The European Physical Journal B, ISSN 1434-6028, 5/2017, Volume 90, Issue 5, pp. 1 - 5

... of superconductivity Christian Hainzl 1,a and Michael Loss 2 1 Mathematisches Institut, Universit¨ at T¨ ubingen, Auf der Morgenstelle 10, 72076 T¨ ubingen, Germany 2 School...

Condensed Matter Physics | Solid State Physics | Fluid- and Aerodynamics | Complex Systems | Solid State and Materials | Physics, general | Physics | PHYSICS, CONDENSED MATTER | Football (College) | Superconductors | Analysis | Physics - Superconductivity

Condensed Matter Physics | Solid State Physics | Fluid- and Aerodynamics | Complex Systems | Solid State and Materials | Physics, general | Physics | PHYSICS, CONDENSED MATTER | Football (College) | Superconductors | Analysis | Physics - Superconductivity

Journal Article

The European Physical Journal B, ISSN 1434-6028, 5/2016, Volume 89, Issue 5, pp. 1 - 10

...-Gennes equations to their linear approximation: a numerical investigation Christian Hainzl and Jonathan Seyrich a Mathematisches Institut, Universit¨ at T¨ ubingen...

Condensed Matter Physics | Solid State Physics | Fluid- and Aerodynamics | Computational Methods | Physics, general | Statistical Physics, Dynamical Systems and Complexity | Physics | WEAK | QUANTUM MOLECULAR-DYNAMICS | PHYSICS, CONDENSED MATTER | SUPERCONDUCTIVITY | GINZBURG-LANDAU THEORY | SCHRODINGER-EQUATION | CONDENSATION | MICROSCOPIC DERIVATION

Condensed Matter Physics | Solid State Physics | Fluid- and Aerodynamics | Computational Methods | Physics, general | Statistical Physics, Dynamical Systems and Complexity | Physics | WEAK | QUANTUM MOLECULAR-DYNAMICS | PHYSICS, CONDENSED MATTER | SUPERCONDUCTIVITY | GINZBURG-LANDAU THEORY | SCHRODINGER-EQUATION | CONDENSATION | MICROSCOPIC DERIVATION

Journal Article

PloS one, ISSN 1932-6203, 2011, Volume 6, Issue 2, p. e17278

... Kitzmuller 5 , Barbara Bohle 5 , Christian G. Huber 3 , Fatima Ferreira 1 Introduction The development of a novel vaccine is a highly complex and demanding process...

BIRCH POLLEN ALLERGEN | LYSOSOMAL PROTEOLYSIS | IMMUNE-RESPONSE | ISOFORMS | IMMUNOTHERAPY | IN-VIVO | BIOLOGY | ANTIGEN PRESENTATION | PROTEASES | EPITOPES | VACCINES | Cell Line | Dendritic Cells - immunology | Humans | Mice, Inbred C57BL | Antibody Formation - physiology | Protein Processing, Post-Translational - physiology | Proteins - immunology | Mice, Knockout | Genes, p53 | Animals | Lysosomes - metabolism | Proteins - metabolism | Vaccines - biosynthesis | Bone Marrow Cells - immunology | Mice | Mice, Inbred BALB C | Protein Processing, Post-Translational - immunology | Lysosomes - immunology | Bone Marrow Cells - metabolism | Dendritic Cells - metabolism | Animal experimentation | Antigens | Medical research | Allergy | Immune response | Dendritic cells | Vaccines | Ribonuclease | T cells | Allergic reaction | Proteases | Proteolysis | Medicine, Experimental | Mass spectrometry | Peptides | Laboratories | Lymphocytes T | Allergic diseases | Assaying | Experiments | Degradation | Proteins | Protein composition | Immunology | Lymphocytes | Immunotherapy | Bone marrow | Bone composition | Antigen presentation | Bet v 1 antigen | Gel electrophoresis | Medical treatment | Hypersensitivity | Mass spectroscopy | Priming | T cell receptors | Allergies | Immunogenicity | Ligands | Kinetics | Molecular biology | In vitro methods and tests | Dendritic structure

