1,008,363 research outputs found
Factorization and Criticality in the Anisotropic XY Chain via Correlations
In this review, we discuss the zero and finite temperature behavior of
various bipartite quantum and total correlation measures, the skew
information-based quantum coherence, and the local quantum uncertainty in the
thermal ground state of the one-dimensional anisotropic XY model in transverse
magnetic field. We compare the ability of considered measures to correctly
detect or estimate the quantum critical point and the non-trivial factorization
point possessed by the spin chain.Comment: 29 pages, 8 figures. A review paper accepted for publication in the
special issue Entanglement Entropy in the journal Entrop
Riemann zeta zeros and prime number spectra in quantum field theory
The Riemann hypothesis states that all nontrivial zeros of the zeta function
lie in the critical line . Hilbert and P\'olya suggested that one
possible way to prove the Riemann hypothesis is to interpret the nontrivial
zeros in the light of spectral theory. Following this approach, we discuss a
necessary condition that such a sequence of numbers should obey in order to be
associated with the spectrum of a linear differential operator of a system with
countably infinite number of degrees of freedom described by quantum field
theory. The sequence of nontrivial zeros is zeta regularizable. Then,
functional integrals associated with hypothetical systems described by
self-adjoint operators whose spectra is given by this sequence can be
constructed. However, if one considers the same situation with primes numbers,
the associated functional integral cannot be constructed, due to the fact that
the sequence of prime numbers is not zeta regularizable. Finally, we extend
this result to sequences whose asymptotic distributions are not "far away" from
the asymptotic distribution of prime numbers.Comment: Revised version, 18 page
Spectrum of the non-commutative spherical well
We give precise meaning to piecewise constant potentials in non-commutative
quantum mechanics. In particular we discuss the infinite and finite
non-commutative spherical well in two dimensions. Using this, bound-states and
scattering can be discussed unambiguously. Here we focus on the infinite well
and solve for the eigenvalues and eigenfunctions. We find that time reversal
symmetry is broken by the non-commutativity. We show that in the commutative
and thermodynamic limits the eigenstates and eigenfunctions of the commutative
spherical well are recovered and time reversal symmetry is restored
Generations of orthogonal surface coordinates
Two generation methods were developed for three dimensional flows where the computational domain normal to the surface is small. With this restriction the coordinate system requires orthogonality only at the body surface. The first method uses the orthogonal condition in finite-difference form to determine the surface coordinates with the metric coefficients and curvature of the coordinate lines calculated numerically. The second method obtains analytical expressions for the metric coefficients and for the curvature of the coordinate lines
Polymeric compositions and their method of manufacture
Filled polymer compositions are made by dissolving the polymer binder in a suitable sublimable solvent, mixing the filler material with the polymer and its solvent, freezing the resultant mixture, and subliming the frozen solvent from the mixture from which it is then removed. The remaining composition is suitable for conventional processing such as compression molding or extruding. A particular feature of the method of manufacture is pouring the mixed solution slowly in a continuous stream into a cryogenic bath wherein frozen particles of the mixture result. The frozen individual particles are then subjected to the sublimation
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