共查询到20条相似文献,搜索用时 62 毫秒
1.
Evgeny N. Pestov Alla N. Besedina Dmitry E. Pestov Vladimir V. Semenov 《Applied magnetic resonance》2020,51(2):195-204
One of the most important problems in achieving daily frequency instability $$\sigma _{y} < 5 \cdot 10^{{ - 14}}$$ of on-board rubidium atomic clocks on absorption cell with working 87Rb atoms and mixture of buffer gases is realization of the TFS parameter — of temperature frequency shift $$\delta \nu \left( T \right)$$ at the level of $$\ \le 3 \cdot 10^{{ - 12}} /\, {^\circ } {\text{C}}.$$ The temperature dependence of the microwave “0–0” transition frequency $$\nu \left( T \right)$$ has an extremum with a small flat top ∆T ~ 0.5 °C to which the 87Rb-cell operating temperature is tuned. Significant difficulties arise in maintaining the high stability of this small ∆T zone under conditions of increased 87Rb cell operating temperature, $$T>70\, ^\circ{\rm C}$$, with an accuracy of < 0.005 °C for a day or more. To solve this problem, authors proposed a new type of 87Rb absorption cell with two dissimilar anti-relaxation (AR) components (wall coating + buffer gas, 40Ar) and created a special physical setup for optical spin pumping of 87Rb atoms at the microwave magnetic resonance frequency, $$\nu \sim \;6.834\,\;{\text{GHz}}$$, with a resolution $$0.01 \,\mathrm{H}\mathrm{z}$$. Investigations have shown TFS $$\sim 1.4 \cdot 10^{{ - 12}} /\;{{^\circ }} {\text{C}}$$ in significantly expanded (by an order of magnitude) zone, $$\Delta T$$ ≃ $$5 \left(\pm 1\right)\,\, ^\circ{\rm C} ,$$ in the operating temperature range of $$\left( {35 \div 41} \right)\;^{ \circ } {\text{C}},$$ which is ensured inside a satellite, for example. The simultaneous effect of AR-components causes the maximum mutual compensation of temperature frequency shifts in the extended ∆T zone. The experimental data show the possibility realizing daily frequency instability $$\sigma _{y} \sim 1 \cdot 10^{{ - 14}}$$ of the on-board atomic clock on 87Rb cell with two dissimilar AR-components (wall coating + inert gas, 40Ar). 相似文献
2.
Journal of Statistical Physics - We consider the d-dimensional fractional Anderson model $$(-\Delta )^\alpha + V_\omega $$ on $$\ell ^2({\mathbb {Z}}^d)$$ where $$0<\alpha \leqslant 1$$.... 相似文献
3.
Salvador Garcia 《advances in applied mathematics and mechanics.》2009,1(4):546-572
The lid-driven square cavity flow is investigated by numerical
experiments. It is found that from $ \mathrm{Re} $$=$ $5,000 $ to $
\mathrm{Re}
$$=$$ 7,307.75 $ the solution is stationary, but at $
\mathrm{Re}$$=$$7,308 $ the solution is time periodic. So the
critical Reynolds number for the first Hopf bifurcation localizes
between $ \mathrm{Re} $$=$$ 7,307.75 $ and $ \mathrm{Re} $$=$$ 7,308
$. Time periodical behavior begins smoothly, imperceptibly at the
bottom left corner at a tiny tertiary vortex; all other vortices
stay still, and then it spreads to the three relevant corners of the
square cavity so that all small vortices at all levels move
periodically. The primary vortex stays still. At $ \mathrm{Re}
$$=$$ 13,393.5 $ the solution is time periodic; the long-term
integration carried out past $ t_{\infty} $$=$$ 126,562.5 $ and the
fluctuations of the kinetic energy look periodic except slight
defects. However, at $ \mathrm{Re} $$=$$ 13,393.75 $ the solution is
not time periodic anymore: losing unambiguously, abruptly time
periodicity, it becomes chaotic. So the critical Reynolds number for
the second Hopf bifurcation localizes between $ \mathrm{Re} $$=$$
13,393.5 $ and $ \mathrm{Re} $$=$$ 13,393.75 $. At high Reynolds
numbers $ \mathrm{Re} $$=$$ 20,000 $ until $ \mathrm{Re} $$=$$
30,000 $ the solution becomes chaotic. The long-term integration is
carried out past the long time $ t_{\infty} $$=$$ 150,000 $,
expecting the time asymptotic regime of the flow has been reached.
