92 research outputs found
Entre psychiatrie et allégorie : le paradoxe du délire dans Berlin Alexanderplatz
Actes du colloque de l'Université Stendhal de Grenoble, 2008.International audienc
Critical properties of an aperiodic model for interacting polymers
We investigate the effects of aperiodic interactions on the critical behavior
of an interacting two-polymer model on hierarchical lattices (equivalent to the
Migadal-Kadanoff approximation for the model on Bravais lattices), via
renormalization-group and tranfer-matrix calculations. The exact
renormalization-group recursion relations always present a symmetric fixed
point, associated with the critical behavior of the underlying uniform model.
If the aperiodic interactions, defined by s ubstitution rules, lead to relevant
geometric fluctuations, this fixed point becomes fully unstable, giving rise to
novel attractors of different nature. We present an explicit example in which
this new attractor is a two-cycle, with critical indices different from the
uniform model. In case of the four-letter Rudin-Shapiro substitution rule, we
find a surprising closed curve whose points are attractors of period two,
associated with a marginal operator. Nevertheless, a scaling analysis indicates
that this attractor may lead to a new critical universality class. In order to
provide an independent confirmation of the scaling results, we turn to a direct
thermodynamic calculation of the specific-heat exponent. The thermodynamic free
energy is obtained from a transfer matrix formalism, which had been previously
introduced for spin systems, and is now extended to the two-polymer model with
aperiodic interactions.Comment: 19 pages, 6 eps figures, to appear in J. Phys A: Math. Ge
Repetitions in beta-integers
Classical crystals are solid materials containing arbitrarily long periodic
repetitions of a single motif. In this paper, we study the maximal possible
repetition of the same motif occurring in beta-integers -- one dimensional
models of quasicrystals. We are interested in beta-integers realizing only a
finite number of distinct distances between neighboring elements. In such a
case, the problem may be reformulated in terms of combinatorics on words as a
study of the index of infinite words coding beta-integers. We will solve a
particular case for beta being a quadratic non-simple Parry number.Comment: 11 page
A note on abscissas of Dirichlet series
[EN] We present an abstract approach to the abscissas of convergence of vector-valued Dirichlet series. As a consequence we deduce that the abscissas for Hardy spaces of Dirichlet series are all equal. We also introduce and study weak versions of the abscissas for scalar-valued Dirichlet series.A. Defant: Partially supported by MINECO and FEDER MTM2017-83262-C2-1-P.
A. PĂ©rez: Supported by La Caixa Foundation, MINECO and FEDER MTM2014-57838-C2-1-P and
FundaciĂłn SĂ©neca - RegiĂłn de Murcia (CARM 19368/PI/14).
P. Sevilla-Peris: Supported by MINECO and FEDER MTM2017-83262-C2-1-P.Defant, A.; PĂ©rez, A.; Sevilla Peris, P. (2019). A note on abscissas of Dirichlet series. Revista de la Real Academia de Ciencias Exactas FĂsicas y Naturales Serie A MatemĂĄticas. 113(3):2639-2653. https://doi.org/10.1007/s13398-019-00647-yS263926531133Bayart, F.: Hardy spaces of Dirichlet series and their composition operators. Mon. Math. 136(3), 203â236 (2002)Bohnenblust, H.F., Hille, E.: On the absolute convergence of Dirichlet series. Ann Math. 32(3), 600â622 (1931)Bohr, H.: Ăber die Bedeutung der Potenzreihen unendlich vieler Variablen in der Theorie der Dirichletâschen Reihen â a n n s . Nachr. Ges. Wiss. Göttingen, Math. Phys. Kl., pp. 441â488 (1913)Bonet, J.: Abscissas of weak convergence of vector valued Dirichlet series. J. Funct. Anal. 269(12), 3914â3927 (2015)Carando, D., Defant, A., Sevilla-Peris, P.: Bohrâs absolute convergence problem for H p -Dirichlet series in Banach spaces. Anal. PDE 7(2), 513â527 (2014)Carando, D., Defant, A., Sevilla-Peris, P.: Some polynomial versions of cotype and applications. J. Funct. Anal. 270(1), 68â87 (2016)Defant, A., GarcĂa, D., Maestre, M., PĂ©rez-GarcĂa, D.: Bohrâs strip for vector valued Dirichlet series. Math. Ann. 342(3), 533â555 (2008)Defant, A., GarcĂa, D., Maestre, M., SevillaâPeris, P.: Dirichlet Series and Holomorphic Funcions in High Dimensions, vol. 37 of New Mathematical