BIRCH POLLEN ALLERGEN | LYSOSOMAL PROTEOLYSIS | IMMUNE-RESPONSE | ISOFORMS | IMMUNOTHERAPY | IN-VIVO | BIOLOGY | ANTIGEN PRESENTATION | PROTEASES | EPITOPES | VACCINES | Cell Line | Dendritic Cells - immunology | Humans | Mice, Inbred C57BL | Antibody Formation - physiology | Protein Processing, Post-Translational - physiology | Proteins - immunology | Mice, Knockout | Genes, p53 | Animals | Lysosomes - metabolism | Proteins - metabolism | Vaccines - biosynthesis | Bone Marrow Cells - immunology | Mice | Mice, Inbred BALB C | Protein Processing, Post-Translational - immunology | Lysosomes - immunology | Bone Marrow Cells - metabolism | Dendritic Cells - metabolism | Animal experimentation | Antigens | Medical research | Allergy | Immune response | Dendritic cells | Vaccines | Ribonuclease | T cells | Allergic reaction | Proteases | Proteolysis | Medicine, Experimental | Mass spectrometry | Peptides | Laboratories | Lymphocytes T | Allergic diseases | Assaying | Experiments | Degradation | Proteins | Protein composition | Immunology | Lymphocytes | Immunotherapy | Bone marrow | Bone composition | Antigen presentation | Bet v 1 antigen | Gel electrophoresis | Medical treatment | Hypersensitivity | Mass spectroscopy | Priming | T cell receptors | Allergies | Immunogenicity | Ligands | Kinetics | Molecular biology | In vitro methods and tests | Dendritic structure

Journal Article

Annales Henri Poincaré, ISSN 1424-0637, 5/2018, Volume 19, Issue 5, pp. 1507 - 1527

.../s00023-018-0665-7 Annales Henri Poincar´ e Persistence of T ranslational Symmetry in the BCS Model with Radial Pair Interaction Andreas Deuchert, Alissa Geisinger, Christian...

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | HARTREE-FOCK THEORY | LOW-DENSITY LIMIT | APPROXIMATION | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | BOGOLIUBOV-DE-GENNES | CRITICAL-TEMPERATURE | PHYSICS, MATHEMATICAL | MICROSCOPIC DERIVATION | PHYSICS, PARTICLES & FIELDS | Football (College)

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | HARTREE-FOCK THEORY | LOW-DENSITY LIMIT | APPROXIMATION | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | BOGOLIUBOV-DE-GENNES | CRITICAL-TEMPERATURE | PHYSICS, MATHEMATICAL | MICROSCOPIC DERIVATION | PHYSICS, PARTICLES & FIELDS | Football (College)

Journal Article

Journal of the American Mathematical Society, ISSN 0894-0347, 09/2012, Volume 25, Issue 3, pp. 667 - 713

We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close...

Integrands | Logical proofs | Superconductivity | Cubes | Ground state | Eigenfunctions | Mathematics | Mathematical functions | Critical temperature | BCS theory | MATHEMATICS | CRITICAL-TEMPERATURE | SUPERCONDUCTIVITY

Integrands | Logical proofs | Superconductivity | Cubes | Ground state | Eigenfunctions | Mathematics | Mathematical functions | Critical temperature | BCS theory | MATHEMATICS | CRITICAL-TEMPERATURE | SUPERCONDUCTIVITY

Journal Article

Experimental neurology, ISSN 0014-4886, 2015, Volume 269, pp. 75 - 89

The presence of neural stem/progenitor cells (NSPCs) in specific areas of the central nervous system (CNS) supports tissue maintenance as well as regeneration....

Neural Stem / Progenitor Cells | Subependymal Zone | Cell Survival | Subventricular Zone | Platelets | Vascular Niche | CNS damage | Neural stem / progenitor cells | Cell survival | Subependymal zone | Subventricular zone | Vascular niche | EXPERIMENTAL AUTOIMMUNE ENCEPHALOMYELITIS | ANGIOGENESIS | PRECURSOR CELL | NEUROSCIENCES | DISEASE | NEUROGENESIS | GROWTH-FACTOR | BRAIN | Adult Stem Cells - cytology | Mice, Inbred C57BL | Male | Neurons - cytology | Neural Stem Cells - cytology | Animals | Blood Platelets - cytology | Neurogenesis - physiology | Female | Demyelinating Diseases - pathology | Brain Injuries - pathology | Cell Differentiation - physiology | Cell Survival - physiology | Disease Models, Animal

