307 research outputs found
Reflection equations and q-Minkowski space algebras
We express the defining relations of the -deformed Minkowski space algebra
as well as that of the corresponding derivatives and differentials in the form
of reflection equations. This formulation encompasses the covariance properties
with respect the quantum Lorentz group action in a straightforward way.Comment: 10 page
Twist Deformation of the rank one Lie Superalgebra
The Drinfeld twist is applyed to deforme the rank one orthosymplectic Lie
superalgebra . The twist element is the same as for the Lie
algebra due to the embedding of the into the superalgebra .
The R-matrix has the direct sum structure in the irreducible representations of
. The dual quantum group is defined using the FRT-formalism. It
includes the Jordanian quantum group as subalgebra and Grassmann
generators as well.Comment: LaTeX, 9 page
Algebraic Bethe ansatz for the gl(12) generalized model II: the three gradings
The algebraic Bethe ansatz can be performed rather abstractly for whole
classes of models sharing the same -matrix, the only prerequisite being the
existence of an appropriate pseudo vacuum state. Here we perform the algebraic
Bethe ansatz for all models with , rational, gl(12)-invariant
-matrix and all three possibilities of choosing the grading. Our Bethe
ansatz solution applies, for instance, to the supersymmetric t-J model, the
supersymmetric model and a number of interesting impurity models. It may be
extended to obtain the quantum transfer matrix spectrum for this class of
models. The properties of a specific model enter the Bethe ansatz solution
(i.e. the expression for the transfer matrix eigenvalue and the Bethe ansatz
equations) through the three pseudo vacuum eigenvalues of the diagonal elements
of the monodromy matrix which in this context are called the parameters of the
model.Comment: paragraph added in section 3, reference added, version to appear in
J.Phys.
F1 rotary motor of ATP synthase is driven by the torsionally-asymmetric drive shaft.
F1F0 ATP synthase (ATPase) either facilitates the synthesis of ATP in a process driven by the proton moving force (pmf), or uses the energy from ATP hydrolysis to pump protons against the concentration gradient across the membrane. ATPase is composed of two rotary motors, F0 and F1, which compete for control of their shared γ -shaft. We present a self-consistent physical model of F1 motor as a simplified two-state Brownian ratchet using the asymmetry of torsional elastic energy of the coiled-coil γ -shaft. This stochastic model unifies the physical concepts of linear and rotary motors, and explains the stepped unidirectional rotary motion. Substituting the model parameters, all independently known from recent experiments, our model quantitatively reproduces the ATPase operation, e.g. the 'no-load' angular velocity is ca. 400 rad/s anticlockwise at 4 mM ATP. Increasing the pmf torque exerted by F0 can slow, stop and overcome the torque generated by F1, switching from ATP hydrolysis to synthesis at a very low value of 'stall torque'. We discuss the motor efficiency, which is very low if calculated from the useful mechanical work it produces - but is quite high when the 'useful outcome' is measured in the number of H(+) pushed against the chemical gradient.The authors have benefited from extensive discussions with J. R. Blundell, C. Prior, and G. Fraser, as well as the conceptual input from J. E. Walker (who has originally suggested that the torsional energy of the γ–shaft might be asymmetric). This work has been funded by the {100 + 100 + 100} program by the Ukrainian Government, and the EPSRC Critical Mass Grant for Cambridge Theoretical Condensed Matter EP/J017639
Extended and Reshetikhin Twists for sl(3)
The properties of the set {L} of extended jordanian twists for algebra sl(3)
are studied. Starting from the simplest algebraic construction --- the
peripheric Hopf algebra U_ P'(0,1)(sl(3)) --- we construct explicitly the
complete family of extended twisted algebras {U_ E(\theta)(sl(3))}
corresponding to the set of 4-dimensional Frobenius subalgebras {L(\theta)} in
sl(3). It is proved that the extended twisted algebras with different values of
the parameter \theta are connected by a special kind of Reshetikhin twist. We
study the relations between the family {U_E(\theta)(sl(3))} and the
one-dimensional set {U_DJR(\lambda)(sl(3))} produced by the standard
Reshetikhin twist from the Drinfeld--Jimbo quantization U_DJ(sl(3)). These sets
of deformations are in one-to-one correspondence: each element of
{U_E(\theta)(sl(3))} can be obtained by a limiting procedure from the unique
point in the set {U_DJR(\lambda)(sl(3))}.Comment: 14 pages, LaTeX 20
Peripheric Extended Twists
The properties of the set L of extended jordanian twists are studied. It is
shown that the boundaries of L contain twists whose characteristics differ
considerably from those of internal points. The extension multipliers of these
"peripheric" twists are factorizable. This leads to simplifications in the
twisted algebra relations and helps to find the explicit form for coproducts.
