11,509 research outputs found
Comparison of LISA and Atom Interferometry for Gravitational Wave Astronomy in Space
One of the atom interferometer gravitational wave missions proposed by
Dimopoulos et al.1 in 2008 was called AGIS-Sat. 2. It had a suggested
gravitational wave sensitivity set by the atom state detection shot noise level
that started at 1 mHz, was comparable to LISA sensitivity from 1 to about 20
mHz, and had better sensitivity from 20 to 500 mHz. The separation between the
spacecraft was 1,000 km, with atom interferometers 200 m long and shades from
sunlight used at each end. A careful analysis of many error sources was
included, but requirements on the time-stability of both the laser wavefront
aberrations and the atom temperatures in the atom clouds were not investigated.
After including these considerations, the laser wavefront aberration stability
requirement to meet the quoted sensitivity level is about 1\times10-8
wavelengths, and is far tighter than for LISA. Also, the temperature
fluctuations between atom clouds have to be less than 1 pK. An alternate atom
interferometer GW mission in Earth orbit called AGIS-LEO with 30 km satellite
separation has been suggested recently. The reduction of wavefront aberration
noise by sending the laser beam through a high-finesse mode-scrubbing optical
cavity is discussed briefly, but the requirements on such a cavity are not
given. Unfortunately, such an Earth-orbiting mission seems to be considerably
more difficult to design than a non-geocentric mission and does not appear to
have comparably attractive scientific goals.Comment: Submitted to Proc. 46th Rencontres de Moriond: Gravitational Waves
and Experimental Gravity, March 20 - 27, 2011, La Thuile, Ital
Chaotic systems in complex phase space
This paper examines numerically the complex classical trajectories of the
kicked rotor and the double pendulum. Both of these systems exhibit a
transition to chaos, and this feature is studied in complex phase space.
Additionally, it is shown that the short-time and long-time behaviors of these
two PT-symmetric dynamical models in complex phase space exhibit strong
qualitative similarities.Comment: 22 page, 16 figure
Spin switching via quantum dot spin valves
We develop a theory for spin transport and magnetization dynamics in a
quantum-dot spin valve, i.e., two magnetic reservoirs coupled to a quantum dot.
Our theory is able to take into account effects of strong correlations. We
demonstrate that, as a result of these strong correlations, the dot gate
voltage enables control over the current-induced torques on the magnets, and,
in particular, enables voltage-controlled magnetic switching. The electrical
resistance of the structure can be used to read out the magnetic state. Our
model may be realized by a number of experimental systems, including magnetic
scanning-tunneling microscope tips and artificial quantum dot systems
PT-Symmetric Representations of Fermionic Algebras
A recent paper by Jones-Smith and Mathur extends PT-symmetric quantum
mechanics from bosonic systems (systems for which ) to fermionic systems
(systems for which ). The current paper shows how the formalism
developed by Jones-Smith and Mathur can be used to construct PT-symmetric
matrix representations for operator algebras of the form ,
, , where
. It is easy to construct matrix
representations for the Grassmann algebra (). However, one can only
construct matrix representations for the fermionic operator algebra
() if ; a matrix representation does not exist for the
conventional value .Comment: 5 pages, 2 figure
Libration driven multipolar instabilities
We consider rotating flows in non-axisymmetric enclosures that are driven by
libration, i.e. by a small periodic modulation of the rotation rate. Thanks to
its simplicity, this model is relevant to various contexts, from industrial
containers (with small oscillations of the rotation rate) to fluid layers of
terrestial planets (with length-of-day variations). Assuming a multipolar
-fold boundary deformation, we first obtain the two-dimensional basic flow.
