7,942 research outputs found
Heavy doping effects in high efficiency silicon solar cells
A model for bandgap shrinkage in semiconductors is developed and applied to silicon. A survey of earlier experiments, and of new ones, give an agreement between the model and experiments on n- and p-type silicon which is good as far as transport measurements in the 300 K range. The discrepancies between theory and experiment are no worse than the discrepancies between the experimental results of various authors. It also gives a good account of recent, optical determinations of band gap shrinkage at 5 K
Representations of the exceptional and other Lie algebras with integral eigenvalues of the Casimir operator
The uniformity, for the family of exceptional Lie algebras g, of the
decompositions of the powers of their adjoint representations is well-known now
for powers up to the fourth. The paper describes an extension of this
uniformity for the totally antisymmetrised n-th powers up to n=9, identifying
(see Tables 3 and 6) families of representations with integer eigenvalues
5,...,9 for the quadratic Casimir operator, in each case providing a formula
(see eq. (11) to (15)) for the dimensions of the representations in the family
as a function of D=dim g. This generalises previous results for powers j and
Casimir eigenvalues j, j<=4. Many intriguing, perhaps puzzling, features of the
dimension formulas are discussed and the possibility that they may be valid for
a wider class of not necessarily simple Lie algebras is considered.Comment: 16 pages, LaTeX, 1 figure, 9 tables; v2: presentation improved, typos
correcte
Rank and border rank of Kronecker powers of tensors and Strassen's laser method
We prove that the border rank of the Kronecker square of the little CoppersmithâWinograd tensor Tcw,q is the square of its border rank for q> 2 and that the border rank of its Kronecker cube is the cube of its border rank for q> 4. This answers questions raised implicitly by Coppersmith & Winograd (1990, §11)and explicitly by BlĂ€ser (2013, Problem 9.8) and rules out the possibility of proving new upper bounds on the exponent of matrix multiplication using the square or cube of a little CoppersmithâWinograd tensor in this range. In the positive direction, we enlarge the list of explicit tensors potentially useful for Strassen's laser method, introducing a skew-symmetric version of the CoppersmithâWinograd tensor, Tskewcw,q. For q= 2 , the Kronecker square of this tensor coincides with the 3 Ă 3 determinant polynomial, det 3â C9â C9â C9, regarded as a tensor. We show that this tensor could potentially be used to show that the exponent of matrix multiplication is two. We determine new upper bounds for the (Waring) rank and the (Waring) border rank of det 3, exhibiting a strict submultiplicative behaviour for Tskewcw,2 which is promising for the laser method. We establish general results regarding border ranks of Kronecker powers of tensors, and make a detailed study of Kronecker squares of tensors in C3â C3â C3
Fick's law and Fokker-Planck Equation in inhomogeneous environments
In inhomogeneous environments, the correct expression of the diffusive flux
is often not given by the Fick's law . The most general
hydrodynamic equation modelling diffusion is indeed the Fokker-Planck Equation
(FPE). The microscopic dynamics of each specific system may affect the form of
the FPE, either establishing connections between the diffusion and the
convection term, as well as providing supplementary terms. In particular, the
Fick's form for the Diffusion Equation may arise only in consequence of a
specific kind of microscopic dynamics. It is also shown how, in the presence of
sharp inhomogeneities, even the hydrodynamic FPE limit may becomes inaccurate
and mask some features of the true solution, as computed from the Master
Equation.Comment: V2: English amended. V3: final version accepted by Physics Letters
Kronecker powers of tensors and Strassenâs laser method
We answer a question, posed implicitly in [18, §11], [11, Rem. 15.44] and explicitly in [9, Problem 9.8], showing the border rank of the Kronecker square of the little Coppersmith-Winograd tensor is the square of the border rank of the tensor for all q > 2, a negative result for complexity theory. We further show that when q > 4, the analogous result holds for the Kronecker cube. In the positive direction, we enlarge the list of explicit tensors potentially useful for the laser method. We observe that a well-known tensor, the 3Ă3 determinant polynomial regarded as a tensor, det3 â C9 C9 C9, could potentially be used in the laser method to prove the exponent of matrix multiplication is two. Because of this, we prove new upper bounds on its Waring rank and rank (both 18), border rank and Waring border rank (both 17), which, in addition to being promising for the laser method, are of interest in their own right. We discuss âskewâ cousins of the little Coppersmith-Winograd tensor and indicate why they may be useful for the laser method. We establish general results regarding border ranks of Kronecker powers of tensors, and make a detailed study of Kronecker squares of tensors in C3 C3 C
Universal restrictions to the conversion of heat into work derived from the analysis of the Nernst theorem as a uniform limit
We revisit the relationship between the Nernst theorem and the Kelvin-Planck
statement of the second law. We propose that the exchange of entropy uniformly
vanishes as the temperature goes to zero. The analysis of this assumption shows
that is equivalent to the fact that the compensation of a Carnot engine scales
with the absorbed heat so that the Nernst theorem should be embedded in the
statement of the second law.
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Se analiza la relaci{\'o}n entre el teorema de Nernst y el enunciado de
Kelvin-Planck del segundo principio de la termodin{\'a}mica. Se{\~n}alamos el
hecho de que el cambio de entrop{\'\i}a tiende uniformemente a cero cuando la
temperatura tiende a cero. El an{\'a}lisis de esta hip{\'o}tesis muestra que es
equivalente al hecho de que la compensaci{\'o}n de una m{\'a}quina de Carnot
escala con el calor absorbido del foco caliente, de forma que el teorema de
Nernst puede derivarse del enunciado del segundo principio.Comment: 8pp, 4 ff. Original in english. Also available translation into
spanish. Twocolumn format. RevTe
Pattern Formation in Semiconductors
In semiconductors, nonlinear generation and recombination processes of free carriers and nonlinear charge transport can give rise to non-equilibrium phase transitions. At low temperatures, the basic nonlinearity is due to the autocatalytic generation of free carriers by impact ionization of shallow impurities. The electric field accelerates free electrons, causing an abrupt increase in free carrier density at a critical electric field. In static electric fields, this nonlinearity is known to yield complex filamentary current patterns bound to electric contacts
Thermodynamics' 0-th-Law in a nonextensive scenario
Tsallis' thermostatistics is by now recognized as a new paradigm for
statistical mechanical considerations. However, it is still affected by a
serious hindrance: the generalization of thermodynamics' zero-th law to a
nonextensive scenario is plagued by difficulties. Here we show how to overcome
this problem.Comment: 4 pages, latex; added references for section
Notes on the Third Law of Thermodynamics.I
We analyze some aspects of the third law of thermodynamics. We first review
both the entropic version (N) and the unattainability version (U) and the
relation occurring between them. Then, we heuristically interpret (N) as a
continuity boundary condition for thermodynamics at the boundary T=0 of the
thermodynamic domain. On a rigorous mathematical footing, we discuss the third
law both in Carath\'eodory's approach and in Gibbs' one. Carath\'eodory's
approach is fundamental in order to understand the nature of the surface T=0.
In fact, in this approach, under suitable mathematical conditions, T=0 appears
as a leaf of the foliation of the thermodynamic manifold associated with the
non-singular integrable Pfaffian form . Being a leaf, it cannot
intersect any other leaf const. of the foliation. We show that (N) is
equivalent to the requirement that T=0 is a leaf. In Gibbs' approach, the
peculiar nature of T=0 appears to be less evident because the existence of the
entropy is a postulate; nevertheless, it is still possible to conclude that the
lowest value of the entropy has to belong to the boundary of the convex set
where the function is defined.Comment: 29 pages, 2 figures; RevTex fil
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