The distinctive feature of the flow is then the appearance of drops:
tiny portions of fluid produced by splitting of a secondary vortex,
becoming loose and then fading away or being absorbed by another
secondary vortex promptly. At $ \mathrm{Re}
$$=$$ 30,000 $ another phenomenon arises—the abrupt appearance at
the bottom left corner of a tiny secondary vortex, not produced by
splitting of a secondary vortex. 相似文献
4.
Paolo Aschieri Leonardo Castellani Marija Dimitrijević 《Letters in Mathematical Physics》2008,85(1):39-53
A -product is defined via a set of commuting vector fields , and used in a theory coupled to the fields. The -product is dynamical, and the vacuum solution , reproduces the usual Moyal product. The action is invariant under rigid translations and Lorentz rotations, and the conserved
energy–momentum and angular momentum tensors are explicitly derived.
相似文献
5.
Dražen Adamović 《Communications in Mathematical Physics》2007,270(1):141-161
We introduce the infinite-dimensional Lie superalgebra and construct a family of mappings from a certain category of –modules to the category of –modules at the critical level. Using this approach, we prove the irreducibility of a large family of –modules at the critical level parameterized by . As a consequence, we present a new proof of irreducibility of certain Wakimoto modules. We also give natural realizations
of irreducible quotients of relaxed Verma modules and calculate characters of these representations.
Partially supported by the MZOS grant 0037125 of the Republic of Croatia 相似文献
6.
We exhibit a finitely generated group whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping
class group associated to a surface of infinite genus, and contains all the pure mapping class groups of compact surfaces of genus g with n boundary components, for any g ≥ 0 and n > 0. We construct a representation of into the restricted symplectic group of the real Hilbert space generated by the homology classes of non-separating circles on , which generalizes the classical symplectic representation of the mapping class groups. Moreover, we show that the first
universal Chern class in is the pull-back of the Pressley-Segal class on the restricted linear group via the inclusion .
L. F. was partially supported by the ANR Repsurf:ANR-06-BLAN-0311. 相似文献
7.
Asao Arai 《Letters in Mathematical Physics》2006,77(3):283-290
A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and the total Hamiltonian is unitarily equivalent to the direct integral
of a family of self-adjoint operators
acting in the Hilbert space
, where
is the Hilbert space of the quantum radiation field. The fiber operator
is called the Hamiltonian of the Dirac polaron with total momentum
. The main result of this paper is concerned with the non-relativistic (scaling) limit of
. It is proven that the non-relativistic limit of
yields a self-adjoint extension of a Hamiltonian of a polaron with spin 1/2 in non-relativistic quantum electrodynamics. 相似文献
8.
Journal of Statistical Physics - We consider the classical geometric Lorenz attractors, showing that the SRB entropy admits $$\gamma $$ -Hölder continuity for any $$0<\gamma <1$$ . 相似文献
9.
A zero modes’ Fock space is constructed for the extended chiral WZNW model. It gives room to a realization of the fusion ring of representations of the restricted quantum universal enveloping
algebra at an even root of unity, and of its infinite dimensional extension by the Lusztig operators We provide a streamlined derivation of the characteristic equation for the Casimir invariant from the defining relations
of A central result is the characterization of the Grothendieck ring of both and in Theorem 3.1. The properties of the fusion ring in are related to the braiding properties of correlation functions of primary fields of the conformal current algebra model.
相似文献
10.
For a Lie algebra with Lie bracket got by taking commutators in a nonunital associative algebra
, let
be the vector space of tensors over
equipped with the Itô Hopf algebra structure derived from the associative multiplication in
. It is shown that a necessary and sufficient condition that the double product integral
satisfy the quantum Yang–Baxter equation over
is that
satisfy the same equation over the unital associative algebra
got by adjoining a unit element to
. In particular, the first-order coefficient r1 of r[h] satisfies the classical Yang–Baxter equation. Using the fact that the multiplicative inverse of
is
where
is the inverse of
in
we construct a quantisation of an arbitrary quasitriangular Lie bialgebra structure on
in the unital associative subalgebra of
consisting of formal power series whose zero order coefficient lies in the space
of symmetric tensors. The deformation coproduct acts on
by conjugating the undeformed coproduct by
and the coboundary structure r of
is given by
where
is the flip.Mathematical Subject Classification (2000). 53D55, 17B62 相似文献
11.
