8,967 research outputs found
Two-mode Bose-Einstein condensate in a high-frequency driving field that directly couples the two modes
A two-mode Bose-Einstein condensate coupled by a high-frequency modulation
field is found to display rich features. An effective stationary Hamiltonian
approach reveals the emergence of additional degenerate eigenstates as well as
new topological structures of the spectrum. Possible applications, such as the
suppression of nonlinear Landau-Zener tunneling, are discussed. An interesting
phenomenon, which we call "deterministic symmetry-breaking trapping" associated
with separatrix crossing, is also found in an adiabatic process.Comment: 5 pages, 3 figures, revised version, to appear in Phys. Rev.
Hierarchical Theory of Quantum Adiabatic Evolution
Quantum adiabatic evolution is a dynamical evolution of a quantum system
under slow external driving. According to the quantum adiabatic theorem, no
transitions occur between non-degenerate instantaneous eigen-energy levels in
such a dynamical evolution. However, this is true only when the driving rate is
infinitesimally small. For a small nonzero driving rate, there are generally
small transition probabilities between the energy levels. We develop a
classical mechanics framework to address the small deviations from the quantum
adiabatic theorem order by order. A hierarchy of Hamiltonians are constructed
iteratively with the zeroth-order Hamiltonian being determined by the original
system Hamiltonian. The th-order deviations are governed by a th-order
Hamiltonian, which depends on the time derivatives of the adiabatic parameters
up to the th-order. Two simple examples, the Landau-Zener model and a
spin-1/2 particle in a rotating magnetic field, are used to illustrate our
hierarchical theory. Our analysis also exposes a deep, previously unknown
connection between classical adiabatic theory and quantum adiabatic theory.Comment: 10 pages, 6 figures, 29 reference
Diffusion Models for Double-ended Queues with Renewal Arrival Processes
We study a double-ended queue where buyers and sellers arrive to conduct
trades. When there is a pair of buyer and seller in the system, they
immediately transact a trade and leave. Thus there cannot be non-zero number of
buyers and sellers simultaneously in the system. We assume that sellers and
buyers arrive at the system according to independent renewal processes, and
they would leave the system after independent exponential patience times. We
establish fluid and diffusion approximations for the queue length process under
a suitable asymptotic regime. The fluid limit is the solution of an ordinary
differential equation, and the diffusion limit is a time-inhomogeneous
asymmetric Ornstein-Uhlenbeck process (O-U process). A heavy traffic analysis
is also developed, and the diffusion limit in the stronger heavy traffic regime
is a time-homogeneous asymmetric O-U process. The limiting distributions of
both diffusion limits are obtained. We also show the interchange of the heavy
traffic and steady state limits
All-optical Imprinting of Geometric Phases onto Matter Waves
Traditional optical phase imprinting of matter waves is of a dynamical
nature. In this paper we show that both Abelian and non-Abelian geometric
phases can be optically imprinted onto matter waves, yielding a number of
interesting phenomena such as wavepacket re-directing and wavepacket splitting.
In addition to their fundamental interest, our results open up new
opportunities for robust optical control of matter waves.Comment: 5 pages, 2 figures, to appear in Phys. Rev.
A Pseudospectral Approach to High Index DAE Optimal Control Problems
Historically, solving optimal control problems with high index differential
algebraic equations (DAEs) has been considered extremely hard. Computational
experience with Runge-Kutta (RK) methods confirms the difficulties. High index
DAE problems occur quite naturally in many practical engineering applications.
Over the last two decades, a vast number of real-world problems have been
solved routinely using pseudospectral (PS) optimal control techniques. In view
of this, we solve a "provably hard," index-three problem using the PS method
implemented in DIDO, a state-of-the-art MATLAB optimal control toolbox. In
contrast to RK-type solution techniques, no laborious index-reduction process
was used to generate the PS solution. The PS solution is independently verified
and validated using standard industry practices. It turns out that proper PS
methods can indeed be used to "directly" solve high index DAE optimal control
problems. In view of this, it is proposed that a new theory of difficulty for
DAEs be put forth.Comment: 14 pages, 9 figure
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