12,433 research outputs found
Scaling for Interfacial Tensions near Critical Endpoints
Parametric scaling representations are obtained and studied for the
asymptotic behavior of interfacial tensions in the \textit{full} neighborhood
of a fluid (or Ising-type) critical endpoint, i.e., as a function \textit{both}
of temperature \textit{and} of density/order parameter \textit{or} chemical
potential/ordering field. Accurate \textit{nonclassical critical exponents} and
reliable estimates for the \textit{universal amplitude ratios} are included
naturally on the basis of the ``extended de Gennes-Fisher'' local-functional
theory. Serious defects in previous scaling treatments are rectified and
complete wetting behavior is represented; however, quantitatively small, but
unphysical residual nonanalyticities on the wetting side of the critical
isotherm are smoothed out ``manually.'' Comparisons with the limited available
observations are presented elsewhere but the theory invites new, searching
experiments and simulations, e.g., for the vapor-liquid interfacial tension on
the two sides of the critical endpoint isotherm for which an amplitude ratio
is predicted.Comment: 42 pages, 6 figures, to appear in Physical Review
Path integrals and symmetry breaking for optimal control theory
This paper considers linear-quadratic control of a non-linear dynamical
system subject to arbitrary cost. I show that for this class of stochastic
control problems the non-linear Hamilton-Jacobi-Bellman equation can be
transformed into a linear equation. The transformation is similar to the
transformation used to relate the classical Hamilton-Jacobi equation to the
Schr\"odinger equation. As a result of the linearity, the usual backward
computation can be replaced by a forward diffusion process, that can be
computed by stochastic integration or by the evaluation of a path integral. It
is shown, how in the deterministic limit the PMP formalism is recovered. The
significance of the path integral approach is that it forms the basis for a
number of efficient computational methods, such as MC sampling, the Laplace
approximation and the variational approximation. We show the effectiveness of
the first two methods in number of examples. Examples are given that show the
qualitative difference between stochastic and deterministic control and the
occurrence of symmetry breaking as a function of the noise.Comment: 21 pages, 6 figures, submitted to JSTA
Photon-number-solving Decoy State Quantum Key Distribution
In this paper, a photon-number-resolving decoy state quantum key distribution
scheme is presented based on recent experimental advancements. A new upper
bound on the fraction of counts caused by multiphoton pulses is given. This
upper bound is independent of intensity of the decoy source, so that both the
signal pulses and the decoy pulses can be used to generate the raw key after
verified the security of the communication. This upper bound is also the lower
bound on the fraction of counts caused by multiphoton pulses as long as faint
coherent sources and high lossy channels are used. We show that Eve's coherent
multiphoton pulse (CMP) attack is more efficient than symmetric individual (SI)
attack when quantum bit error rate is small, so that CMP attack should be
considered to ensure the security of the final key. finally, optimal intensity
of laser source is presented which provides 23.9 km increase in the
transmission distance. 03.67.DdComment: This is a detailed and extended version of quant-ph/0504221. In this
paper, a detailed discussion of photon-number-resolving QKD scheme is
presented. Moreover, the detailed discussion of coherent multiphoton pulse
attack (CMP) is presented. 2 figures and some discussions are added. A
detailed cauculation of the "new" upper bound 'is presente
Imagine Math Day: Encouraging Secondary School Students and Teachers to Engage in Authentic Mathematical Discovery
Research mathematicians and school children experience mathematics in profoundly different ways. Ask a group of mathematicians what it means to “do mathematics” and you are likely to get a myriad of responses: mathematics involves analyzing and organizing patterns and relationships, reasoning and drawing conclusions about the world, or creating languages and tools to describe and solve important problems. Students of mathematics often report “doing mathematics” as performing calculations or following rules. It’s natural that they see mathematics as monolithic rather than an evolving, growing, socially constructed body of knowledge, because most mathematical training in primary and secondary schools consists of learning how to use pre-existing mathematical tools. They rarely get to see the process by which those tools came about, let alone authentically participate in the construction of those tools
P-wave Pairing and Colossal Magnetoresistance in Manganese Oxides
We point out that the existing experimental data of most manganese oxides
show the {\sl frustrated} p-wave superconducting condensation in the
ferromagnetic phase in the sense that the superconducting coherence is not long
enough to cover the whole system. The superconducting state is similar to the
state in superfluid He-3. The sharp drop of resistivity, the steep jump
of specific heat, and the gap opening in tunneling are well understood in terms
of the p-wave pairing. In addition, colossal magnetoresistance (CMR) is
naturally explained by the superconducting fluctuations with increasing
magnetic fields. The finite resistivity may be due to some magnetic
inhomogeneities. This study leads to the possibility of room temperature
superconductivity.Comment: LaTex, 14 pages, For more information, please send me an e-mail.
