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12. Bogoliubov quasi-averages: spontaneous symmetry breaking and algebra of fluctuations

Author

Walter F. Wreszinski, Valentin A. Zagrebnov, Departamento de Fisica Matematica, Universidade de São Paulo (USP), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Aix-Marseille Université - Faculté des Sciences (AMU SCI), Aix Marseille Université (AMU), Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU), and Universidade de São Paulo = University of São Paulo (USP)

Subjects
Quantum phase transition, Spontaneous symmetry breaking, FOS: Physical sciences, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], 0103 physical sciences, FOS: Mathematics, quasiaverages, Algebra over a field, Connection (algebraic framework), 010306 general physics, Commutative property, Quantum, Mathematical Physics, Quantum fluctuation, Physics, Condensed Matter::Quantum Gases, 010308 nuclear & particles physics, Condensed Matter::Other, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Noncommutative geometry, Physics::History of Physics, Functional Analysis (math.FA), critical quantum fluctuations, Mathematics - Functional Analysis, Algebra, generalized condensation, 82B10 (81-02 81R40 82-02 82-03)
Abstract

The paper advocates the Bogoliubov method of quasi-averages for quantum systems. First, we elucidate its applications to study the phase transitions with Spontaneous Symmetry Breaking (SSB). To this aim we consider example of Bose-Einstein condensation (BEC) in continuous systems. Our analysis of different type of generalised condensations demonstrates that the only physically reliable quantities are those that defined by Bogoliubov quasi-averages. In this connection we also give a solution of the problem posed by Lieb, Seiringer and Yngvason in [SY07]. Second, using the scaled Bogoliubov method of quasi-averages and taking the structural quantum phase transition as a basic example, we scrutinise a relation between SSB and the critical quantum fluctuations. Our analysis shows that again the quasi-averages give an adequate tool for description of the algebra of critical quantum fluctuation operators in the both commutative and noncommutative cases.

Published
2018
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14. The SDSS-IV Extended Baryon Oscillation Spectroscopic Survey : overview and early data

