5,044 research outputs found
Casimir interaction between two concentric cylinders at nonzero temperature
We study the finite temperature Casimir interaction between two concentric
cylinders. When the separation between the cylinders is much smaller than the
radii of the cylinders, the asymptotic expansions of the Casimir interaction
are derived. Both the low temperature and the high temperature regions are
considered. The leading terms are found to agree with the proximity force
approximations. The low temperature leading term of the temperature correction
is also computed and it is found to be independent of the boundary conditions
imposed on the larger cylinder.Comment: 6 pages, 1 figur
Spin texture on the Fermi surface of tensile strained HgTe
We present ab initio and k.p calculations of the spin texture on the Fermi
surface of tensile strained HgTe, which is obtained by stretching the
zincblende lattice along the (111) axis. Tensile strained HgTe is a semimetal
with pointlike accidental degeneracies between a mirror symmetry protected
twofold degenerate band and two nondegenerate bands near the Fermi level. The
Fermi surface consists of two ellipsoids which contact at the point where the
Fermi level crosses the twofold degenerate band along the (111) axis. However,
the spin texture of occupied states indicates that neither ellipsoid carries a
compensating Chern number. Consequently, the spin texture is locked in the
plane perpendicular to the (111) axis, exhibits a nonzero winding number in
that plane, and changes winding number from one end of the Fermi ellipsoids to
the other. The change in the winding of the spin texture suggests the existence
of singular points. An ordered alloy of HgTe with ZnTe has the same effect as
stretching the zincblende lattice in the (111) direction. We present ab initio
calculations of ordered Hg_xZn_1-xTe that confirm the existence of a spin
texture locked in a 2D plane on the Fermi surface with different winding
numbers on either end.Comment: 8 pages, 8 figure
Finite Temperature Casimir Effect in Randall-Sundrum Models
The finite temperature Casimir effect for a scalar field in the bulk region
of the two Randall-Sundrum models, RSI and RSII, is studied. We calculate the
Casimir energy and the Casimir force for two parallel plates with separation
on the visible brane in the RSI model. High-temperature and low-temperature
cases are covered. Attractiveness versus repulsiveness of the temperature
correction to the force is discussed in the typical special cases of
Dirichlet-Dirichlet, Neumann-Neumann, and Dirichlet-Neumann boundary conditions
at low temperature. The Abel-Plana summation formula is made use of, as this
turns out to be most convenient. Some comments are made on the related
contemporary literature.Comment: 33 pages latex, 2 figures. Some changes in the discussion. To appear
in New J. Phy
Manipulation Strategies for the Rank Maximal Matching Problem
We consider manipulation strategies for the rank-maximal matching problem. In
the rank-maximal matching problem we are given a bipartite graph such that denotes a set of applicants and a set of posts. Each
applicant has a preference list over the set of his neighbours in
, possibly involving ties. Preference lists are represented by ranks on the
edges - an edge has rank , denoted as , if post
belongs to one of 's -th choices. A rank-maximal matching is one in which
the maximum number of applicants is matched to their rank one posts and subject
to this condition, the maximum number of applicants is matched to their rank
two posts, and so on. A rank-maximal matching can be computed in time, where denotes the number of applicants, the
number of edges and the maximum rank of an edge in an optimal solution.
A central authority matches applicants to posts. It does so using one of the
rank-maximal matchings. Since there may be more than one rank- maximal matching
of , we assume that the central authority chooses any one of them randomly.