Neural Stem / Progenitor Cells | Subependymal Zone | Cell Survival | Subventricular Zone | Platelets | Vascular Niche | CNS damage | Neural stem / progenitor cells | Cell survival | Subependymal zone | Subventricular zone | Vascular niche | EXPERIMENTAL AUTOIMMUNE ENCEPHALOMYELITIS | ANGIOGENESIS | PRECURSOR CELL | NEUROSCIENCES | DISEASE | NEUROGENESIS | GROWTH-FACTOR | BRAIN | Adult Stem Cells - cytology | Mice, Inbred C57BL | Male | Neurons - cytology | Neural Stem Cells - cytology | Animals | Blood Platelets - cytology | Neurogenesis - physiology | Female | Demyelinating Diseases - pathology | Brain Injuries - pathology | Cell Differentiation - physiology | Cell Survival - physiology | Disease Models, Animal

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 08/2013, Volume 265, Issue 3, pp. 399 - 423

We show that the time evolution of the wave function describing the macroscopic variations of the pair density in BCS theory can be approximated, in the dilute...

BEC–BCS crossover | Gross–Pitaevskii equation | Time-dependent BCS theory | Gross-Pitaevskii equation | BEC-BCS crossover | WEAK | MATHEMATICS | SUPERCONDUCTIVITY | TEMPERATURE | GINZBURG-LANDAU THEORY | CROSSOVER

BEC–BCS crossover | Gross–Pitaevskii equation | Time-dependent BCS theory | Gross-Pitaevskii equation | BEC-BCS crossover | WEAK | MATHEMATICS | SUPERCONDUCTIVITY | TEMPERATURE | GINZBURG-LANDAU THEORY | CROSSOVER

Journal Article

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Unconditional Uniqueness for the Cubic Gross-Pitaevskii Hierarchy via Quantum de Finetti

Communications on pure and applied mathematics, ISSN 0010-3640, 2015, Volume 68, Issue 10, pp. 1845 - 1884

We present a new, simpler proof of the unconditional uniqueness of solutions to the cubic Gross‐Pitaevskii hierarchy in ℝ3. One of the main tools in our...

RIGOROUS DERIVATION | MATHEMATICS | MATHEMATICS, APPLIED | MEAN-FIELD-LIMIT | CLASSICAL-LIMIT | DYNAMICS | NONLINEAR SCHRODINGER-EQUATION | GLOBAL WELL-POSEDNESS | BOSE-EINSTEIN CONDENSATION | BOSONS

RIGOROUS DERIVATION | MATHEMATICS | MATHEMATICS, APPLIED | MEAN-FIELD-LIMIT | CLASSICAL-LIMIT | DYNAMICS | NONLINEAR SCHRODINGER-EQUATION | GLOBAL WELL-POSEDNESS | BOSE-EINSTEIN CONDENSATION | BOSONS

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 5/2013, Volume 208, Issue 2, pp. 603 - 665

... acuum in Electromagnetic Fields Philippe Gravejat, Christian Hainzl, Mathieu Lewin & Éric Séré Communicated by C. Le Bris Abstract Using the Pauli–Villars...

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | CHARGE RENORMALIZATION | POLARIZED VACUUM | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | APPROXIMATION | POSITRON THEORY | STABILITY | QUANTUM ELECTRODYNAMICS | MODEL | Construction | Mathematical Physics | Mathematics

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | CHARGE RENORMALIZATION | POLARIZED VACUUM | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | APPROXIMATION | POSITRON THEORY | STABILITY | QUANTUM ELECTRODYNAMICS | MODEL | Construction | Mathematical Physics | Mathematics

Journal Article

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Translation-invariant quasi-free states for fermionic systems and the BCS approximation

Reviews in Mathematical Physics, ISSN 0129-055X, 08/2014, Volume 26, Issue 7, p. 1450012

We study translation-invariant quasi-free states for a system of fermions with two-particle interactions. The associated energy functional is similar to the...

