共查询到20条相似文献,搜索用时 625 毫秒
1.
Anton Gerasimov Dimitri Lebedev Sergey Oblezin 《Communications in Mathematical Physics》2010,294(1):97-119
We propose a new explicit form of q-deformed Whittaker functions solving q-deformed ${\mathfrak{gl}_{\ell+1}}A representation of a specialization of a q-deformed class one lattice
\mathfrakgll+1{\mathfrak{gl}_{\ell+1}}-Whittaker function in terms of cohomology groups of line bundles on the space
QMd(\mathbbPl){\mathcal{QM}_d(\mathbb{P}^{\ell})} of quasi-maps
\mathbbP1 ? \mathbbPl{\mathbb{P}^1 \to \mathbb{P}^{\ell}} of degree d is proposed. For ℓ = 1, this provides an interpretation of the non-specialized q-deformed
\mathfrakgl2{\mathfrak{gl}_{2}}-Whittaker function in terms of
QMd(\mathbbP1){\mathcal{QM}_d(\mathbb{P}^1)}. In particular the (q-version of the) Mellin-Barnes representation of the
\mathfrakgl2{\mathfrak{gl}_2}-Whittaker function is realized as a semi-infinite period map. The explicit form of the period map manifests an important
role of q-version of Γ-function as a topological genus in semi-infinite geometry. A relation with the Givental-Lee universal solution
(J-function) of q-deformed
\mathfrakgl2{\mathfrak{gl}_2}-Toda chain is also discussed. 相似文献
2.
In this paper, we identify q-deformed
\mathfrakgll+1{\mathfrak{gl}_{\ell+1}}-Whittaker functions with a specialization of the Macdonald polynomials. This provides a representation of q-deformed
\mathfrakgll+1{\mathfrak{gl}_{\ell+1}}-Whittaker functions in terms of the Demazure characters of affine Lie algebra
[^(\mathfrakgl)]l+1{\widehat{\mathfrak{gl}}_{\ell+1}}. We also define a system of dual Hamiltonians for q-deformed
\mathfrakgll+1{\mathfrak{gl}_{\ell+1}}-Toda chains and give a new integral representation for the q-deformed
\mathfrakgll+1{\mathfrak{gl}_{\ell+1}}-Whittaker functions. Finally, we represent the q-deformed
\mathfrakgll+1{\mathfrak{gl}_{\ell+1}}-Whittaker function as a matrix element of a quantum torus algebra. 相似文献
3.
This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order
operators on the half-line is developed, and the trace inequality
tr( (-D)2 - CHRd,2\frac1|x|4 - V(x) )-g £ Cgò\mathbbRd V(x)+g+ \fracd4 dx, g 3 1 - \frac d 4,\mathrm{tr}\left( (-\Delta)^2 - C^{\mathrm{HR}}_{d,2}\frac{1}{|x|^4} - V(x) \right)_-^{\gamma}\leq C_\gamma\int\limits_{\mathbb{R}^d} V(x)_+^{\gamma + \frac{d}{4}}\,\mathrm{d}x, \quad \gamma \geq 1 - \frac d 4, 相似文献
4.
Thomas Bartsch Angela Pistoia Tobias Weth 《Communications in Mathematical Physics》2010,297(3):653-686
We prove the existence of equilibria of the N-vortex Hamiltonian in a bounded domain ${\Omega\subset\mathbb{R}^2}
5.
Pierre van Baal 《Communications in Mathematical Physics》1982,85(4):529-547
We show how to prove and to understand the formula for the “Pontryagin” indexP for SU(N) gauge fields on the HypertorusT 4, seen as a four-dimensional euclidean box with twisted boundary conditions. These twists are defined as gauge invariant integers moduloN and labelled byN μv (=?N μv ). In terms of these we can write (ν∈#x2124;) $$P = \frac{1}{{16\pi ^2 }}\int {Tr(G_{\mu v} \tilde G_{\mu v} )d_4 x = v + \left( {\frac{{N - 1}}{N}} \right) \cdot \frac{{n_{\mu v} \tilde n_{\mu v} }}{4}} $$ . Furthermore we settle the last link in the proof of the existence of zero action solutions with all possible twists satisfying \(\frac{{n_{\mu v} \tilde n_{\mu v} }}{4} = \kappa (n) = 0(\bmod N)\) for arbitraryN. 相似文献
6.
E. V. Gryzlova A. N. Grum-Grzhimailo A. I. Magunov S. I. Strakhova 《Optics and Spectroscopy》2010,109(1):59-65
Optical activity of xenon atoms in the vacuum UV range induced by circularly polarized laser light is studied theoretically.
The optical activity arises in the vicinity of the autoionizing state 5p
5(2
P
1/2)8s′$
\left[ {\frac{1}
{2}} \right]_1
$
\left[ {\frac{1}
{2}} \right]_1
as a result of its coupling via the laser field with the discrete state 5p
5(2
P
3/2)7p
$
\left[ {\frac{1}
{2}} \right]_1
$
\left[ {\frac{1}
{2}} \right]_1
. Polarization variations of the vacuum UV radiation upon its propagation through the atomic medium are calculated, and the
possibility of controlling this polarization is discussed. Manifestations of nonresonant coupling of the discrete state with
the broad autoionizing state 5p
5(2
P
1/2)6d′$
\left[ {\frac{1}
{2}} \right]_1
$
\left[ {\frac{1}
{2}} \right]_1
induced by the overlap of the Rydberg autoionizing series in xenon are studied. 相似文献
7.