Asao Arai 《Letters in Mathematical Physics》2008,85(1):15-25
Let (T, H) be a weak Weyl representation of the canonical commutation relation (CCR) with one degree of freedom. Namely T is a symmetric operator and H is a self-adjoint operator on a complex Hilbert space satisfying the weak Weyl relation: for all (the set of real numbers), e−itH
D(T) ⊂ D(T) (i is the imaginary unit and D(T) denotes the domain of T) and . In the context of quantum theory where H is a Hamiltonian, T is called a strong time operator of H. In this paper we prove the following theorem on uniqueness of weak Weyl representations: Let be separable. Assume that H is bounded below with and , where is the set of complex numbers and, for a linear operator A on a Hilbert space, σ(A) denotes the spectrum of A. Then ( is the closure of T) is unitarily equivalent to a direct sum of the weak Weyl representation on the Hilbert space , where is the multiplication operator by the variable and with . Using this theorem, we construct a Weyl representation of the CCR from the weak Weyl representation .
This work is supported by the Grant-in-Aid No.17340032 for Scientific Research from Japan Society for the Promotion of Science
(JSPS). 相似文献
12.
O. W. Greenberg 《Foundations of Physics》2006,36(10):1535-1553
Lüders and Pauli proved the theorem based on Lagrangian quantum field theory almost half a century ago. Jost gave a more general proof based on “axiomatic” field theory nearly as long ago. The axiomatic point of view has two advantages over the Lagrangian one. First, the axiomatic point of view makes clear why is fundamental—because it is intimately related to Lorentz invariance. Secondly, the axiomatic proof gives a simple way to calculate the transform of any relativistic field without calculating , and separately and then multiplying them. The purpose of this pedagogical paper is to “deaxiomatize” the theorem by explaining it in a few simple steps. We use theorems of distribution theory and of several complex variables without proof to make the exposition elementary. 相似文献
13.
Physics of Atomic Nuclei - Based on the behavior of elastic scattering of proton and anti-proton at $$\sqrt{s}=1.96$$ TeV for squared four-momentum transfer $$0.26<{-}t<1.2($$ GeV... 相似文献
14.
For a (co)monad T
l
on a category , an object X in , and a functor , there is a (co)simplex in . The aim of this paper is to find criteria for para-(co)cyclicity of Z
*. Our construction is built on a distributive law of T
l
with a second (co)monad T
r
on , a natural transformation , and a morphism in . The (symmetrical) relations i and w need to satisfy are categorical versions of Kaygun’s axioms of a transposition map. Motivation comes from the observation
that a (co)ring T over an algebra R determines a distributive law of two (co)monads and on the category of R-bimodules. The functor Π can be chosen such that is the cyclic R-module tensor product. A natural transformation is given by the flip map and a morphism is constructed whenever T is a (co)module algebra or coring of an R-bialgebroid. The notion of a stable anti-Yetter-Drinfel’d module over certain bialgebroids, the so-called ×
R
-Hopf algebras, is introduced. In the particular example when T is a module coring of a ×
R
-Hopf algebra and X is a stable anti-Yetter-Drinfel’d -module, the para-cyclic object Z
* is shown to project to a cyclic structure on . For a -Galois extension , a stable anti-Yetter-Drinfel’d -module T
S
is constructed, such that the cyclic objects and are isomorphic. This extends a theorem by Jara and Ştefan for Hopf Galois extensions. As an application, we compute Hochschild
and cyclic homologies of a groupoid with coefficients in a stable anti-Yetter-Drinfel’d module, by tracing it back to the
group case. In particular, we obtain explicit expressions for (coinciding relative and ordinary) Hochschild and cyclic homologies
of a groupoid. The latter extends results of Burghelea on cyclic homology of groups. 相似文献
15.