critical temperature | BCS functional | Birman-Schwinger principle | quasi-free states | Superconductivity | WEAK | MODEL | FOCK-BOGOLIUBOV THEORY | CRITICAL-TEMPERATURE | PHYSICS, MATHEMATICAL | Football (College)

critical temperature | BCS functional | Birman-Schwinger principle | quasi-free states | Superconductivity | WEAK | MODEL | FOCK-BOGOLIUBOV THEORY | CRITICAL-TEMPERATURE | PHYSICS, MATHEMATICAL | Football (College)

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 2/2016, Volume 342, Issue 1, pp. 189 - 216

... Dependence of the BCS Critical T emperature Rupert L. Frank 1 , Christian Hainzl 2 , Robert Seiringer 3 , Jan Philip Solovej 4 1 Mathematics 253-37, Caltech, Pasadena...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | SUPERCONDUCTIVITY | MODEL | PHYSICS, MATHEMATICAL | MICROSCOPIC DERIVATION | Football (College)

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | SUPERCONDUCTIVITY | MODEL | PHYSICS, MATHEMATICAL | MICROSCOPIC DERIVATION | Football (College)

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 5/2012, Volume 100, Issue 2, pp. 119 - 138

...DOI 10.1007/s11005-011-0535-4 Lett Math Phys (2012) 100:119–138 Low Density Limit of BCS Theory and Bose–Einstein Condensation of Fermion Pairs CHRISTIAN...

Bose–Einstein condensation | Theoretical, Mathematical and Computational Physics | 82D50 | semiclassics | Statistical Physics, Dynamical Systems and Complexity | Physics | Geometry | 46N50 | Cooper pairs | dilute Bose gas | Group Theory and Generalizations | 81Q10 | superfluidity | Bose-Einstein condensation | WEAK | SUPERCONDUCTIVITY | GAS | CROSSOVER | CRITICAL-TEMPERATURE | PHYSICS, MATHEMATICAL | VORTEX

Bose–Einstein condensation | Theoretical, Mathematical and Computational Physics | 82D50 | semiclassics | Statistical Physics, Dynamical Systems and Complexity | Physics | Geometry | 46N50 | Cooper pairs | dilute Bose gas | Group Theory and Generalizations | 81Q10 | superfluidity | Bose-Einstein condensation | WEAK | SUPERCONDUCTIVITY | GAS | CROSSOVER | CRITICAL-TEMPERATURE | PHYSICS, MATHEMATICAL | VORTEX

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 6/2009, Volume 192, Issue 3, pp. 453 - 499

... Approximation of No-Photon Quantum Electrodynamics Christian Hainzl, Mathieu Lewin & Éric Séré Communicated by G. Friesecke Abstract The Bogoliubov–Dirac–Fock (BDF) model...

Essential Spectrum | Fluid- and Aerodynamics | Weak Coupling Regime | Theoretical, Mathematical and Computational Physics | Complex Systems | Classical Mechanics | Physics, general | Charge Sector | Quantum Electrodynamic | Lewin | Physics | MATHEMATICS, APPLIED | VARIATIONAL PRINCIPLE | POLARIZED VACUUM | ENERGY | MECHANICS | ELECTRONS | STABILITY | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | DIRAC-FOCK EQUATIONS | PAIR | Atoms | Analysis | Electric fields | Mathematical Physics | Mathematics

Essential Spectrum | Fluid- and Aerodynamics | Weak Coupling Regime | Theoretical, Mathematical and Computational Physics | Complex Systems | Classical Mechanics | Physics, general | Charge Sector | Quantum Electrodynamic | Lewin | Physics | MATHEMATICS, APPLIED | VARIATIONAL PRINCIPLE | POLARIZED VACUUM | ENERGY | MECHANICS | ELECTRONS | STABILITY | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | DIRAC-FOCK EQUATIONS | PAIR | Atoms | Analysis | Electric fields | Mathematical Physics | Mathematics

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 10/2015, Volume 105, Issue 10, pp. 1449 - 1466

...Lett Math Phys (2015) 105:1449–1466 DOI 10.1007/s11005-015-0787-5 Note on a Family of Monotone Quantum Relative Entropies ANDREAS DEUCHERT 1 , CHRISTIAN HAINZL...