Author

Joe Huehnerhoff, Jo Bovy, Jean-Marc Le Goff, Nicolás G. Busca, Matthew A. Bershady, Will J. Percival, Yipeng Jing, Marcio A. G. Maia, Conor Sayres, Diana Holder, Xiaohui Fan, Eric Jullo, Flavia Sobreira, Sergio Rodríguez-Torres, Vikrant Kamble, Antonio D. Montero-Dorta, Yu Liang, Andreas A. Berlind, Patrick Gaulme, Beth Reid, Stephen Bailey, Peter Nugent, Andrea Merloni, Peter M. Frinchaboy, Dmitry Bizyaev, A. C. Rosell, Gong-Bo Zhao, Tracy Naugle, Yen-Ting Lin, Vivek Mariappan, Zhongxu Zhai, Julien Guy, Hélion du Mas des Bourboux, Shirley Ho, Martin White, Éric Aubourg, Abhishek Prakash, Pasquier Noterdaeme, Yuting Wang, Audrey Oravetz, Dustin Lang, Uroš Seljak, W. N. Brandt, Demitri Muna, Patrick Petitjean, Sylvain de la Torre, M. C. Cousinou, Ian D. McGreer, Pierre Laurent, Adam D. Myers, Isabelle Paris, Andres Meza, John J. Ruan, Franco D. Albareti, Etienne Burtin, Kyle S. Dawson, Adam S. Bolton, Alina Streblyanska, Nikhil Padmanabhan, Marcos Lima, Chia-Hsun Chuang, Kaike Pan, Benjamin A. Weaver, Daniel J. Eisenstein, Branimir Sesar, Mariana Vargas-Magaña, Ashley J. Ross, Alice Pisani, Axel de la Macorra, Mark A. Klaene, Nathalie Palanque-Delabrouille, Karen Kinemuchi, Nicholas R. MacDonald, Rita Tojeiro, Nicolas Clerc, Nao Suzuki, Scott F. Anderson, Dan Long, John A. Peacock, Kirpal Nandra, Johan Comparat, D. Kirkby, Anze Slosar, Timothy A. Hutchinson, Michael Blomqvist, Donald P. Schneider, Stephanie Escoffier, Jeremy L. Tinker, Charling Tao, Irene Cruz-González, Jon Brinkmann, Michael Eracleous, Francisco-Shu Kitaura, Hu Zou, Elena Malanushenko, Yiping Shu, Anand Raichoor, W. M. Wood-Vasey, Andreu Font-Ribera, Tom Dwelly, J. Ridl, Graziano Rossi, Hee-Jong Seo, Britt Lundgren, Sarah Shandera, Brice Ménard, Luiz N. da Costa, Shadab Alam, Ricardo L. C. Ogando, Christophe Yèche, Daniel Oravetz, Matthew M. Pieri, Jean-Paul Kneib, Julian E. Bautista, Weipeng Lin, Mara Salvato, Antonis Georgakakis, Alexis Finoguenov, Hong Guo, Florian Beutler, Guangtun Zhu, Jeremy Darling, Zheng Zheng, Frances Cope, Donna Taylor, Francisco Prada, David H. Weinberg, Cheng Li, Rupert A. C. Croft, Joel R. Brownstein, Viktor Malanushenko, Paul J. Green, Jeffrey A. Newman, John K. Parejko, David J. Schlegel, Matthew D. Olmstead, Russ R. Laher, Cameron K. McBride, Cheng Zhao, Timothée Delubac, James Rich, Michael R. Blanton, Eric Armengaud, Anne Ealet, Zheng Cai, Qiufan Lin, University of St Andrews. School of Physics and Astronomy, AVL, AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Department of Astronomy and Astrophysics [PennState], Pennsylvania State University (Penn State), Penn State System-Penn State System, Departamento de FisicaTeorica e IFT-UAM/CSIC, Universidad Autónoma de Madrid (UAM), Centre de Physique des Particules de Marseille (CPPM), Aix Marseille Université (AMU)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), EPFL Laboratoire d’astrophysique, Ecole Polytechnique Fédérale de Lausanne (EPFL), Max-Planck-Institut für Astronomie (MPIA), Max-Planck-Gesellschaft, Laboratoire d'études spatiales et d'instrumentation en astrophysique (LESIA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Centre Hospitalier Universitaire de Dijon - Hôpital François Mitterrand (CHU Dijon), McMaster University [Hamilton, Ontario], Laboratoire d'Astrophysique de Marseille (LAM), Aix Marseille Université (AMU)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS), Department of Physics and Astronomy [Irvine], University of California [Irvine] (UC Irvine), University of California (UC)-University of California (UC), Département de Physique des Particules (ex SPP) (DPhP), Institut de Recherches sur les lois Fondamentales de l'Univers (IRFU), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Shanghai Astronomical Observatory [Shanghai] (SHAO), Chinese Academy of Sciences [Beijing] (CAS), Departamento de Fisica Matematica, Universidade de São Paulo = University of São Paulo (USP), Max-Planck-Institut für Astrophysik (MPA), Department of Physics and Astronomy [Pittsburgh], University of Pittsburgh (PITT), Pennsylvania Commonwealth System of Higher Education (PCSHE)-Pennsylvania Commonwealth System of Higher Education (PCSHE), Institut d'Astrophysique de Paris (IAP), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Universidad de Chile = University of Chile [Santiago] (UCHILE), Galaxies, Etoiles, Physique, Instrumentation (GEPI), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, Lawrence Berkeley National Laboratory [Berkeley] (LBNL), APC - Cosmologie, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Department of Electrical and Computer Engineering [Minneapolis] (ECE), University of Minnesota [Twin Cities] (UMN), University of Minnesota System-University of Minnesota System, China National Research Center of Intelligent Equipment for Agriculture [Beijing] (NRCIEA), Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Shandong University, Laboratoire de Chimie - UMR5182 (LC), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Universidad Autonoma de Madrid (UAM), Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Aix Marseille Université (AMU), Laboratoire d'Astrophysique, Ecole Polytechnique Fédérale de Lausanne (EPFL), Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC), Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Aix Marseille Université (AMU)-Centre National d'Études Spatiales [Toulouse] (CNES), University of California [Irvine] (UCI), University of California-University of California, Département de Physique des Particules (ex SPP) (DPP), Universidade de São Paulo (USP), Universidad Santiago de Chile, PSL Research University (PSL)-PSL Research University (PSL)-Centre National de la Recherche Scientifique (CNRS), Physique Corpusculaire et Cosmologie - Collège de France (PCC), Collège de France (CdF)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Collège de France (CdF)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-AstroParticule et Cosmologie (APC (UMR_7164)), PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, University of Minnesota [Twin Cities], École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), UAM. Departamento de Física Teórica, Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-École normale supérieure - Lyon (ENS Lyon)-Institut de Chimie du CNRS (INC), PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Observatoire de Paris, and PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Cosmology and Gravitation, Cosmology and Nongalactic Astrophysics (astro-ph.CO), FOS: Physical sciences, Astrophysics, Astrophysics::Cosmology and Extragalactic Astrophysics, Surveys, 01 natural sciences, surveys, Tests of general relativity, 0103 physical sciences, ST/K0090X/1, QB Astronomy, Emission spectrum, observations [Cosmology], 010303 astronomy & astrophysics, STFC, Astrophysics::Galaxy Astrophysics, QC, QB, Physics, 010308 nuclear & particles physics, Física, RCUK, Astronomy and Astrophysics, Quasar, 3rd-DAS, Redshift, Galaxy, Baryon, QC Physics, Space and Planetary Science, cosmology: observations, astro-ph.CO, Baryon acoustic oscillations, Neutrino, [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract

