774 research outputs found
On sectorial matrices
AbstractA square complex matrix A is said to be sectorial if the values of the corresponding quadratic form x*Ax belong to the sector {z:|argz|⩽α} of the complex plane with α∈[0,π/2). We prove criterions for square matrix to be sectorial. The case of sectorial block matrix is considered and the corresponding criterions by means of Schur complements and quadratic forms are established. We also consider square matrices of the class C connected with sectorial matrices via the Cayley transform
Negative-Index Metamaterials: Second-Harmonic Generation, Manley-Rowe Relations and Parametric Amplification
Second harmonic generation and optical parametric amplification in
negative-index metamaterials (NIMs) are studied. The opposite directions of the
wave vector and the Poynting vector in NIMs results in a "backward"
phase-matching condition, causing significant changes in the Manley-Rowe
relations and spatial distributions of the coupled field intensities. It is
shown that absorption in NIMs can be compensated by backward optical parametric
amplification. The possibility of distributed-feedback parametric oscillation
with no cavity has been demonstrated. The feasibility of the generation of
entangled pairs of left- and right-handed counter-propagating photons is
discussed.Comment: 7 pages, 6 figure
Spontaneous magnetostriction in the Gd-Y system: analysis of phase transformations
The transformations of magnetic and lattice subsystems states of Gd₁₀₀₋xYx (x=0, 5.5, 7.5, 10.2) alloys have been studied at temperatures 5-370 K in magnetic fields up to 4 kOe. The temperature dependences of elastic modules, thermal expansion, low field magnetization and magnetic anisotropy parameters were obtained. The linear spontaneous striction ΔL(T)/L=xh² was analized, and the effective order parameters η and magnetostrictive parameters ξ were evaluated for the four magnetic phases (canted ferromagnetic, deforming ferromagnetic helix, ferromagnetic helix, and the ferromagnetic cone, respectively): ξcf=2.2×10⁻⁵, ξdh=- 5.3×10⁻⁵, ξfh=7.1×10⁻⁵, ξfc=1.4×10⁻³
Vacuum instability in external fields
We study particles creation in arbitrary space-time dimensions by external
electric fields, in particular, by fields, which are acting for a finite time.
The time and dimensional analysis of the vacuum instability is presented. It is
shown that the distributions of particles created by quasiconstant electric
fields can be written in a form which has a thermal character and seems to be
universal. Its application, for example, to the particles creation in external
constant gravitational field reproduces the Hawking temperature exactly.Comment: 36 pages, LaTe
Finite Temperature Properties of Quantum Antiferromagnets in a Uniform Magnetic Field in One and Two Dimensions
Consider a -dimensional antiferromagnet with a quantum disordered ground
state and a gap to bosonic excitations with non-zero spin. In a finite external
magnetic field, this antiferromagnet will undergo a phase transition to a
ground state with non-zero magnetization, describable as the condensation of a
dilute gas of bosons. The finite temperature properties of the Bose gas in the
vicinity of this transition are argued to obey a hypothesis of ZERO
SCALE-FACTOR UNIVERSALITY for , with logarithmic violations in .
Scaling properties of various experimental observables are computed in an
expansion in , and exactly in .Comment: 27 pages, REVTEX 3.0, 8 Postscript figures appended, YCTP-xyz
Magnetoelectric ordering of BiFeO3 from the perspective of crystal chemistry
In this paper we examine the role of crystal chemistry factors in creating
conditions for formation of magnetoelectric ordering in BiFeO3. It is generally
accepted that the main reason of the ferroelectric distortion in BiFeO3 is
concerned with a stereochemical activity of the Bi lone pair. However, the lone
pair is stereochemically active in the paraelectric orthorhombic beta-phase as
well. We demonstrate that a crucial role in emerging of phase transitions of
the metal-insulator, paraelectric-ferroelectric and magnetic disorder-order
types belongs to the change of the degree of the lone pair stereochemical
activity - its consecutive increase with the temperature decrease. Using the
structural data, we calculated the sign and strength of magnetic couplings in
BiFeO3 in the range from 945 C down to 25 C and found the couplings, which
undergo the antiferromagnetic-ferromagnetic transition with the temperature
decrease and give rise to the antiferromagnetic ordering and its delay in
regard to temperature, as compared to the ferroelectric ordering. We discuss
the reasons of emerging of the spatially modulated spin structure and its
suppression by doping with La3+.Comment: 18 pages, 5 figures, 3 table
Schwinger Pair Production via Instantons in Strong Electric Fields
In the space-dependent gauge, each mode of the Klein-Gordon equation in a
strong electric field takes the form of a time-independent Schr\"{o}dinger
equation with a potential barrier. We propose that the single- and
multi-instantons of quantum tunneling may be related with the single- and
multi-pair production of bosons and the relative probability for the no-pair
production is determined by the total tunneling probability via instantons. In
the case of a uniform electric field, the instanton interpretation recovers
exactly the well-known pair production rate for bosons and when the Pauli
blocking is taken into account, it gives the correct fermion production rate.
