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Analog and Mixed Signal Verification
More and more electronic systems have components that are not purely digital. Verification of such systems is a much less developed discipline than the digital equivalents and the application of formal (mathematically complete) techniques is a nascent area. In this paper, we will discuss the nature of analog circuit design and describe the way verification is done in practice today. We will describe some “formal” approaches coming from the analog design community. We will describe some of the approaches to formal verification that have been presented in recent literature. Finally, we will mention some areas where there are opportunities for future work
Higher-Order Differential Operators on a Lie Group and Quantization
This talk is devoted mainly to the concept of higher-order polarization on a
group, which is introduced in the framework of a Group Approach to
Quantization, as a powerful tool to guarantee the irreducibility of
quantizations and/or representations of Lie groups in those anomalous cases
where the Kostant-Kirilov co-adjoint method or the Borel-Weyl-Bott
representation algorithm do not succeed.Comment: 9 pages, latex, no figures, uses IJMPB.sty (included). New version
partially rewritten (title changed!), presented to the II Int. Workshop on
Class. and Quant. Integrable Systems, Dubna (Rusia) 1996, and published in
Int. J. Mod. Phys.
Bargmann representations for deformed harmonic oscillators
Generalizing the case of the usual harmonic oscillator, we look for Bargmann
representations corresponding to deformed harmonic oscillators. Deformed
harmonic oscillator algebras are generated by four operators
and the unity 1 such as , and . We discuss the conditions of existence of
a scalar product expressed with a true integral on the space spanned by the
eigenstates of (or ). We give various examples, in particular we
consider functions that are linear combinations of , and
unity and that correspond to q-oscillators with Fock-representations or with
non-Fock-representations.Comment: 23 pages, Late
Network of Time-Multiplexed Optical Parametric Oscillators as a Coherent Ising Machine
Finding the ground states of the Ising Hamiltonian [1] maps to various
combinatorial optimization problems in biology, medicine, wireless
communications, artificial intelligence, and social network. So far no
efficient classical and quantum algorithm is known for these problems, and
intensive research is focused on creating physical systems - Ising machines -
capable of finding the absolute or approximate ground states of the Ising
Hamiltonian [2-6]. Here we report a novel Ising machine using a network of
degenerate optical parametric oscillators (OPOs). Spins are represented with
above-threshold binary phases of the OPOs and the Ising couplings are realized
by mutual injections [7]. The network is implemented in a single OPO ring
cavity with multiple trains of femtosecond pulses and configurable mutual
couplings, and operates at room temperature. We programed the smallest
non-deterministic polynomial time (NP)- hard Ising problem on the machine, and
in 1000 runs of the machine no computational error was detected
Stochastic Schroedinger equation from optimal observable evolution
In this article, we consider a set of trial wave-functions denoted by | Q
\right> and an associated set of operators which generate
transformations connecting those trial states. Using variational principles, we
show that we can always obtain a quantum Monte-Carlo method where the quantum
evolution of a system is replaced by jumps between density matrices of the form
, and where the average evolutions of the moments of
up to a given order , i.e. , $< A_{\alpha_1}
A_{\alpha_2} >$,..., , are constrained to
follow the exact Ehrenfest evolution at each time step along each stochastic
trajectory. Then, a set of more and more elaborated stochastic approximations
of a quantum problem is obtained which approach the exact solution when more
and more constraints are imposed, i.e. when increases. The Monte-Carlo
process might even become exact if the Hamiltonian applied on the trial
state can be written as a polynomial of . The formalism makes a
natural connection between quantum jumps in Hilbert space and phase-space
dynamics. We show that the derivation of stochastic Schroedinger equations can
be greatly simplified by taking advantage of the existence of this hierarchy of
approximations and its connection to the Ehrenfest theorem. Several examples
are illustrated: the free wave-packet expansion, the Kerr oscillator, a
generalized version of the Kerr oscillator, as well as interacting bosons or
fermions.Comment: 13 pages, 1 figur
Retention and application of Skylab experiences to future programs
The problems encountered and special techniques and procedures developed on the Skylab program are described along with the experiences and practical benefits obtained for dissemination and use on future programs. Three major topics are discussed: electrical problems, mechanical problems, and special techniques. Special techniques and procedures are identified that were either developed or refined during the Skylab program. These techniques and procedures came from all manufacturing and test phases of the Skylab program and include both flight and GSE items from component level to sophisticated spaceflight systems
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