The Astrophysical Journal 151.2 (2016): 44 reproduced by permission of the AAS, In a six-year program started in 2014 July, the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) will conduct novel cosmological observations using the BOSS spectrograph at Apache Point Observatory. These observations will be conducted simultaneously with the Time Domain Spectroscopic Survey (TDSS) designed for variability studies and the Spectroscopic Identification of eROSITA Sources (SPIDERS) program designed for studies of X-ray sources. In particular, eBOSS will measure with percent-level precision the distance-redshift relation with baryon acoustic oscillations (BAO) in the clustering of matter. eBOSS will use four different tracers of the underlying matter density field to vastly expand the volume covered by BOSS and map the large-scale-structures over the relatively unconstrained redshift range 0.6 < z < 2.2. Using more than 250,000 new, spectroscopically confirmed luminous red galaxies at a median redshift z = 0.72, we project that eBOSS will yield measurements of the angular diameter distance dA(z) to an accuracy of 1.2% and measurements of H(z) to 2.1% when combined with the z > 0.6 sample of BOSS galaxies. With ∼195,000 new emission line galaxy redshifts, we expect BAO measurements of dA(z) to an accuracy of 3.1% and H(z) to 4.7% at an effective redshift of z = 0.87. A sample of more than 500,000 spectroscopically confirmed quasars will provide the first BAO distance measurements over the redshift range 0.9 < z < 2.2, with expected precision of 2.8% and 4.2% on dA(z) and H(z), respectively. Finally, with 60,000 new quasars and re-observation of 60,000 BOSS quasars, we will obtain new Lyα forest measurements at redshifts z > 2.1; these new data will enhance the precision of dA(z) and H(z) at z > 2.1 by a factor of 1.44 relative to BOSS. Furthermore, eBOSS will provide improved tests of General Relativity on cosmological scales through redshift-space distortion measurements, improved tests for non-Gaussianity in the primordial density field, and new constraints on the summed mass of all neutrino species. Here, we provide an overview of the cosmological goals, spectroscopic target sample, demonstration of spectral quality from early data, and projected cosmological constraints from eBOSS, K.D. acknowledges support from the U.S. Department of Energy under Grant DE-SC000995. J.P.K. and T.D. acknowledge support from the ERC advanced grant LIDA. W.J.P. acknowledges support from the UK STFC through the consolidated grant ST/K0090X/1, and from the European Research Council through grant Darksurvey

Published
2016
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15. On the intrinsic coupling between constant-phase element parameters α and Q in electrochemical impedance spectroscopy

Author

O. Devos, P. Córdoba-Torres, Ricardo P. Nogueira, V. Roche, Bernard Tribollet, T.J. Mesquita, Departamento de Fisica Matematica y de Fluidos, Facultad de Ciencas, Laboratoire d'Electrochimie et de Physico-chimie des Matériaux et des Interfaces (LEPMI ), Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National Polytechnique de Grenoble (INPG)-Institut de Chimie du CNRS (INC)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Institut d'Ingénierie et de Mécanique, Université Sciences et Technologies - Bordeaux 1, Laboratoire Interfaces et Systèmes Electrochimiques (LISE), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Electrochimie Interfaciale et Procédés (EIP), Laboratoire d'Electrochimie et de Physico-chimie des Matériaux et des Interfaces (LEPMI), Institut de Chimie du CNRS (INC)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut de Chimie du CNRS (INC)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Université Sciences et Technologies - Bordeaux 1 (UB), and Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National Polytechnique de Grenoble (INPG)-Institut de Chimie du CNRS (INC)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National Polytechnique de Grenoble (INPG)-Institut de Chimie du CNRS (INC)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)