Leonid Malozemov 《Communications in Mathematical Physics》1993,156(2):387-397
We consider the integrated density of statesN(λ) of the difference Laplacian ?Δ on the modified Koch graph. We show thatN(λ) increases only with jumps and a set of jump points ofN(λ) is the set of eigenvalues of ?Δ with the infinite multiplicity. We establish also that $$0< C_1 \leqslant \mathop {\lim }\limits_{\lambda \to 0} \frac{{N(\lambda )}}{{\lambda ^{d_s /2} }}< \overline {\mathop {\lim }\limits_{\lambda \to 0} } \frac{{N(\lambda )}}{{\lambda ^{d_s /2} }} \leqslant C_2< \infty$$ whered s =2log5/log(40/3) is the spectral dimension of MKG. 相似文献
8.
The Blume-Emery-Griffiths model with the dipole-quadrupole interaction ($
\ell = \frac{I}
{J}
$
\ell = \frac{I}
{J}
) has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton (CCA) on the face centered
cubic (fcc) lattice. The finite-size scaling relations and the power laws of the order parameter (M) and the susceptibility (χ) are proposed for the dipole-quadrupole interaction (ℓ). The dipole-quadrupole critical exponent
δχ has been estimated from the data of the order parameter (M) and the susceptibility (χ). The simulations have been done in the interval $
0 \leqslant \ell = \frac{I}
{J}0 \leqslant 0.01
$
0 \leqslant \ell = \frac{I}
{J}0 \leqslant 0.01
for $
d = \frac{D}
{J} = 0,k = \frac{K}
{J} = 0
$
d = \frac{D}
{J} = 0,k = \frac{K}
{J} = 0
and $
h = \frac{H}
{J} = 0
$
h = \frac{H}
{J} = 0
parameter values on a face centered cubic (fcc) lattice with periodic boundary conditions. The results indicate that the
effect of the ℓ parameter is similar to the external magnetic field (h). The critical exponent δℓ are in good agreement with the universal value (δ
h
= 5) of the external magnetic field. 相似文献
9.
We characterize averages of ?l=1N|x - tl|a- 1{\prod_{l=1}^N|x - t_l|^{\alpha - 1}} with respect to the Selberg density, further constrained so that tl ? [0,x] (l=1,...,q){t_l \in [0,x] (l=1,\dots,q)} and tl ? [x,1] (l=q+1,...,N){t_l \in [x,1] (l=q+1,\dots,N)} , in terms of a basis of solutions of a particular Fuchsian matrix differential equation. By making use of the Dotsenko-Fateev
integrals, the explicit form of the connection matrix from the Frobenius type power series basis to this basis is calculated,
thus allowing us to explicitly compute coefficients in the power series expansion of the averages. From these we are able
to compute power series for the marginal distributions of the tj (j=1,...,N){t_j (j=1,\dots,N)} . In the case q = 0 and α < 1 we compute the explicit leading order term in the x ? 0{x \to 0} asymptotic expansion, which is of interest to the study of an effect known as singularity dominated strong fluctuations.
In the case q = 0 and
a ? \mathbbZ+{\alpha \in \mathbb{Z}^+} , and with the absolute values removed, the average is a polynomial, and we demonstrate that its zeros are highly structured. 相似文献
10.
E. A. Kataeva A. D. Bozhko S. V. Demishev 《Bulletin of the Lebedev Physics Institute》2010,37(11):347-351
The conductivity of carbon films grown by polymethylphenylsiloxane vapor decomposition in stimulated dc discharge plasma was
studied. It is found that the Mott hopping conductivity $
\sigma \left( T \right) = \sigma _0 \left( T \right)\exp \left\{ { - \frac{{T_0 }}
{T}^{{1 \mathord{\left/
{\vphantom {1 4}} \right.
\kern-\nulldelimiterspace} 4}} } \right\}
$
\sigma \left( T \right) = \sigma _0 \left( T \right)\exp \left\{ { - \frac{{T_0 }}
{T}^{{1 \mathord{\left/
{\vphantom {1 4}} \right.
\kern-\nulldelimiterspace} 4}} } \right\}
is characteristic of the samples under study in the temperature range of 80–400 K in the electric field E to 5 · 104 V/cm. An analysis of the pre-exponential factor σ
0(T) = σ
00(T
0)T
α allowed the conclusion that the hopping transport is most adequately described in the model with the exponential energy dependence
of the density of localized states for which α = −1/2 and the universal relation ln σ
00 −T
01/4 0 is valid, which is satisfied in the range where the parameter σ
00 varies by eight orders of magnitude. 相似文献
11.
12.
S. G. Karshenboim 《Physics of Particles and Nuclei Letters》2009,6(6):450-454
Oscillations of neutral meson (K
0-$
\overline {K^0 }
$
\overline {K^0 }
, D
0-$
\overline {D^0 }
$
\overline {D^0 }
, and B
0-$
\overline {B^0 }
$
\overline {B^0 }
are extremely sensitive to the meson and antimeson energies at rest. This energy is determined as mc
2—with the corresponding inertial mass—and as the energy of gravitational interaction. Assuming that the CPT theorem is correct
for inertial masses and estimating the gravitational potential for which the largest contribution originates from the field
of the galaxy center, we obtain the estimate from experimental data on K
0-$
\overline {K^0 }
$
\overline {K^0 }
oscillations:
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