674 research outputs found
On the spatial Markov property of soups of unoriented and oriented loops
We describe simple properties of some soups of unoriented Markov loops and of
some soups of oriented Markov loops that can be interpreted as a spatial Markov
property of these loop-soups. This property of the latter soup is related to
well-known features of the uniform spanning trees (such as Wilson's algorithm)
while the Markov property of the former soup is related to the Gaussian Free
Field and to identities used in the foundational papers of Symanzik, Nelson,
and of Brydges, Fr\"ohlich and Spencer or Dynkin, or more recently by Le Jan
Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle
We prove that for any matrix, , and with ,
we have that \|(z-A)^{-1}\|\leq\cot (\frac{\pi}{4n}) \dist (z,
\spec(A))^{-1}. We apply this result to the study of random orthogonal
polynomials on the unit circle.Comment: 27 page
Experimental demonstration of a suspended diffractively coupled optical cavity
All-reflective optical systems are under consideration for future gravitational wave detector topologies. One approach in proposed designs is to use diffraction gratings as input couplers for Fabry–Perot cavities. We present an experimental demonstration of a fully suspended diffractively coupled cavity and investigate the use of conventional Pound–Drever–Hall length sensing and control techniques to maintain the required operating condition
Classical Vs Quantum Probability in Sequential Measurements
We demonstrate in this paper that the probabilities for sequential
measurements have features very different from those of single-time
measurements. First, they cannot be modelled by a classical stochastic process.
Second, they are contextual, namely they depend strongly on the specific
measurement scheme through which they are determined. We construct
Positive-Operator-Valued measures (POVM) that provide such probabilities. For
observables with continuous spectrum, the constructed POVMs depend strongly on
the resolution of the measurement device, a conclusion that persists even if we
consider a quantum mechanical measurement device or the presence of an
environment. We then examine the same issues in alternative interpretations of
quantum theory. We first show that multi-time probabilities cannot be naturally
defined in terms of a frequency operator. We next prove that local hidden
variable theories cannot reproduce the predictions of quantum theory for
sequential measurements, even when the degrees of freedom of the measuring
apparatus are taken into account. Bohmian mechanics, however, does not fall in
this category. We finally examine an alternative proposal that sequential
measurements can be modelled by a process that does not satisfy the Kolmogorov
axioms of probability. This removes contextuality without introducing
non-locality, but implies that the empirical probabilities cannot be always
defined (the event frequencies do not converge). We argue that the predictions
of this hypothesis are not ruled out by existing experimental results
(examining in particular the "which way" experiments); they are, however,
distinguishable in principle.Comment: 56 pages, latex; revised and restructured. Version to appear in
Found. Phy
Optimal Hypercontractivity for Fermi Fields and Related Non-Commutative Integration
Optimal hypercontractivity bounds for the fermion oscillator semigroup are
obtained. These are the fermion analogs of the optimal hypercontractivity
bounds for the boson oscillator semigroup obtained by Nelson. In the process,
several results of independent interest in the theory of non-commutative
integration are established. {}.Comment: 18 p., princeton/ecel/7-12-9
Sensitivity, Specificity and the Hybridization Isotherms of DNA Chips
Competitve hybridization, at the surface and in the bulk, lowers the
sensitivity of DNA chips. Competitive surface hybridization occurs when
different targets can hybridize with the same probe. Competitive bulk
hybridization takes place when the targets can hybridize with free
complementary chains in the solution. The effects of competitive hybridization
on the thermodynamically attainable performance of DNA chips are quantified in
terms of the hybridization isotherms of the spots. These relate the equilibrium
degree of the hybridization to the bulk composition. The hybridization isotherm
emerges as a Langmuir isotherm modified for electrostatic interactions within
the probe layer. The sensitivity of the assay in equilibrium is directly
related to the slope of the isotherm. A simpler description is possible in
terms of s specifying the bulk composition corresponding to 50%
hybridization at the surface. The effects of competitive hybridization are
important for the quantitative analysis of DNA chip results especially when
used to study point mutations.Comment: 18 pages and 7 figures. To be published in Biophys.
