust against a pulse length error. We also prove
that a minimal robust SWAP gate cannot be constructed with N=3, but requires
N=6 elementary two-qubit gates.Comment: 7 pages, 2 figure
Recursive Encoding and Decoding of Noiseless Subsystem and Decoherence Free Subspace
When the environmental disturbace to a quantum system has a wavelength much
larger than the system size, all qubits localized within a small area are under
action of the same error operators. Noiseless subsystem and decoherence free
subspace are known to correct such collective errors. We construct simple
quantum circuits, which implement these collective error correction codes, for
a small number of physical qubits. A single logical qubit is encoded with
and , while two logical qubits are encoded with . The recursive
relations among the subspaces employed in noiseless subsystem and decoherence
free subspace play essential r\^oles in our implementation. The recursive
relations also show that the number of gates required to encode logical
qubits increases linearly in .Comment: 9 pages, 3 figure
Strongly Correlated Topological Superconductors and Topological Phase Transitions via Green's Function
We propose several topological order parameters expressed in terms of Green's
function at zero frequency for topological superconductors, which generalizes
the previous work for interacting insulators. The coefficient in topological
field theory is expressed in terms of zero frequency Green's function. We also
study topological phase transition beyond noninteracting limit in this zero
frequency Green's function approach.Comment: 10 pages. Published versio
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