Let be a manipulative applicant, who knows the preference lists of all
the other applicants and wants to falsify his preference list so that he has a
chance of getting better posts than if he were truthful. In the first problem
addressed in this paper the manipulative applicant wants to ensure that
he is never matched to any post worse than the most preferred among those of
rank greater than one and obtainable when he is truthful. In the second problem
the manipulator wants to construct such a preference list that the worst post
he can become matched to by the central authority is best possible or in other
words, wants to minimize the maximal rank of a post he can become matched
to
Control parameterization for optimal control problems with continuous inequality constraints: New convergence results
Control parameterization is a powerful numerical technique for solving optimal control problems with general nonlinear constraints. The main idea of control parameterization is to discretize the control space by approximating the control by a piecewise-constant or piecewise-linear function, thereby yielding an approximate nonlinear programming problem. This approximate problem can then be solved using standard gradient-based optimization techniques. In this paper, we consider the control parameterization method for a class of optimal control problems in which the admissible controls are functions of bounded variation and the state and control are subject to continuous inequality constraints. We show that control parameterization generates a sequence of suboptimal controls whose costs converge to the true optimal cost. This result has previously only been proved for the case when the admissible controls are restricted to piecewise continuous functions
SIC~POVMs and Clifford groups in prime dimensions
We show that in prime dimensions not equal to three, each group covariant
symmetric informationally complete positive operator valued measure (SIC~POVM)
is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover,
the symmetry group of the SIC~POVM is a subgroup of the Clifford group. Hence,
two SIC~POVMs covariant with respect to the HW group are unitarily or
antiunitarily equivalent if and only if they are on the same orbit of the
extended Clifford group. In dimension three, each group covariant SIC~POVM may
be covariant with respect to three or nine HW groups, and the symmetry group of
the SIC~POVM is a subgroup of at least one of the Clifford groups of these HW
groups respectively. There may exist two or three orbits of equivalent
SIC~POVMs for each group covariant SIC~POVM, depending on the order of its
symmetry group. We then establish a complete equivalence relation among group
covariant SIC~POVMs in dimension three, and classify inequivalent ones
according to the geometric phases associated with fiducial vectors. Finally, we
uncover additional SIC~POVMs by regrouping of the fiducial vectors from
different SIC~POVMs which may or may not be on the same orbit of the extended
Clifford group.Comment: 30 pages, 1 figure, section 4 revised and extended, published in J.
Phys. A: Math. Theor. 43, 305305 (2010
Quantization of non-Abelian Berry phase for time reversal invariant systems
We present a quantized non-Abelian Berry phase for time reversal invariant
systems such as quantum spin Hall effect. Ordinary Berry phase is defined by an
integral of Berry's gauge potential along a loop (an integral of the
Chern-Simons one-form), whereas we propose that a similar integral but over
five dimensional parameter space (an integral of the Chern-Simons five-form) is
suitable to define a non-Abelian Berry phase. We study its global topological
aspects and show that it is indeed quantized into two values. We also discuss
its close relationship with the nonperturbative anomalies.Comment: 5 page
Propagation of Bose-Einstein condensates in a magnetic waveguide
Gaseous Bose-Einstein condensates of 2-3 million atoms were loaded into a
microfabricated magnetic trap using optical tweezers. Subsequently, the
condensates were released into a magnetic waveguide and propagated 12 mm.
Single-mode propagation was observed along homogeneous segments of the
waveguide. Inhomogeneities in the guiding potential arose from geometric
deformations of the microfabricated wires and caused strong transverse
excitations. Such deformations may restrict the waveguide physics that can be
explored with propagating condensates.Comment: 5 pages, 4 figure
Parafermionic edge zero modes in Z_n-invariant spin chains
A sign of topological order in a gapped one-dimensional quantum chain is the
existence of edge zero modes. These occur in the Z_2-invariant Ising/Majorana
chain, where they can be understood using free-fermion techniques. Here I
discuss their presence in spin chains with Z_n symmetry, and prove that for
appropriate coupling they are exact, even in this strongly interacting system.
These modes are naturally expressed in terms of parafermions, generalizations
of fermions to the Z_n case. I show that parafermionic edge zero modes do not
occur in the usual ferromagnetic and antiferromagnetic cases, but rather only
when the interactions are chiral, so that spatial-parity and time-reversal
symmetries are broken.Comment: 22 pages. v2: small changes, added reference
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