1,755 research outputs found
Deformation theory of objects in homotopy and derived categories II: pro-representability of the deformation functor
This is the second paper in a series. In part I we developed deformation
theory of objects in homotopy and derived categories of DG categories. Here we
extend these (derived) deformation functors to an appropriate bicategory of
artinian DG algebras and prove that these extended functors are
pro-representable in a strong sense.Comment: Alexander Efimov is a new co-author of this paper. New material was
added: A_{\infty}-structures, Maurer-Cartan theory for A_{\infty}-algebras.
This allows us to strengthen our main results on the pro-representability of
pseudo-functors coDEF_{-} and DEF_{-}. We also obtain an equivalence between
homotopy and derived deformation functors under weaker hypothese
The Four-Boson System with Short-Range Interactions
We consider the non-relativistic four-boson system with short-range forces
and large scattering length in an effective quantum mechanics approach. We
construct the effective interaction potential at leading order in the large
scattering length and compute the four-body binding energies using the
Yakubovsky equations. Cutoff independence of the four-body binding energies
does not require the introduction of a four-body force. This suggests that two-
and three-body interactions are sufficient to renormalize the four-body system.
We apply the equations to 4He atoms and calculate the binding energy of the 4He
tetramer. We observe a correlation between the trimer and tetramer binding
energies similar to the Tjon line in nuclear physics. Over the range of binding
energies relevant to 4He atoms, the correlation is approximately linear.Comment: 23 pages, revtex4, 5 PS figures, discussion expanded, results
unchange
Deformation theory of objects in homotopy and derived categories III: abelian categories
This is the third paper in a series. In part I we developed a deformation
theory of objects in homotopy and derived categories of DG categories. Here we
show how this theory can be used to study deformations of objects in homotopy
and derived categories of abelian categories. Then we consider examples from
(noncommutative) algebraic geometry. In particular, we study noncommutative
Grassmanians that are true noncommutative moduli spaces of structure sheaves of
projective subspaces in projective spaces.Comment: Alexander Efimov is a new co-author of this paper. Besides some minor
changes, a new part (part 3) about noncommutative Grassmanians was adde
Influence of Facial Features on Reservoir Properties of the Bashkirian Carbonate Deposits of the Lake Field
Представлены результаты исследований влияния фациальных условий на коллекторские свойства карбонатных отложений Озерного месторождения, в которых были использованы описания кернового материала и промыслового исследования скважин.Results of study are dedicated to the influence of facial conditions on reservoir properties in the carbonate deposits of the Lake field, Perm kray. Description of the core material and field test data were used for comprehensive analysis
Point-Coupling Models from Mesonic Hypermassive Limit and Mean-Field Approaches
In this work we show how nonlinear point-coupling models, described by a
Lagrangian density that presents only terms up to fourth order in the fermion
condensate , are derived from a modified meson-exchange
nonlinear Walecka model. The derivation can be done through two distinct
methods, namely, the hypermassive meson limit within a functional integral
approach, and the mean-field approximation in which equations of state at zero
temperature of the nonlinear point-coupling models are directly obtained.Comment: 18 pages. Accepted for publication in Braz. J. Phy
Three-body problem for ultracold atoms in quasi-one-dimensional traps
We study the three-body problem for both fermionic and bosonic cold atom
gases in a parabolic transverse trap of lengthscale . For this
quasi-one-dimensional (1D) problem, there is a two-body bound state (dimer) for
any sign of the 3D scattering length , and a confinement-induced scattering
resonance. The fermionic three-body problem is universal and characterized by
two atom-dimer scattering lengths, and . In the tightly bound
`dimer limit', , we find , and is linked
to the 3D atom-dimer scattering length. In the weakly bound `BCS limit',
, a connection to the Bethe Ansatz is established, which
allows for exact results. The full crossover is obtained numerically. The
bosonic three-body problem, however, is non-universal: and
depend both on and on a parameter related to the sharpness of
the resonance. Scattering solutions are qualitatively similar to fermionic
ones. We predict the existence of a single confinement-induced three-body bound
state (trimer) for bosons.Comment: 20 pages, 6 figures, accepted for publication in PRA, appendix on the
derivation of an integral formula for the Hurvitz zeta functio
A Single-Loop DC Motor Control System Design with a Desired Aperiodic Degree of Stability
The application of the original analytical approach for Pi-controller synthesis of a stable second-order plant is considered. This approach allows finding controller parameters without any intensive computing by using the direct expressions. The plant model is obtained on the basis of identification, which is based on the automated real-interpolation method. The results of natural experiments are given
Universal description of the rotational-vibrational spectrum of three particles with zero-range interactions
A comprehensive universal description of the rotational-vibrational spectrum
for two identical particles of mass and the third particle of the mass
in the zero-range limit of the interaction between different particles is
given for arbitrary values of the mass ratio and the total angular
momentum . If the two-body scattering length is positive, a number of
vibrational states is finite for , zero for
, and infinite for . If the two-body scattering
length is negative, a number of states is either zero for or
infinite for . For a finite number of vibrational states, all the
binding energies are described by the universal function , where ,
,and is the vibrational
quantum number. This scaling dependence is in agreement with the numerical
calculations for and only slightly deviates from those for .
The universal description implies that the critical values and
increase as and ,
respectively, while a number of vibrational states for is
within the range
Analytical solution of the bosonic three-body problem
We revisit the problem of three identical bosons in free space, which
exhibits a universal hierarchy of bound states (Efimov trimers). Modelling a
narrow Feshbach resonance within a two-channel description, we map the integral
equation for the three-body scattering amplitude to a one-dimensional
Schr\"odinger-type single-particle equation, where an analytical solution of
exponential accuracy is obtained. We give exact results for the trimer binding
energies, the three-body parameter, the threshold to the three-atom continuum,
and the recombination rate.Comment: 4 pages, published versio
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