Subjects
Coupling, Electrochemical impedance, Materials science, Constant phase element, General Chemical Engineering, Double-layer capacitance, Time constant, Analytical chemistry, Thermodynamics, 02 engineering and technology, 010402 general chemistry, 021001 nanoscience & nanotechnology, 01 natural sciences, Capacitance, 0104 chemical sciences, Equivalent electrical circuit, Phase (matter), Electrochemistry, Curve fitting, [CHIM.OTHE]Chemical Sciences/Other, 0210 nano-technology, Constant (mathematics)
Abstract

International audience; This paper presents experimental evidences of an intrinsic coupling between the alpha and Q parameters of constant phase elements (CPE) used in equivalent electrical circuits for EIS data fitting. Clear correlations have been found for two different experimental conditions, anodic dissolution and scale deposit, for which CPE behavior appears as the result of a time constant distribution originated from surface inhomogeneity. Results are in agreement with a coupling function that relates CPE parameters with interfacial quantities such as the ohmic and charge transfer resistances, and also with a characteristic interfacial capacitance whose meaning is addressed here. Although this relationship was initially derived from a theoretical model in which perfect CPE behavior was caused by a double-layer capacity distribution along the interface, it has been extensively used in the literature to estimate interface capacitance from CPE parameters in very different complex systems without any definitive evidence of it. However, its exportability to real systems can be explained from the fact that it can be deduced from simple and general arguments. In this paper we argue on these ideas in the basis of experimental evidences.

Published
2012
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16. On ergodic states, spontaneous symmetry breaking and the Bogoliubov quasi-averages

Author

Wreszinski, Walter F., Zagrebnov, Valentin, Departamento de Fisica Matematica, Universidade de São Paulo = University of São Paulo (USP), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Universidade de São Paulo (USP), and Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU)

Subjects
Mathematics - Functional Analysis, Condensed Matter::Quantum Gases, Condensed Matter::Other, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Mathematical Physics, Functional Analysis (math.FA)
Abstract

Some of the issues dealt with in this paper originate in the open problem posed in Sec.3 of [SW09] and at the of [JaZ10]. One of us (W.F.W.) would like to thank G. L. Sewell for sharing with him his views on ODLRO along several years. He would also like to thank the organisers of the Satellite conference ”Operator Algebras and Quantum Physics” of the XVIII conference of the IAMP (Santiago de Chile) in Sao Paulo, July 17th-23rd 2015, for the opportunity to present a talk in which some of the ideas of the present paper were discussed. We are thankful to Bruno Nachtergaele for very useful remarks, suggestions, and corrections, which greatly improved and clarified the paper.; It is shown that Bogoliubov quasi-averages select the pure or ergodic states in the ergodic decomposition of the thermal (Gibbs) state. Our examples include quantum spin systems and many-body boson systems. As a consequence, we elucidate the problem of equivalence between Bose-Einstein condensation and the quasi-average spontaneous symmetry breaking (SSB) discussed for continuous boson systems. The multi-mode extended van den Berg-Lewis-Pul\'{e} condensation of type III demonstrates that the only physically reliable quantities are those that defined by Bogoliubov quasi-averages.

Published
2016
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17. Statistical mechanics of self-gravitating systems: Mixing as a criterion for indistinguishability

Author

Jérôme Perez, Laerte Sodré, Marcos Lima, Leandro Beraldo e Silva, Departamento de Fisica Matematica, Universidade de São Paulo (USP), Instituto de Astronomia, Geofísica e Ciências Atmosféricas [São Paulo] (IAG), Optimisation et commande (OC), Unité de Mathématiques Appliquées (UMA), and École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)

Subjects
Physics, [PHYS]Physics [physics], Nuclear and High Energy Physics, Statistical Mechanics (cond-mat.stat-mech), Distribution (number theory), Vlasov equation, FOS: Physical sciences, Statistical mechanics, Astrophysics - Astrophysics of Galaxies, Symmetry (physics), Distribution function, Classical mechanics, Astrophysics of Galaxies (astro-ph.GA), GRAVIDADE, Relaxation (physics), Condensed Matter - Statistical Mechanics, Mixing (physics), Einasto profile
Abstract

