14,598 research outputs found
Wigner functions of thermo number state, photon subtracted and added thermo vacuum state at finite temperature
Based on Takahashi-Umezawa thermo field dynamics and the order-invariance of
Weyl ordered operators under similar transformations, we present a new approach
to deriving the exact Wigner functions of thermo number state, photon
subtracted and added thermo vacuum state. We find that these Wigner functions
are related to the Gaussian-Laguerre type functions of temperature, whose
statistical properties are then analysed.Comment: 10 pages and 2 figure
Figure of Merit for Dark Energy Constraints from Current Observational Data
Choosing the appropriate figure of merit (FoM) for dark energy (DE)
constraints is key in comparing different DE experiments. Here we show that for
a set of DE parameters {f_i}, it is most intuitive to define FoM =
1/\sqrt{Cov(f1,f2,f3,...)}, where Cov(f1,f2,f3,...) is the covariance matrix of
{f_i}. The {f_i} should be minimally correlated. We demonstrate two useful
choices of {f_i} using 182 SNe Ia (compiled by Riess et al. 2007), [R(z_*),
l_a(z_*), \Omega_b h^2] from the five year Wilkinson Microwave Anisotropy Probe
(WMAP) observations, and SDSS measurement of the baryon acoustic oscillation
(BAO) scale, assuming the HST prior of H_0=72+/-8 km/s Mpc^{-1} and without
assuming spatial flatness. We find that the correlation of (w_0,w_{0.5})
[w_0=w_X(z=0), w_{0.5}=w_X(z=0.5), w_X(a) = 3w_{0.5}-2w_0+3(w_0-w_{0.5})a] is
significantly smaller than that of (w_0,w_a) [w_X(a)=w_0+(1-a)w_a]. In order to
obtain model-independent constraints on DE, we parametrize the DE density
function X(z)=\rho_X(z)/\rho_X(0) as a free function with X_{0.5}, X_{1.0}, and
X_{1.5} [values of X(z) at z=0.5, 1.0, and 1.5] as free parameters estimated
from data. If one assumes a linear DE equation of state, current data are
consistent with a cosmological constant at 68% C.L. If one assumes X(z) to be a
free function parametrized by (X_{0.5}, X_{1.0}, X_{1.5}), current data deviate
from a cosmological constant at z=1 at 68% C.L., but are consistent with a
cosmological constant at 95% C.L.. Future DE experiments will allow us to
dramatically increase the FoM of constraints on (w_0,w_{0.5}) and of (X_{0.5},
X_{1.0}, X_{1.5}). This will significantly shrink the DE parameter space to
enable the discovery of DE evolution, or the conclusive evidence for a
cosmological constant.Comment: 7 pages, 3 color figures. Submitte
Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming
The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints
Quantum mechanical photon-count formula derived by entangled state representation
By introducing the thermo entangled state representation, we derived four new
photocount distribution formulas for a given density operator of light field.
It is shown that these new formulas, which is convenient to calculate the
photocount, can be expressed as such integrations over Laguree-Gaussian
function with characteristic function, Wigner function, Q-function, and
P-function, respectively.Comment: 5 pages, no figur
Nonclassicality of photon-added squeezed vacuum and its decoherence in thermal environment
We study the nonclassicality of photon-added squeezed vacuum (PASV) and its
decoherence in thermal environment in terms of the sub-Poissonian statistics
and the negativity of Wigner function (WF). By converting the PASV to a
squeezed Hermite polynomial excitation state, we derive a compact expression
for the normalization factor of m-PASV, which is an m-order Legendre polynomial
of squeezing parameter r. We also derive the explicit expression of WF of
m-PASV and find the negative region of WF in phase space. We show that there is
an upper bound value of r for this state to exhibit sub-Poissonian statistics
increasing as m increases. Then we derive the explicit analytical expression of
time evolution of WF of m-PASV in the thermal channel and discuss the loss of
nonclassicality using the negativity of WF. The threshold value of decay time
is presented for the single PASV.Comment: 14 pages and 7 figure
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