e-mail adrress : [email protected]
Transport optimization on complex networks
We present a comparative study of the application of a recently introduced
heuristic algorithm to the optimization of transport on three major types of
complex networks. The algorithm balances network traffic iteratively by
minimizing the maximum node betweenness with as little path lengthening as
possible. We show that by using this optimal routing, a network can sustain
significantly higher traffic without jamming than in the case of shortest path
routing. A formula is proved that allows quick computation of the average
number of hops along the path and of the average travel times once the
betweennesses of the nodes are computed. Using this formula, we show that
routing optimization preserves the small-world character exhibited by networks
under shortest path routing, and that it significantly reduces the average
travel time on congested networks with only a negligible increase in the
average travel time at low loads. Finally, we study the correlation between the
weights of the links in the case of optimal routing and the betweennesses of
the nodes connected by them.Comment: 19 pages, 7 figure
Quantum Tomographic Cryptography with a Semiconductor Single Photon Source
In this paper we analyze the security of the so-called quantum tomographic
cryptography with the source producing entangled photons via an experimental
scheme proposed in Phys. Rev. Lett. 92, 37903 (2004). We determine the range of
the experimental parameters for which the protocol is secure against the most
general incoherent attacks
The possible explanation of electric-field-doped C60 phenomenology in the framework of Eliashberg theory
In a recent paper (J.H. Schon, Ch. Kloc, R.C. Haddon and B. Batlogg, Nature
408 (2000) 549) a large increase in the superconducting critical temperature
was observed in C60 doped with holes by application of a high electric field.
We demonstrate that the measured Tc versus doping curves can be explained by
solving the (four) s-wave Eliashberg equations in the case of a finite,
non-half-filled energy band. In order to reproduce the experimental data, we
assume a Coulomb pseudopotential depending on the filling in a very simple and
plausible way. Reasonable values of the physical parameters involved are
obtained. The application of the same approach to new experimental data (J.H.
Schon, Ch. Kloc and B. Batlogg, Science 293 (2001) 2432) on electric
field-doped, lattice-expanded C60 single crystals (Tc=117 K in the hole-doped
case) gives equally good results and sets a theoretical limit to the linear
increase of Tc at the increase of the lattice spacing.Comment: latex2e, 6 pages, 7 figures, 1 table, revised versio
Competitive market for multiple firms and economic crisis
The origin of economic crises is a key problem for economics. We present a
model of long-run competitive markets to show that the multiplicity of
behaviors in an economic system, over a long time scale, emerge as statistical
regularities (perfectly competitive markets obey Bose-Einstein statistics and
purely monopolistic-competitive markets obey Boltzmann statistics) and that how
interaction among firms influences the evolutionary of competitive markets. It
has been widely accepted that perfect competition is most efficient. Our study
shows that the perfectly competitive system, as an extreme case of competitive
markets, is most efficient but not stable, and gives rise to economic crises as
society reaches full employment. In the economic crisis revealed by our model,
many firms condense (collapse) into the lowest supply level (zero supply,
namely bankruptcy status), in analogy to Bose-Einstein condensation. This
curious phenomenon arises because perfect competition (homogeneous
competitions) equals symmetric (indistinguishable) investment direction, a fact
abhorred by nature. Therefore, we urge the promotion of monopolistic
competition (heterogeneous competitions) rather than perfect competition. To
provide early warning of economic crises, we introduce a resolving index of
investment, which approaches zero in the run-up to an economic crisis. On the
other hand, our model discloses, as a profound conclusion, that the
technological level for a long-run social or economic system is proportional to
the freedom (disorder) of this system; in other words, technology equals the
entropy of system. As an application of this new concept, we give a possible
answer to the Needham question: "Why was it that despite the immense
achievements of traditional China it had been in Europe and not in China that
the scientific and industrial revolutions occurred?"Comment: 17 pages; 3 figure
A_4 flavour symmetry breaking scheme for understanding quark and neutrino mixing angles
We propose a spontaneous A_4 flavour symmetry breaking scheme to understand
the observed pattern of quark and neutrino mixing. The fermion mass eigenvalues
are arbitrary, but the mixing angles are constrained in such a way that the
overall patterns are explained while also leaving sufficient freedom to fit the
detailed features of the observed values, including CP violating phases. The
scheme realises the proposal of Low and Volkas to generate zero quark mixing
and tribimaximal neutrino mixing at tree-level, with deviations from both
arising from small corrections after spontaneous A_4 breaking. In the neutrino
sector, the breaking is A_4 --> Z_2, while in the quark and charged-lepton
sectors it is A_4 --> Z_3 = C_3. The full theory has A_4 completely broken, but
the two different unbroken subgroups in the two sectors force the dominant
mixing patterns to be as stated above. Radiative effects within each sector are
shown to deviate neutrino mixing from tribimaximal, while maintaining zero
quark mixing. Interactions between the two sectors -- "cross-talk" -- induce
nonzero quark mixing, and additional deviation from tribimaximal neutrino
mixing. We discuss the vacuum alignment challenge the scenario faces, and
suggest three generic ways to approach the problem. We follow up one of those
ways by sketching how an explicit model realising the symmetry breaking
structure may be constructed.Comment: 14 pages, no figures; v3: Section 5 rewritten to correct an error;
new section added to the appendix; added references; v4: minor change to
appendix C, version to be published by JHE
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