341 research outputs found
Pulsating Front Speed-up and Quenching of Reaction by Fast Advection
We consider reaction-diffusion equations with combustion-type non-linearities
in two dimensions and study speed-up of their pulsating fronts by general
periodic incompressible flows with a cellular structure. We show that the
occurence of front speed-up in the sense ,
with the amplitude of the flow and the (minimal) front speed, only
depends on the geometry of the flow and not on the reaction function. In
particular, front speed-up happens for KPP reactions if and only if it does for
ignition reactions. We also show that the flows which achieve this speed-up are
precisely those which, when scaled properly, are able to quench any ignition
reaction.Comment: 16p
Gaussian approximation and single-spin measurement in OSCAR MRFM with spin noise
A promising technique for measuring single electron spins is magnetic
resonance force microscopy (MRFM), in which a microcantilever with a permanent
magnetic tip is resonantly driven by a single oscillating spin. If the quality
factor of the cantilever is high enough, this signal will be amplified over
time to the point that it can be detected by optical or other techniques. An
important requirement, however, is that this measurement process occur on a
time scale short compared to any noise which disturbs the orientation of the
measured spin. We describe a model of spin noise for the MRFM system, and show
how this noise is transformed to become time-dependent in going to the usual
rotating frame. We simplify the description of the cantilever-spin system by
approximating the cantilever wavefunction as a Gaussian wavepacket, and show
that the resulting approximation closely matches the full quantum behavior. We
then examine the problem of detecting the signal for a cantilever with thermal
noise and spin with spin noise, deriving a condition for this to be a useful
measurement.Comment: 12 pages, 8 figures in EPS format, RevTeX 4.
Precautionary Measures for Credit Risk Management in Jump Models
Sustaining efficiency and stability by properly controlling the equity to
asset ratio is one of the most important and difficult challenges in bank
management. Due to unexpected and abrupt decline of asset values, a bank must
closely monitor its net worth as well as market conditions, and one of its
important concerns is when to raise more capital so as not to violate capital
adequacy requirements. In this paper, we model the tradeoff between avoiding
costs of delay and premature capital raising, and solve the corresponding
optimal stopping problem. In order to model defaults in a bank's loan/credit
business portfolios, we represent its net worth by Levy processes, and solve
explicitly for the double exponential jump diffusion process and for a general
spectrally negative Levy process.Comment: 31 pages, 4 figure
Noncommutative geometry and stochastic processes
The recent analysis on noncommutative geometry, showing quantization of the
volume for the Riemannian manifold entering the geometry, can support a view of
quantum mechanics as arising by a stochastic process on it. A class of
stochastic processes can be devised, arising as fractional powers of an
ordinary Wiener process, that reproduce in a proper way a stochastic process on
a noncommutative geometry. These processes are characterized by producing
complex values and so, the corresponding Fokker-Planck equation resembles the
Schroedinger equation. Indeed, by a direct numerical check, one can recover the
kernel of the Schroedinger equation starting by an ordinary Brownian motion.
This class of stochastic processes needs a Clifford algebra to exist. In four
dimensions, the full set of Dirac matrices is needed and the corresponding
stochastic process in a noncommutative geometry is easily recovered as is the
Dirac equation in the Klein-Gordon form being it the Fokker--Planck equation of
the process.Comment: 16 pages, 2 figures. Updated a reference. A version of this paper
will appear in the proceedings of GSI2017, Geometric Science of Information,
November 7th to 9th, Paris (France
Continuous quantum feedback of coherent oscillations in a solid-state qubit
We have analyzed theoretically the operation of the Bayesian quantum feedback
of a solid-state qubit, designed to maintain perfect coherent oscillations in
the qubit for arbitrarily long time. In particular, we have studied the
feedback efficiency in presence of dephasing environment and detector
nonideality. Also, we have analyzed the effect of qubit parameter deviations
and studied the quantum feedback control of an energy-asymmetric qubit.Comment: 11 page
Magnetometry via a double-pass continuous quantum measurement of atomic spin
We argue that it is possible in principle to reduce the uncertainty of an
atomic magnetometer by double-passing a far-detuned laser field through the
atomic sample as it undergoes Larmor precession. Numerical simulations of the
quantum Fisher information suggest that, despite the lack of explicit
multi-body coupling terms in the system's magnetic Hamiltonian, the parameter
estimation uncertainty in such a physical setup scales better than the
conventional Heisenberg uncertainty limit over a specified but arbitrary range
of particle number N. Using the methods of quantum stochastic calculus and
filtering theory, we demonstrate numerically an explicit parameter estimator
(called a quantum particle filter) whose observed scaling follows that of our
calculated quantum Fisher information. Moreover, the quantum particle filter
quantitatively surpasses the uncertainty limit calculated from the quantum
Cramer-Rao inequality based on a magnetic coupling Hamiltonian with only
single-body operators. We also show that a quantum Kalman filter is
insufficient to obtain super-Heisenberg scaling, and present evidence that such
scaling necessitates going beyond the manifold of Gaussian atomic states.Comment: 17 pages, updated to match print versio
Errors in quantum optimal control and strategy for the search of easily implementable control pulses
We introduce a new approach to assess the error of control problems we aim to
optimize. The method offers a strategy to define new control pulses that are
not necessarily optimal but still able to yield an error not larger than some
fixed a priori threshold, and therefore provide control pulses that might be
more amenable for an experimental implementation. The formalism is applied to
an exactly solvable model and to the Landau-Zener model, whose optimal control
problem is solvable only numerically. The presented method is of importance for
applications where a high degree of controllability of the dynamics of quantum
systems is required.Comment: 13 pages, 3 figure
Uncollapsing the wavefunction by undoing quantum measurements
We review and expand on recent advances in theory and experiments concerning
the problem of wavefunction uncollapse: Given an unknown state that has been
disturbed by a generalized measurement, restore the state to its initial
configuration. We describe how this is probabilistically possible with a
subsequent measurement that involves erasing the information extracted about
the state in the first measurement. The general theory of abstract measurements
is discussed, focusing on quantum information aspects of the problem, in
addition to investigating a variety of specific physical situations and
explicit measurement strategies. Several systems are considered in detail: the
quantum double dot charge qubit measured by a quantum point contact (with and
without Hamiltonian dynamics), the superconducting phase qubit monitored by a
SQUID detector, and an arbitrary number of entangled charge qubits.
Furthermore, uncollapse strategies for the quantum dot electron spin qubit, and
the optical polarization qubit are also reviewed. For each of these systems the
physics of the continuous measurement process, the strategy required to ideally
uncollapse the wavefunction, as well as the statistical features associated
with the measurement is discussed. We also summarize the recent experimental
realization of two of these systems, the phase qubit and the polarization
qubit.Comment: 19 pages, 4 figure
A Feynman-Kac Formula for Anticommuting Brownian Motion
Motivated by application to quantum physics, anticommuting analogues of
Wiener measure and Brownian motion are constructed. The corresponding Ito
integrals are defined and the existence and uniqueness of solutions to a class
of stochastic differential equations is established. This machinery is used to
provide a Feynman-Kac formula for a class of Hamiltonians. Several specific
examples are considered.Comment: 21 page
- …