Effective dynamics for particles coupled to a quantized scalar field
We consider a system of N non-relativistic spinless quantum particles
(``electrons'') interacting with a quantized scalar Bose field (whose
excitations we call ``photons''). We examine the case when the velocity v of
the electrons is small with respect to the one of the photons, denoted by c
(v/c= epsilon << 1). We show that dressed particle states exist (particles
surrounded by ``virtual photons''), which, up to terms of order (v/c)^3, follow
Hamiltonian dynamics. The effective N-particle Hamiltonian contains the kinetic
energies of the particles and Coulomb-like pair potentials at order (v/c)^0 and
the velocity dependent Darwin interaction and a mass renormalization at order
(v/c)^{2}. Beyond that order the effective dynamics are expected to be
dissipative.
The main mathematical tool we use is adiabatic perturbation theory. However,
in the present case there is no eigenvalue which is separated by a gap from the
rest of the spectrum, but its role is taken by the bottom of the absolutely
continuous spectrum, which is not an eigenvalue.
Nevertheless we construct approximate dressed electrons subspaces, which are
adiabatically invariant for the dynamics up to order (v/c)\sqrt{\ln
(v/c)^{-1}}. We also give an explicit expression for the non adiabatic
transitions corresponding to emission of free photons. For the radiated energy
we obtain the quantum analogue of the Larmor formula of classical
electrodynamics.Comment: 67 pages, 2 figures, version accepted for publication in
Communications in Mathematical Physic
Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale
In the context of Markov evolution, we present two original approaches to
obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the
language of stochastic derivatives and by using a family of exponential
martingales functionals. We show that GFDT are perturbative versions of
relations verified by these exponential martingales. Along the way, we prove
GFDT and Fluctuation Relations (FR) for general Markov processes, beyond the
usual proof for diffusion and pure jump processes. Finally, we relate the FR to
a family of backward and forward exponential martingales.Comment: 41 pages, 7 figures; version2: 45 pages, 7 figures, minor revisions,
new results in Section
Passing through the bounce in the ekpyrotic models
By considering a simplified but exact model for realizing the ekpyrotic
scenario, we clarify various assumptions that have been used in the literature.
In particular, we discuss the new ekpyrotic prescription for passing the
perturbations through the singularity which we show to provide a spectrum
depending on a non physical normalization function. We also show that this
prescription does not reproduce the exact result for a sharp transition. Then,
more generally, we demonstrate that, in the only case where a bounce can be
obtained in Einstein General Relativity without facing singularities and/or
violation of the standard energy conditions, the bounce cannot be made
arbitrarily short. This contrasts with the standard (inflationary) situation
where the transition between two eras with different values of the equation of
state can be considered as instantaneous. We then argue that the usually
conserved quantities are not constant on a typical bounce time scale. Finally,
we also examine the case of a test scalar field (or gravitational waves) where
similar results are obtained. We conclude that the full dynamical equations of
the underlying theory should be solved in a non singular case before any
conclusion can be drawn.Comment: 17 pages, ReVTeX 4, 13 figures, minor corrections, conclusions
unchange
Multicloud solutions with massless and massive monopoles
Certain spontaneously broken gauge theories contain massless magnetic
monopoles. These are realized classically as clouds of non-Abelian fields
surrounding one or more massive monopoles. In order to gain a better
understanding of these clouds, we study BPS solutions with four massive and six
massless monopoles in an SU(6) gauge theory. We develop an algebraic procedure,
based on the Nahm construction, that relates these solutions to previously
known examples. Explicit implementation of this procedure for a number of
limiting cases reveals that the six massless monopoles condense into four
distinct clouds, of two different types. By analyzing these limiting solutions,
we clarify the correspondence between clouds and massless monopoles, and infer
a set of rules that describe the conditions under which a finite size cloud can
be formed. Finally, we identify the parameters entering the general solution
and describe their physical significance.Comment: 58 pages, 5 figure
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