52,202 research outputs found
Young measures in a nonlocal phase transition problem
A nonlocal variational problem modelling phase transitions is studied
in the framework of Young measures. The existence of global minimisers
among functions
with internal layers on an infinite tube is proved by combining
a weak convergence result for Young measures and the principle of
concentration-compactness. The regularity of such global minimisers is
discussed, and the nonlocal variational problem is also considered on
asymptotic tubes
Dark matter cores and cusps in spiral galaxies and their explanations
We compare proposed solutions to the core vs cusp issue of spiral galaxies, which has also been framed as a diversity problem, and demonstrate that the cuspiness of dark matter halos is correlated with the stellar surface brightness. We compare the rotation curve fits to the SPARC sample from a self-interacting dark matter (SIDM) model, which self-consistently includes the impact of baryons on the halo profile, and hydrodynamical N-body simulations with cold dark matter (CDM). The SIDM model predicts a strong correlation between the core size and the stellar surface density, and it provides the best global fit to the data. The CDM simulations without strong baryonic feedback effects fail to explain the large dark matter cores seen in low surface brightness galaxies. On the other hand, with strong feedback, CDM simulations do not produce galaxy analogs with high stellar and dark matter densities, and therefore they have trouble in explaining the rotation curves of high surface brightness galaxies. This implies that current feedback implementations need to be modified. We also explicitly show how the concentration-mass and stellar-to-halo mass relations together lead to a radial acceleration relation (RAR) in an averaged sense, and reiterate the point that the RAR does not capture the diversity of galaxy rotation curves in the inner regions. These results make a strong case for SIDM as the explanation for the cores and cusps of field galaxies
Vanishing Integral Relations and Expectation Values for Bloch Functions in Finite Domains
Integral identities for particular Bloch functions in finite periodic systems
are derived. All following statements are proven for a finite domain consisting
of an integer number of unit cells. It is shown that matrix elements of
particular Bloch functions with respect to periodic differential operators
vanish identically. The real valuedness, the time-independence and a summation
property of the expectation values of periodic differential operators applied
to superpositions of specific Bloch functions are derived.Comment: 10 page
Quench Dynamics of Entanglement in an Opened Anisotropic Spin-1/2 Heisenberg Chain
The quantum entanglement dynamics of a one-dimensional spin-1/2 anisotropic
XXZ model is studied using the method of the adaptive time-dependent
density-matrix renormalization-group when two cases of quenches are performed
in the system. An anisotropic interaction quench and the maximum number of
domain walls of staggered magnetization quench are considered. The dynamics of
pairwise entanglement between the nearest two qubits in the spin chain is
investigated. The entanglement of the two-spin qubits can be created and
oscillates in both cases of the quench. The anisotropic interaction has a
strong influence on the oscillation frequency of entanglement.Comment: 13 pages, 4 figure
Quasinormal Modes of Self-Dual Warped AdS Black Hole in Topological Massive Gravity
We consider the various perturbations of self-dual warped AdS black hole
and obtain the exact expressions of quasinormal modes by imposing the vanishing
Dirichlet boundary condition at asymptotic infinity. It is expected that the
quasinormal modes agree with the poles of retarded Green's functions of the
dual CFT. Our results provide a quantitative test of the warped AdS/CFT
correspondence.Comment: 10 pages, no figure, some references and comments on gravitational
perturbations are adde
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