In this paper we introduce Baxter integral -operators for finite-dimensional Lie algebras and . Whittaker functions corresponding to these algebras are eigenfunctions of the -operators with the eigenvalues expressed in terms of Gamma-functions. The appearance of the Gamma-functions is one of the
manifestations of an interesting connection between Mellin-Barnes and Givental integral representations of Whittaker functions,
which are in a sense dual to each other. We define a dual Baxter operator and derive a family of mixed Mellin-Barnes-Givental
integral representations. Givental and Mellin-Barnes integral representations are used to provide a short proof of the Friedberg-Bump
and Bump conjectures for G = GL(ℓ + 1) proved earlier by Stade. We also identify eigenvalues of the Baxter -operator acting on Whittaker functions with local Archimedean L-factors. The Baxter -operator introduced in this paper is then described as a particular realization of the explicitly defined universal Baxter
operator in the spherical Hecke algebra , K being a maximal compact subgroup of G. Finally we stress an analogy between -operators and certain elements of the non-Archimedean Hecke algebra . 相似文献
16.
We introduce a newfamily of C
2-cofinite N = 1 vertex operator superalgebras , m ≥ 1, which are natural super analogs of the triplet vertex algebra family , p ≥ 2, important in logarithmic conformal field theory. We classify irreducible -modules and discuss logarithmic modules. We also compute bosonic and fermionic formulas of irreducible characters. Finally, we contemplate possible connections between the category of -modules and the category of modules for the quantum group , , by focusing primarily on properties of characters and the Zhu’s algebra . This paper is a continuation of our paper Adv. Math. 217, no.6, 2664–2699 (2008).
The second author was partially supported by NSF grant DMS-0802962. 相似文献
17.
Claude Cibils Andrea Solotar Robert Wisbauer 《Communications in Mathematical Physics》2007,272(3):837-849
We consider -complexes as functors over an appropriate linear category in order to show first that the Krull-Schmidt Theorem holds, then
to prove that amplitude cohomology (called generalized cohomology by M. Dubois-Violette) only vanishes on injective functors
providing a well defined functor on the stable category. For left truncated -complexes, we show that amplitude cohomology discriminates the isomorphism class up to a projective functor summand. Moreover
amplitude cohomology of positive -complexes is proved to be isomorphic to an Ext functor of an indecomposable -complex inside the abelian functor category. Finally we show that for the monoidal structure of -complexes a Clebsch-Gordan formula holds, in other words the fusion rules for -complexes can be determined.
This work has been supported by the projects PICT 08280 (ANPCyT), UBACYTX169, PIP-CONICET 5099 and the German Academic Exchange
Service (DAAD). The second author is a research member of CONICET (Argentina) and a Regular Associate of ICTP Associate Scheme. 相似文献
18.
We construct a continuous transition density of the semigroup generated by for and b in the Kato class on . For small time the transition density is comparable with that of the fractional Laplacian.
Partially supported by KBN and MEN. 相似文献
19.
We define the twisted loop Lie algebra of a finite dimensional Lie algebra
as the Fréchet space of all twisted periodic smooth mappings from
to
. Here the Lie algebra operation is continuous. We call such Lie algebras Fréchet Lie algebras. We introduce the notion of an integrable
-gradation of a Fréchet Lie algebra, and find all inequivalent integrable
-gradations with finite dimensional grading subspaces of twisted loop Lie algebras of complex simple Lie algebras.On leave of absence from the Institute for Nuclear Research of the Russian Academy of Sciences, 117312 Moscow, Russia. 相似文献
20.
Ruqian Lu 《International Journal of Theoretical Physics》2005,44(9):1495-1530
We propose the concept of finite stop quantum automata (ftqa) based on Hilbert space and compare it with the finite state
quantum automata (fsqa) proposed by Moore and Crutchfield (Theoretical Computer Science 237(1–2), 2000, 275–306). The languages accepted by fsqa form a proper subset of the languages accepted by ftqa. In addition,
the fsqa form an infinite hierarchy of language inclusion with respect to the dimensionality of unitary matrices. We introduce
complex-valued acceptance degrees and two types of finite stop quantum automata based on them: the invariant ftqa (icftq)
and the variant ftqa (vcftq). The languages accepted by icftq form a proper subset of the languages accepted by vcftq. In
addition, the icftq form an infinite hierarchy of language inclusion with respect to the dimensionality of unitary matrices.
In this way, we establish two proper inclusion relations
(fsqa) ⊂
(ftqa) and
(icftq) ⊂
(vcftq), where the symbol
means languages, and two infinite language hierarchies
(fsqa) ⊂
(fsqa),
(icftq)
(icftq). 相似文献