7,949 research outputs found
Comment on "Why quantum mechanics cannot be formulated as a Markov process"
In the paper with the above title, D. T. Gillespie [Phys. Rev. A 49, 1607,
(1994)] claims that the theory of Markov stochastic processes cannot provide an
adequate mathematical framework for quantum mechanics. In conjunction with the
specific quantum dynamics considered there, we give a general analysis of the
associated dichotomic jump processes. If we assume that Gillespie's
"measurement probabilities" \it are \rm the transition probabilities of a
stochastic process, then the process must have an invariant (time independent)
probability measure. Alternatively, if we demand the probability measure of the
process to follow the quantally implemented (via the Born statistical
postulate) evolution, then we arrive at the jump process which \it can \rm be
interpreted as a Markov process if restricted to a suitable duration time.
However, there is no corresponding Markov process consistent with the
event space assumption, if we require its existence for all times .Comment: Latex file, resubm. to Phys. Rev.
Exact Ground State and Finite Size Scaling in a Supersymmetric Lattice Model
We study a model of strongly correlated fermions in one dimension with
extended N=2 supersymmetry. The model is related to the spin XXZ
Heisenberg chain at anisotropy with a real magnetic field on the
boundary. We exploit the combinatorial properties of the ground state to
determine its exact wave function on finite lattices with up to 30 sites. We
compute several correlation functions of the fermionic and spin fields. We
discuss the continuum limit by constructing lattice observables with well
defined finite size scaling behavior. For the fermionic model with periodic
boundary conditions we give the emptiness formation probability in closed form.Comment: 4 pages, 4 eps figure
Impossibility of spontaneously breaking local symmetries and the sign problem
Elitzur's theorem stating the impossibility of spontaneous breaking of local
symmetries in a gauge theory is reexamined. The existing proofs of this theorem
rely on gauge invariance as well as positivity of the weight in the Euclidean
partition function. We examine the validity of Elitzur's theorem in gauge
theories for which the Euclidean measure of the partition function is not
positive definite. We find that Elitzur's theorem does not follow from gauge
invariance alone. We formulate a general criterion under which spontaneous
breaking of local symmetries in a gauge theory is excluded. Finally we
illustrate the results in an exactly solvable two dimensional abelian gauge
theory.Comment: Latex 6 page
Exact Monte Carlo time dynamics in many-body lattice quantum systems
On the base of a Feynman-Kac--type formula involving Poisson stochastic
processes, recently a Monte Carlo algorithm has been introduced, which
describes exactly the real- or imaginary-time evolution of many-body lattice
quantum systems. We extend this algorithm to the exact simulation of
time-dependent correlation functions. The techniques generally employed in
Monte Carlo simulations to control fluctuations, namely reconfigurations and
importance sampling, are adapted to the present algorithm and their validity is
rigorously proved. We complete the analysis by several examples for the
hard-core boson Hubbard model and for the Heisenberg model
A dynamic analysis of stock markets using a hidden Markov model
none2siThis paper proposes a framework to detect financial crises, pinpoint the end of a crisis in stock markets and support investment decision-making processes. This proposal is based on a hidden Markov model (HMM) and allows for a specific focus on conditional mean returns. By analysing weekly changes in the US stock market indexes over a period of 20 years, this study obtains an accurate detection of stable and turmoil periods and a probabilistic measure of switching between different stock market conditions. The results
contribute to the discussion of the capabilities of Markov-switching models of analysing stock market behaviour. In particular, we find evidence that HMM outperforms threshold GARCH model with Student-t innovations both in-sample and out-of-sample, giving financial operators some appealing investment strategies.openL. De Angelis; L.J. PaasL. De Angelis; L.J. Paa
Interview of Edward J. Sheehy, F.S.C., Ph.D.
Edward J. Sheehy was born in 1946 to Edward and Rosemary Sheehy. His father was a naval commander and later the head of an aerospace company called Hercules. He entered the novitiate of the Christian Brothers in 1963, received his undergraduate degree in history from La Salle College in 1968, his Master of Liberal Arts from Johns Hopkins University in 1973, and his Ph.D. in History from George Washington University in 1983. He worked at St. Gabriel\u27s Hall, Calvert College High School, Hudson Catholic High School, Central Catholic High School in Pittsburgh, PA, and La Salle University. A specialist on U.S. naval history, he is a professor in the History Department of La Salle University and Vice President of the Corporation. His honors include the Lindback Award for Distinguished Teaching and the Dr. Roland Holroyd Award for contributions made to the community
Drag Reduction by Polymers in Turbulent Channel Flows: Energy Redistribution Between Invariant Empirical Modes
We address the phenomenon of drag reduction by dilute polymeric additive to
turbulent flows, using Direct Numerical Simulations (DNS) of the FENE-P model
of viscoelastic flows. It had been amply demonstrated that these model
equations reproduce the phenomenon, but the results of DNS were not analyzed so
far with the goal of interpreting the phenomenon. In order to construct a
useful framework for the understanding of drag reduction we initiate in this
paper an investigation of the most important modes that are sustained in the
viscoelastic and Newtonian turbulent flows respectively. The modes are obtained
empirically using the Karhunen-Loeve decomposition, allowing us to compare the
most energetic modes in the viscoelastic and Newtonian flows. The main finding
of the present study is that the spatial profile of the most energetic modes is
hardly changed between the two flows. What changes is the energy associated
with these modes, and their relative ordering in the decreasing order from the
most energetic to the least. Modes that are highly excited in one flow can be
strongly suppressed in the other, and vice versa. This dramatic energy
redistribution is an important clue to the mechanism of drag reduction as is
proposed in this paper. In particular there is an enhancement of the energy
containing modes in the viscoelastic flow compared to the Newtonian one; drag
reduction is seen in the energy containing modes rather than the dissipative
modes as proposed in some previous theories.Comment: 11 pages, 13 figures, included, PRE, submitted, REVTeX
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