Monographs. Cambridge University Press, Cambridge (2019)Defant, A., PĂ©rez, A.: Optimal comparison of the p -norms of Dirichlet polynomials. Israel J. Math. 221(2), 837â852 (2017)Defant, A., PĂ©rez, A.: Hardy spaces of vector-valued Dirichlet series. Studia Math. 243(1), 53â78 (2018)Diestel, J., Jarchow, H., Tonge, A.: Absolutely summing operators, vol. 43 of Cambridge studies in advanced mathematics. Cambridge University Press, Cambridge (1995)Maurizi, B., QueffĂ©lec, H.: Some remarks on the algebra of bounded Dirichlet series. J. Fourier Anal. Appl. 16(5), 676â692 (2010)QueffĂ©lec, H., QueffĂ©lec, M.: Diophantine approximation and Dirichlet series, vol. 2 of HarishâChandra research institute lecture notes. Hindustan Book Agency, New Delhi (2013
Tight Binding Hamiltonians and Quantum Turing Machines
This paper extends work done to date on quantum computation by associating
potentials with different types of computation steps. Quantum Turing machine
Hamiltonians, generalized to include potentials, correspond to sums over tight
binding Hamiltonians each with a different potential distribution. Which
distribution applies is determined by the initial state. An example, which
enumerates the integers in succession as binary strings, is analyzed. It is
seen that for some initial states the potential distributions have
quasicrystalline properties and are similar to a substitution sequence.Comment: 4 pages Latex, 2 postscript figures, submitted to Phys Rev Letter
Quantum Return Probability for Substitution Potentials
We propose an effective exponent ruling the algebraic decay of the average
quantum return probability for discrete Schrodinger operators. We compute it
for some non-periodic substitution potentials with different degrees of
randomness, and do not find a complete qualitative agreement with the spectral
type of the substitution sequences themselves, i.e., more random the sequence
smaller such exponent.Comment: Latex, 13 pages, 6 figures; to be published in Journal of Physics
Almost sure-sign convergence of Hardy-type Dirichlet series
[EN] Hartman proved in 1939 that the width of the largest possible strip in the complex plane on which a Dirichlet series is uniformly a.s.- sign convergent (i.e., converges uniformly for almost all sequences of signs epsilon (n) = +/- 1) but does not convergent absolutely, equals 1/2. We study this result from a more modern point of view within the framework of so-called Hardytype Dirichlet series with values in a Banach space.Supported by CONICET-PIP 11220130100329CO, PICT 2015-2299 and UBACyT 20020130100474BA.
Supported by MICINN MTM2017-83262-C2-1-P.
Supported by MICINN MTM2017-83262-C2-1-P and UPV-SP20120700.Carando, D.; Defant, A.; Sevilla Peris, P. (2018). Almost sure-sign convergence of Hardy-type Dirichlet series. Journal d Analyse MathĂ©matique. 135(1):225-247. https://doi.org/10.1007/s11854-018-0034-yS2252471351A. Aleman, J.-F. Olsen, and E. Saksman, Fourier multipliers for Hardy spaces of Dirichlet series, Int. Math. Res. Not. IMRN 16 (2014), 4368â4378.R. Balasubramanian, B. Calado, and H. QueffĂ©lec, The Bohr inequality for ordinary Dirichlet series Studia Math. 175 (2006), 285â304.F. Bayart, Hardy spaces of Dirichlet series and their composition operators, Monatsh. Math. 136 (2002), 203â236.F. Bayart, A. Defant, L. Frerick, M. Maestre, and P. Sevilla-Peris, Monomial series expansion of Hp-functions and multipliers ofHp-Dirichlet series, Math. Ann. 368 (2017), 837â876.F. Bayart, D. Pellegrino, and J. B. Seoane-SepĂșlveda, The Bohr radius of the n-dimensional polydisk is equivalent to ( log n ) / n , Adv. Math. 264 (2014), 726â746.F. Bayart, H. QueffĂ©lec, and K. Seip, Approximation numbers of composition operators on Hp spaces of Dirichlet series, Ann. Inst. Fourier (Grenoble) 66 (2016), 551â588.H. F. Bohnenblust and E. Hille. On the absolute convergence of Dirichlet series, Ann. of Math. (2) 32 (1931), 600â622.H. Bohr, Ăber die Bedeutung der Potenzreihen unendlich vieler Variablen in der Theorie der Dirichletâschen Reihen â a n n s , Nachr. Ges.Wiss. Göttingen, Math. Phys. Kl., 1913, pp. 441â488.D. Carando, A. Defant, and P. Sevilla-Peris, Bohrâs absolute convergence problem for Hp- Dirichlet series in Banach spaces, Anal. PDE 7 (2014), 513â527.D. Carando, A. Defant, and P. Sevilla-Peris, Some polynomial versions of cotype and applications, J. Funct. Anal. 270 (2016), 68â87.B. J. Cole and T. W. Gamelin, Representing measures and Hardy spaces for the infinite polydisk algebra, Proc. London Math. Soc. (3) 53 (1986), 112â142.R. de la BretĂšche. Sur lâordre de grandeur des polynĂŽmes de Dirichlet, Acta Arith. 