We then perform a short-wavelength local stability analysis of the basic flow,
showing that an instability may occur in three dimensions. We christen it the
Libration Driven Multipolar Instability (LDMI). The growth rates of the LDMI
are computed by a Floquet analysis in a systematic way, and compared to
analytical expressions obtained by perturbation methods. We then focus on the
simplest geometry allowing the LDMI, a librating deformed cylinder. To take
into account viscous and confinement effects, we perform a global stability
analysis, which shows that the LDMI results from a parametric resonance of
inertial modes. Performing numerical simulations of this librating cylinder, we
confirm that the basic flow is indeed established and report the first
numerical evidence of the LDMI. Numerical results, in excellent agreement with
the stability results, are used to explore the non-linear regime of the
instability (amplitude and viscous dissipation of the driven flow). We finally
provide an example of LDMI in a deformed spherical container to show that the
instability mechanism is generic. Our results show that the previously studied
libration driven elliptical instability simply corresponds to the particular
case of a wider class of instabilities. Summarizing, this work shows that
any oscillating non-axisymmetric container in rotation may excite intermittent,
space-filling LDMI flows, and this instability should thus be easy to observe
experimentally
Spontaneous Symmetry Breaking of phi4(1+1) in Light Front Field Theory
We study spontaneous symmetry breaking in phi^4_(1+1) using the light-front
formulation of the field theory. Since the physical vacuum is always the same
as the perturbative vacuum in light-front field theory the fields must develop
a vacuum expectation value through the zero-mode components of the field. We
solve the nonlinear operator equation for the zero-mode in the one-mode
approximation. We find that spontaneous symmetry breaking occurs at
lambda_critical = 4 pi(3+sqrt 3), which is consistent with the value
lambda_critical = 54.27 obtained in the equal time theory. We calculate the
value of the vacuum expectation value as a function of the coupling constant in
the broken phase both numerically and analytically using the delta expansion.
We find two equivalent broken phases. Finally we show that the energy levels of
the system have the expected behavior within the broken phase.Comment: 17 pages, OHSTPY-HEP-TH-92-02
PT-symmetry and its spontaneous breakdown explained by anti-linearity
The impact of an anti-unitary symmetry on the spectrum of non-Hermitian operators is studied. Wigner's normal form of an anti-unitary operator accounts for the spectral properties of non-Hermitian, PE-symmetric Harniltonians. The occurrence of either single real or complex conjugate pairs of eigenvalues follows from this theory. The corresponding energy eigenstates span either one- or two-dimensional irreducible representations of the symmetry PE. In this framework, the concept of a spontaneously broken PE-symmetry is not needed
Homogeneity of Stellar Populations in Early-Type Galaxies with Different X-ray Properties
We have found the stellar populations of early-type galaxies are homogeneous
with no significant difference in color or Mg2 index, despite the dichotomy
between X-ray extended early-type galaxies and X-ray compact ones. Since the
X-ray properties reflect the potential gravitational structure and hence the
process of galaxy formation, the homogeneity of the stellar populations implies
that the formation of stars in early-type galaxies predat es the epoch when the
dichotomy of the potential structure was established.Comment: 6 pages, 5 figures, accepted for publication in Ap
On the eigenproblems of PT-symmetric oscillators
We consider the non-Hermitian Hamiltonian H=
-\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a
polynomial of degree at most n \geq 1 with all nonnegative real coefficients
(possibly P\equiv 0). It is proved that the eigenvalues \lambda must be in the
sector | arg \lambda | \leq \frac{\pi}{2n+3}. Also for the case
H=-\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the
eigenfunction u and its derivative u^\prime and we find some other interesting
properties of eigenfunctions.Comment: 21pages, 9 figure
Regularization of second-order scalar perturbation produced by a point-particle with a nonlinear coupling
Accurate calculation of the motion of a compact object in a background
spacetime induced by a supermassive black hole is required for the future
detection of such binary systems by the gravitational-wave detector LISA.
Reaching the desired accuracy requires calculation of the second-order
gravitational perturbations produced by the compact object. At the point
particle limit the second-order gravitational perturbation equations turn out
to have highly singular source terms, for which the standard retarded solutions
diverge. Here we study a simplified scalar toy-model in which a point particle
induces a nonlinear scalar field in a given curved spacetime. The corresponding
second-order scalar perturbation equation in this model is found to have a
similar singular source term, and therefore its standard retarded solutions
diverge. We develop a regularization method for constructing well-defined
causal solutions for this equation. Notably these solutions differ from the
standard retarded solutions, which are ill-defined in this case.Comment: 14 page
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