103 research outputs found
Relativistic Mechanics of Continuous Media
In this work we study the relativistic mechanics of continuous media on a
fundamental level using a manifestly covariant proper time procedure. We
formulate equations of motion and continuity (and constitutive equations) that
are the starting point for any calculations regarding continuous media. In the
force free limit, the standard relativistic equations are regained, so that
these equations can be regarded as a generalization of the standard procedure.
In the case of an inviscid fluid we derive an analogue of the Bernoulli
equations. For irrotational flow we prove that the velocity field can be
derived from a potential. If, in addition, the fluid is incompressible, the
potential must obey the d'Alembert equation, and thus the problem is reduced to
solving the d'Alembert equation with specific boundary conditions (in both
space and time). The solutions indicate the existence of light velocity sound
waves in an incompressible fluid (a result known from previous literature
[19]). Relaxing the constraints and allowing the fluid to become linearly
compressible, one can derive a wave equation from which the sound velosity can
again be computed. For a stationary background flow, it has been demonstrated
that the sound velocity attains its corrrect values for the incompressible and
non-relatvistic limits. Finally, viscosity is introduced, bulk and shear
viscosity constants are defined, and we formulate equations for the motion of a
viscous fluid.Comment: Latex, 44 pages, 5 figure
ACross-Sectional Analysis of CapRates by MSA
Much attention has been paid to capitalization rates or “cap rates?defined as the net operating income over transaction price, also known as a “going-in?current yield on commercial real estate when calculated at the time of purchase. We know that there are a number of global factors that drive capital markets and required rates of return that help to explain observed cap rates over time, but we know little about factors driving the geographical cross-sectional variation of these cap rates. Why are cap rates for similar sized and type property so much lower or higher in one metropolitan statistical area than another? Using data from Real Capital Analytics for multifamily properties we explore several models that combine the expected influences from housing demand growth, supply constraints, liquidity risk and the interaction of these. We document a very strong and robust relation between supply constraints and cap rates as well as evidence of capital flowing from larger markets to smaller markets in recent years. We also find weak but generally supportive evidence of influences from expected growth rates, liquidity and other risk factors.
Japanese Purchases, Exchange Rates, and Speculation in Residential Real Estate Markets
Several luxury single-family home markets in Hawaii have experienced significant price movements in 1987 and 1988, along with a tremendous influx of Japanese buyers. Most noteworthy is the Waialae-Kahala neighborhood in Honolulu, where average price increases of over 60% in the past two years have occurred. This surge in prices has stimulated a great deal of speculative interest. The purpose of this article is to examine the effect of exchange rates (yen/dollar) and Japanese buyers on selected residential market prices and turnover. Using the most exhaustive and complete data set available in Hawaii covering 1986 through early 1988, hedonic pricing models as well as descriptive statistics are used to examine the effects of strong foreign interest in local housing submarkets.
Loading a Bose-Einstein Condensate onto an Optical Lattice: an Application of Optimal Control Theory to The Non Linear Schr\"odinger Equation
Using a set of general methods developed by Krotov [A. I. Konnov and V. A.
Krotov, Automation and Remote Control, {\bf 60}, 1427 (1999)], we extend the
capabilities of Optimal Control Theory to the Nonlinear Schr\"odinger Equation
(NLSE). The paper begins with a general review of the Krotov approach to
optimization. Although the linearized version of the method is sufficient for
the linear Schr\"odinger equation, the full flexibility of the general method
is required for treatment of the nonlinear Schr\"odinger equation. Formal
equations for the optimization of the NLSE, as well as a concrete algorithm are
presented. As an illustration, we consider a Bose-Einstein condensate initially
at rest in a harmonic trap. A phase develops across the BEC when an optical
lattice potential is turned on. The goal is to counter this effect and keep the
phase flat by adjusting the trap strength. The problem is formulated in the
language of Optimal Control Theory (OCT) and solved using the above
methodology. To our knowledge, this is the first rigorous application of OCT to
the Nonlinear Schr\"odinger equation, a capability that is bound to have
numerous other applications.Comment: 11 pages, 4 figures, A reference added, Some typos correcte
Fidelity of optimally controlled quantum gates with randomly coupled multiparticle environments
This work studies the feasibility of optimal control of high-fidelity quantum
gates in a model of interacting two-level particles. One particle (the qubit)
serves as the quantum information processor, whose evolution is controlled by a
time-dependent external field. The other particles are not directly controlled
and serve as an effective environment, coupling to which is the source of
decoherence. The control objective is to generate target one-qubit gates in the
presence of strong environmentally-induced decoherence and under physically
motivated restrictions on the control field. It is found that interactions
among the environmental particles have a negligible effect on the gate fidelity
and require no additional adjustment of the control field. Another interesting
result is that optimally controlled quantum gates are remarkably robust to
random variations in qubit-environment and inter-environment coupling
strengths. These findings demonstrate the utility of optimal control for
management of quantum-information systems in a very precise and specific
manner, especially when the dynamics complexity is exacerbated by inherently
uncertain environmental coupling.Comment: tMOP LaTeX, 9 pages, 3 figures; Special issue of the Journal of
Modern Optics: 37th Winter Colloquium on the Physics of Quantum Electronics,
2-6 January 200
Optimal control theory for unitary transformations
The dynamics of a quantum system driven by an external field is well
described by a unitary transformation generated by a time dependent
Hamiltonian. The inverse problem of finding the field that generates a specific
unitary transformation is the subject of study. The unitary transformation
which can represent an algorithm in a quantum computation is imposed on a
subset of quantum states embedded in a larger Hilbert space. Optimal control
theory (OCT) is used to solve the inversion problem irrespective of the initial
input state. A unified formalism, based on the Krotov method is developed
leading to a new scheme. The schemes are compared for the inversion of a
two-qubit Fourier transform using as registers the vibrational levels of the
electronic state of Na. Raman-like transitions through the
electronic state induce the transitions. Light fields are found
that are able to implement the Fourier transform within a picosecond time
scale. Such fields can be obtained by pulse-shaping techniques of a femtosecond
pulse. Out of the schemes studied the square modulus scheme converges fastest.
A study of the implementation of the qubit Fourier transform in the Na
molecule was carried out for up to 5 qubits. The classical computation effort
required to obtain the algorithm with a given fidelity is estimated to scale
exponentially with the number of levels. The observed moderate scaling of the
pulse intensity with the number of qubits in the transformation is
rationalized.Comment: 32 pages, 6 figure
Encoding a qubit into multilevel subspaces
We present a formalism for encoding the logical basis of a qubit into
subspaces of multiple physical levels. The need for this multilevel encoding
arises naturally in situations where the speed of quantum operations exceeds
the limits imposed by the addressability of individual energy levels of the
qubit physical system. A basic feature of the multilevel encoding formalism is
the logical equivalence of different physical states and correspondingly, of
different physical transformations. This logical equivalence is a source of a
significant flexibility in designing logical operations, while the multilevel
structure inherently accommodates fast and intense broadband controls thereby
facilitating faster quantum operations. Another important practical advantage
of multilevel encoding is the ability to maintain full quantum-computational
fidelity in the presence of mixing and decoherence within encoding subspaces.
The formalism is developed in detail for single-qubit operations and
generalized for multiple qubits. As an illustrative example, we perform a
simulation of closed-loop optimal control of single-qubit operations for a
model multilevel system, and subsequently apply these operations at finite
temperatures to investigate the effect of decoherence on operational fidelity.Comment: IOPart LaTeX, 2 figures, 31 pages; addition of a numerical simulatio
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