The peripheric twisted algebra U(sl(4)) is obtained to illustrate the
construction. It is shown that the corresponding deformation U_{P}(sl(4))
cannot be connected with the Drinfeld--Jimbo one by a smooth limit procedure.
All the carrier algebras for the extended and the peripheric extended twists
are proved to be Frobenius.Comment: 16 pages, LaTeX 209. Some misprints have been corrected and new
Comments adde
Weyl approach to representation theory of reflection equation algebra
The present paper deals with the representation theory of the reflection
equation algebra, connected with a Hecke type R-matrix. Up to some reasonable
additional conditions the R-matrix is arbitrary (not necessary originated from
quantum groups). We suggest a universal method of constructing finite
dimensional irreducible non-commutative representations in the framework of the
Weyl approach well known in the representation theory of classical Lie groups
and algebras. With this method a series of irreducible modules is constructed
which are parametrized by Young diagrams. The spectrum of central elements
s(k)=Tr_q(L^k) is calculated in the single-row and single-column
representations. A rule for the decomposition of the tensor product of modules
into the direct sum of irreducible components is also suggested.Comment: LaTeX2e file, 27 pages, no figure
Selfconsistent Model of Photoconversion Efficiency for Multijunction Solar Cells
To accurately calculate efficiencies of experimentally produced
multijunction solar cells (MJSCs) and optimize their parameters, we offer
semi-analytical photoconversion formalism that incorporates radiative
recombination, Shockley-Read-Hall (SRH) recombination, surface recombination at
the front and back surfaces of the cells, recombination in the space charge
region (SCR) and the recombination at the heterojunction boundaries.
Selfconsistent balance between the MJSC temperature and efficiency was imposed
by jointly solving the equations for the photocurrent, photovoltage, and heat
balance. Finally, we incorporate into the formalism the effect of additional
photocurrent decrease with subcell number increase. It is shown that for an
experimentally observed Shockley-Read-Hall lifetimes, the effect of
re-absorption and re-emission of photons on MJSC efficiency can be neglected
for non-concentrated radiation conditions. A significant efficiency
increase can be achieved by improving the heat dissipation using radiators and
bringing the MJSC emissivity to unity, that is closer to black body radiation
rather than grey body radiation. Our calculated efficiencies compare well with
other numerical results available and are consistent with the experimentally
achieved efficiencies. The formalism can be used to optimize parameters of
MJSCs for maximum photoconversion efficiency.Comment: 40th IEEE Photovoltaic Specialists Conference, June 8-13, 2014,
Denver, Colorado, III-V Epitaxy and Solar Cells, F30 16
Quantum Jordanian twist
The quantum deformation of the Jordanian twist F_qJ for the standard quantum
Borel algebra U_q(B) is constructed. It gives the family U_qJ(B) of quantum
algebras depending on parameters x and h. In a generic point these algebras
represent the hybrid (standard-nonstandard) quantization. The quantum Jordanian
twist can be applied to the standard quantization of any Kac-Moody algebra. The
corresponding classical r-matrix is a linear combination of the Drinfeld- Jimbo
and the Jordanian ones. The obtained two-parametric families of Hopf algebras
are smooth and for the limit values of the parameters the standard and
nonstandard quantizations are recovered. The twisting element F_qJ also has the
correlated limits, in particular when q tends to unity it acquires the
canonical form of the Jordanian twist. To illustrate the properties of the
quantum Jordanian twist we construct the hybrid quantizations for U(sl(2)) and
for the corresponding affine algebra U(hat(sl(2))). The universal quantum
R-matrix and its defining representation are presented.Comment: 12 pages, Late
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