We propose an association between the phase-space mixing level of a self-gravitating system and the indistinguishability of its constituents (stars or dark matter particles). This represents a refinement in the study of systems exhibiting incomplete violent relaxation. Within a combinatorial analysis similar to that of Lynden-Bell, we make use of this association to obtain a distribution function that deviates from the Maxwell-Boltzmann distribution, increasing its slope for high energies. Considering the smallness of the occupation numbers for large distances from the center of the system, we apply a correction to Stirling's approximation which increases the distribution slope also for low energies. The distribution function thus obtained presents some resemblance to the "S" shape of distributions associated with cuspy density profiles (as compared to the distribution function obtained from the Einasto profile), although it is not quite able to produce sharp cusps. We also argue how the association between mixing level and indistinguishability can provide a physical meaning to the assumption of particle-permutation symmetry in the N-particle distribution function, when it is used to derive the one-particle Vlasov equation, which raises doubts about the validity of this equation during violent relaxation., Minor changes; Published in PRD

Published
2014
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18. Product Approximations for Solutions to a Class of Evolution Equations in Hilbert Space

Author

Pierre-A. Vuillermot, Walter F. Wreszinski, Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Departamento de Fisica Matematica, Universidade de São Paulo (USP), and Universidade de São Paulo = University of São Paulo (USP)

Subjects
Weak convergence, General Mathematics, 010102 general mathematics, Mathematical analysis, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], Hilbert space, Weak formulation, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, symbols.namesake, Weak operator topology, Simultaneous equations, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Product (mathematics), 0103 physical sciences, symbols, Applied mathematics, 010307 mathematical physics, Unitary operator, 0101 mathematics, C0-semigroup, Mathematics
Abstract

International audience; In this article we prove approximation formulae for a class of unitary evolution operators $U (t,s)_{s,t \in \left[0,T\right]}$ associated with linear non-autonomous evolution equations of Schrödinger type defi…ned in a Hilbert space $\mathcal{H}$. An important feature of the equations we consider is that both the corresponding self-adjoint generators and their domains may depend explicitly on time, whereas the associated quadratic form domains may not. Furthermore the evolution operators we are interested in satisfy the equations in a weak sense. Under such conditions the approximation formulae we prove for $U(t,s)$ involve weak operator limits of products of suitable approximating functions taking values in $\mathcal{L(H)}$, the algebra of all linear bounded operators on $\mathcal{H}$. Our results may be relevant to the numerical analysis of $U(t,s)$ and we illustrate them by considering two evolution problems in quantum mechanics.

Published
2011
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19. Density scaling laws for the structure of granular deposits.

Author

Rodríguez-Pérez D, Castillo JL, and Antoranz JC

Abstract

The structure of granular deposits growing by arriving particles is analyzed using three-dimensional on-lattice Monte Carlo modeling of convective-diffusive particle deposition. The deposit density profile rho(h) depends on the particle dynamics and becomes formed by three different regions: a denser near-wall region at the deposit bottom in contact with the original plain surface, a middle uniform region with constant mean density, and an open and lighter active-growth region at the deposit outer surface. Fitting expressions for rho(h) valid in each region are proposed, based on the known features of deposits formed in the two limiting cases: ballistic deposition and diffusion-limited deposition. Also, a composite expression for rho(h) fitting the density profile throughout the deposit is given. All these expressions are written in terms of a length scale l(Pe) dependent on the particle Péclet number, which provides the relative importance of the convective motion to the diffusive transport for the particle.

Published
2007
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20. Relationship between particle deposit characteristics and the mechanism of particle arrival.

Author

Rodríguez-Pérez D, Castillo JL, and Antoranz JC

Abstract

An on-lattice Monte Carlo model is implemented for the simulation of particle deposit growth by advection and diffusion towards a flat surface. The particle deposit structure is characterized by its bulk (density) and interface (mean height and surface width) properties. Numerical correlations, fitted by simple expressions, are reported for these magnitudes, relating them to time (number of deposited particles) and Peclet number. Also a heuristic argument is presented which relates deposit density to local diffusion-limited-aggregation-like processes and interfacial dynamics to the KPZ model.

Published
2005
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