134 (2008), 141â148.A. Defant, L. Frerick, J. Ortega-CerdĂ , M. OunĂ€ies, and K. Seip, The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive, Ann. of Math. (2) 174 (2011), 485â497.A. Defant, D. GarcĂa, M. Maestre, and D. PĂ©rez-GarcĂa, Bohrâs strip for vector valued Dirichlet series, Math. Ann. 342 (2008), 533â555.A. Defant, M. Maestre, and U. Schwarting, Bohr radii of vector valued holomorphic functions, Adv. Math. 231 (2012), 2837â2857.A. Defant and A. PĂ©rez, Hardy spaces of vector-valued Dirichlet series, StudiaMath. (to appear), 2018 DOI: 10.4064/sm170303-26-7.A. Defant, U. Schwarting, and P. Sevilla-Peris, Estimates for vector valued Dirichlet polynomials, Monatsh. Math. 175 (2014), 89â116.J. Diestel, H. Jarchow, and A. Tonge, Absolutely Summing Operators, Cambridge University Press, Cambridge, 1995.P. Hartman, On Dirichlet series involving random coefficients, Amer. J. Math. 61 (1939), 955â964.H. Hedenmalm, P. Lindqvist, and K. Seip, A Hilbert space of Dirichlet series and systems of dilated functions in L2(0, 1), Duke Math. J. 86 (1997), 1â37.A. Hildebrand, and G. Tenenbaum, Integers without large prime factors, J. Thor. Nombres Bordeaux 5 (1993), 411â484.S. V. Konyagin and H. QueffĂ©lec, The translation 1/2 in the theory of Dirichlet series, Real Anal. Exchange 27 (2001/02) 155â175.J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. II, Springer-Verlag, Berlin, 1979.B. Maurizi and H. QueffĂ©lec, Some remarks on the algebra of bounded Dirichlet series, J. Fourier Anal. Appl. 16 (2010), 676â692.H. QueffĂ©lec, H. Bohrâs vision of ordinary Dirichlet series; old and new results, J. Anal. 3 (1995), 43â60.H. QueffĂ©lec and M. QueffĂ©lec, Diophantine Approximation and Dirichlet Series, Hindustan Book Agency, New Delhi, 2013.G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory, Cambridge University Press, Cambridge, 1995
Pure point diffraction and cut and project schemes for measures: The smooth case
We present cut and project formalism based on measures and continuous weight
functions of sufficiently fast decay. The emerging measures are strongly almost
periodic. The corresponding dynamical systems are compact groups and
homomorphic images of the underlying torus. In particular, they are strictly
ergodic with pure point spectrum and continuous eigenfunctions. Their
diffraction can be calculated explicitly. Our results cover and extend
corresponding earlier results on dense Dirac combs and continuous weight
functions with compact support. They also mark a clear difference in terms of
factor maps between the case of continuous and non-continuous weight functions.Comment: 30 page
Log-periodic corrections to scaling: exact results for aperiodic Ising quantum chains
Log-periodic amplitudes of the surface magnetization are calculated
analytically for two Ising quantum chains with aperiodic modulations of the
couplings. The oscillating behaviour is linked to the discrete scale invariance
of the perturbations. For the Fredholm sequence, the aperiodic modulation is
marginal and the amplitudes are obtained as functions of the deviation from the
critical point. For the other sequence, the perturbation is relevant and the
critical surface magnetization is studied.Comment: 12 pages, TeX file, epsf, iopppt.tex, xref.tex which are joined. 4
postcript figure
Interface Fluctuations on a Hierarchical Lattice
We consider interface fluctuations on a two-dimensional layered lattice where
the couplings follow a hierarchical sequence. This problem is equivalent to the
diffusion process of a quantum particle in the presence of a one-dimensional
hierarchical potential. According to a modified Harris criterion this type of
perturbation is relevant and one expects anomalous fluctuating behavior. By
transfer-matrix techniques and by an exact renormalization group transformation
we have obtained analytical results for the interface fluctuation exponents,
which are discontinuous at the homogeneous lattice limit.Comment: 14 pages plain Tex, one Figure upon request, Phys Rev E (in print
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