The instanton is used to calculate the pair production rate even in an
inhomogeneous electric field. Furthermore, the instanton interpretation
confirms the fact that bosons and fermions can not be produced by a static
magnetic field only.Comment: RevTex 7 Pages, No figure; Formulae for the production rate in very
strong fields and references added; the final version accepted in Phys. Rev.
Quantum magnetism in two dimensions: From semi-classical N\'eel order to magnetic disorder
This is a review of ground-state features of the s=1/2 Heisenberg
antiferromagnet on two-dimensional lattices. A central issue is the interplay
of lattice topology (e.g. coordination number, non-equivalent nearest-neighbor
bonds, geometric frustration) and quantum fluctuations and their impact on
possible long-range order. This article presents a unified summary of all 11
two-dimensional uniform Archimedean lattices which include e.g. the square,
triangular and kagome lattice. We find that the ground state of the spin-1/2
Heisenberg antiferromagnet is likely to be semi-classically ordered in most
cases. However, the interplay of geometric frustration and quantum fluctuations
gives rise to a quantum paramagnetic ground state without semi-classical
long-range order on two lattices which are precisely those among the 11 uniform
Archimedean lattices with a highly degenerate ground state in the classical
limit. The first one is the famous kagome lattice where many low-lying singlet
excitations are known to arise in the spin gap. The second lattice is called
star lattice and has a clear gap to all excitations.
Modification of certain bonds leads to quantum phase transitions which are
also discussed briefly. Furthermore, we discuss the magnetization process of
the Heisenberg antiferromagnet on the 11 Archimedean lattices, focusing on
anomalies like plateaus and a magnetization jump just below the saturation
field. As an illustration we discuss the two-dimensional Shastry-Sutherland
model which is used to describe SrCu2(BO3)2.Comment: This is now the complete 72-page preprint version of the 2004 review
article. This version corrects two further typographic errors (three total
with respect to the published version), see page 2 for detail
Spin asymmetry A_1^d and the spin-dependent structure function g_1^d of the deuteron at low values of x and Q^2
We present a precise measurement of the deuteron longitudinal spin asymmetry
A_1^d and of the deuteron spin-dependent structure function g_1^d at Q^2 < 1
GeV^2 and 4*10^-5 < x < 2.5*10^-2 based on the data collected by the COMPASS
experiment at CERN during the years 2002 and 2003. The statistical precision is
tenfold better than that of the previous measurement in this region. The
measured A_1^d and g_1^d are found to be consistent with zero in the whole
range of x.Comment: 17 pages, 10 figure
Gluon polarization in the nucleon from quasi-real photoproduction of high-pT hadron pairs
We present a determination of the gluon polarization Delta G/G in the
nucleon, based on the helicity asymmetry of quasi-real photoproduction events,
Q^2<1(GeV/c)^2, with a pair of large transverse-momentum hadrons in the final
state. The data were obtained by the COMPASS experiment at CERN using a 160 GeV
polarized muon beam scattered on a polarized 6-LiD target. The helicity
asymmetry for the selected events is = 0.002 +- 0.019(stat.) +-
0.003(syst.). From this value, we obtain in a leading-order QCD analysis Delta
G/G=0.024 +- 0.089(stat.) +- 0.057(syst.) at x_g = 0.095 and mu^2 =~ 3
(GeV}/c)^2.Comment: 10 pages, 3 figure
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