39,222 research outputs found
Bose-Einstein Condensation with Entangled Order Parameter
We propose a practically accessible non-mean-field ground state of
Bose-Einstein condensation (BEC), which occurs in an interspecies two-particle
entangled state, and is thus described by an entangled order parameter. A
suitably defined entanglement entropy is used as the characterization of the
non-mean-field nature, and is found to persist in a wide parameter regime. The
interspecies entanglement leads to novel interference terms in the dynamical
equations governing the single particle orbital wavefunctions. Experimental
feasibility and several methods of probe are discussed. We urge the study of
multi-channel scattering between different species of atoms.Comment: V1: 5 pages, 4 figures. Accepted by Phys. Rev. Lett.; V2: A couple of
very minor typos corrected, publishe
Properties of solutions of stochastic differential equations driven by the G-Brownian motion
In this paper, we study the differentiability of solutions of stochastic
differential equations driven by the -Brownian motion with respect to the
initial data and the parameter. In addition, the stability of solutions of
stochastic differential equations driven by the -Brownian motion is
obtained
Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms
Let and be two integers with , and let and be
integers with and . In this paper, we prove that , where is a constant depending on and .Comment: 8 pages. To appear in Archiv der Mathemati
Irreversible Thermodynamics in Multiscale Stochastic Dynamical Systems
This work extends the results of the recently developed theory of a rather
complete thermodynamic formalism for discrete-state, continuous-time Markov
processes with and without detailed balance. We aim at investigating the
question that whether and how the thermodynamic structure is invariant in a
multiscale stochastic system. That is, whether the relations between
thermodynamic functions of state and process variables remain unchanged when
the system is viewed at different time scales and resolutions. Our results show
that the dynamics on a fast time scale contribute an entropic term to the
"internal energy function", , for the slow dynamics. Based on the
conditional free energy , one can then treat the slow dynamics as if
the fast dynamics is nonexistent. Furthermore, we show that the free energy,
which characterizes the spontaneous organization in a system without detailed
balance, is invariant with or without the fast dynamics: The fast dynamics is
assumed to reach stationarity instantaneously on the slow time scale; they have
no effect on the system's free energy. The same can not be said for the entropy
and the internal energy, both of which contain the same contribution from the
fast dynamics. We also investigate the consequences of time-scale separation in
connection to the concepts of quasi-stationaryty and steady-adiabaticity
introduced in the phenomenological steady-state thermodynamics
Superconducting phase with a chiral -wave pairing symmetry and Majorana fermions induced in a hole-doped semiconductor
We show that a chiral -wave superconducting pairing may be induced in
the lowest heavy hole band of a hole-doped semiconductor thin film through
proximity contact with an \textit{s}-wave superconductor. The chirality of the
pairing originates from the Berry phase accumulated for a heavy hole
moving along a close path on the Fermi surface. There exist three chiral
gapless Majorana edge states, in consistence with the chiral % -wave
pairing. We show the existence of zero energy Majorana fermions in vortices in
the semiconductor-superconductor heterostructure by solving the
Bogoliubov-de-Gennes equations numerically as well as analytically in the
strong confinement limit.Comment: 5 pages, 4 figure
Relative Entropy: Free Energy Associated with Equilibrium Fluctuations and Nonequilibrium Deviations
Using a one-dimensional macromolecule in aqueous solution as an illustration,
we demonstrate that the relative entropy from information theory, , has a natural role in the energetics of equilibrium and
nonequilibrium conformational fluctuations of the single molecule. It is
identified as the free energy difference associated with a fluctuating density
in equilibrium, and is associated with the distribution deviate from the
equilibrium in nonequilibrium relaxation. This result can be generalized to any
other isothermal macromolecular systems using the mathematical theories of
large deviations and Markov processes, and at the same time provides the
well-known mathematical results with an interesting physical interpretations.Comment: 5 page
Neutrino Mass Hierarchy and Stepwise Spectral Swapping of Supernova Neutrino Flavors
We examine a phenomenon recently predicted by numerical simulations of
supernova neutrino flavor evolution: the swapping of supernova and
energy spectra below (above) energy \EC for the normal
(inverted) neutrino mass hierarchy. We present the results of large-scale
numerical calculations which show that in the normal neutrino mass hierarchy
case, \EC decreases as the assumed
effective vacuum mixing angle () is decreased.
However, these calculations also indicate that \EC is essentially independent
of the vacuum mixing angle in the inverted neutrino mass hierarchy case. With a
good neutrino signal from a future Galactic supernova, the above results could
be used to determine the neutrino mass hierarchy even if is too
small to be detected in terrestrial neutrino oscillation experiments.Comment: 4 pages, 2 figures. Version accepted by PR
Flavor Evolution of the Neutronization Neutrino Burst from an O-Ne-Mg Core-Collapse Supernova
We present results of 3-neutrino flavor evolution simulations for the
neutronization burst from an O-Ne-Mg core-collapse supernova. We find that
nonlinear neutrino self-coupling engineers a single spectral feature of
stepwise conversion in the inverted neutrino mass hierarchy case and in the
normal mass hierarchy case, a superposition of two such features corresponding
to the vacuum neutrino mass-squared differences associated with solar and
atmospheric neutrino oscillations. These neutrino spectral features offer a
unique potential probe of the conditions in the supernova environment and may
allow us to distinguish between O-Ne-Mg and Fe core-collapse supernovae.Comment: 4 pages, 2 figures. Version accepted by PR
Neutrino-Neutrino Scattering and Matter-Enhanced Neutrino Flavor Transformation in Supernovae
We examine matter-enhanced neutrino flavor transformation
() in the region above the neutrino
sphere in Type II supernovae. Our treatment explicitly includes contributions
to the neutrino-propagation Hamiltonian from neutrino-neutrino forward
scattering. A proper inclusion of these contributions shows that they have a
completely negligible effect on the range of - vacuum
mass-squared difference, , and vacuum mixing angle, , or
equivalently , required for enhanced supernova shock re-heating.
When neutrino background effects are included, we find that -process
nucleosynthesis from neutrino-heated supernova ejecta remains a sensitive probe
of the mixing between a light and a with a
cosmologically significant mass. Neutrino-neutrino scattering contributions are
found to have a generally small effect on the
parameter region probed by -process nucleosynthesis. We point out that the
nonlinear effects of the neutrino background extend the range of sensitivity of
-process nucleosynthesis to smaller values of .Comment: 38 pages, tex, DOE/ER/40561-150-INT94-00-6
- …