Geometry | 46N50 | 81Q99 | Theoretical, Mathematical and Computational Physics | relative entropy | 47A99 | Group Theory and Generalizations | operator monotonicity | Statistical Physics, Dynamical Systems and Complexity | Physics | PHYSICS, MATHEMATICAL

Geometry | 46N50 | 81Q99 | Theoretical, Mathematical and Computational Physics | relative entropy | 47A99 | Group Theory and Generalizations | operator monotonicity | Statistical Physics, Dynamical Systems and Complexity | Physics | PHYSICS, MATHEMATICAL

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 7/2016, Volume 106, Issue 7, pp. 913 - 923

.... FRANK 1 , CHRISTIAN HAINZL 2 , BENJAMIN SCHLEIN 3 and ROBERT SEIRINGER 4 1 2 Mathematics 253-37, Caltech, Pasadena, CA 91125, USA. Mathematisches Institut...

Geometry | critical temperature | 46N50 | superconductivity | Theoretical, Mathematical and Computational Physics | 82D50 | Group Theory and Generalizations | Statistical Physics, Dynamical Systems and Complexity | quasi-free states | Physics | BCS theory | WEAK | FERMION PAIRS | LOW-DENSITY LIMIT | DYNAMICS | CONDENSATION | CRITICAL-TEMPERATURE | PHYSICS, MATHEMATICAL

Geometry | critical temperature | 46N50 | superconductivity | Theoretical, Mathematical and Computational Physics | 82D50 | Group Theory and Generalizations | Statistical Physics, Dynamical Systems and Complexity | quasi-free states | Physics | BCS theory | WEAK | FERMION PAIRS | LOW-DENSITY LIMIT | DYNAMICS | CONDENSATION | CRITICAL-TEMPERATURE | PHYSICS, MATHEMATICAL

Journal Article

Oberwolfach Reports, ISSN 1660-8933, 2016, Volume 13, Issue 3, pp. 2465 - 2511

In the last years, substantial progress has been made in many areas of mathematical physics. The goal of this workshop was to bring together researchers...

Partial differential equations | Quantum theory | Statistical mechanics, structure of matter

Partial differential equations | Quantum theory | Statistical mechanics, structure of matter

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 09/2012, Volume 53, Issue 9, p. 95220

...JOURNAL OF MATHEMATICAL PHYSICS 53, 095220 (2012) Ground state properties of graphene in Hartree-Fock theory Christian Hainzl, 1,a) Mathieu Lewin, 2,b...

CHARGE RENORMALIZATION | MINIMAL CONDUCTIVITY | ELECTRON-POSITRON FIELD | POLARIZED VACUUM | DIRAC FERMIONS | STABILITY | MEAN-FIELD APPROXIMATION | QUANTUM ELECTRODYNAMICS | PHYSICS, MATHEMATICAL | NONLINEAR MODEL | BILAYER GRAPHENE | Construction | Coulomb friction | Approximation | Graphene | Mathematical analysis | Ground state | Electric fields | Defects | Condensed Matter | Mathematics | Mathematical Physics | Physics | Other

CHARGE RENORMALIZATION | MINIMAL CONDUCTIVITY | ELECTRON-POSITRON FIELD | POLARIZED VACUUM | DIRAC FERMIONS | STABILITY | MEAN-FIELD APPROXIMATION | QUANTUM ELECTRODYNAMICS | PHYSICS, MATHEMATICAL | NONLINEAR MODEL | BILAYER GRAPHENE | Construction | Coulomb friction | Approximation | Graphene | Mathematical analysis | Ground state | Electric fields | Defects | Condensed Matter | Mathematics | Mathematical Physics | Physics | Other

Journal Article

Physical Review B - Condensed Matter and Materials Physics, ISSN 1098-0121, 05/2008, Volume 77, Issue 18

We derive upper and lower bounds on the critical temperature T-c and the energy gap Xi (at zero temperature) for the BCS gap equation, describing spin-1/2...

WEAK | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | MATERIALS SCIENCE, MULTIDISCIPLINARY | SPIN | CRITICAL TEMPERATURE | EQUATIONS | FERMIONS | CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY | POTENTIALS | COUPLING | INTERACTIONS | ENERGY GAP | TWO-BODY PROBLEM | SCATTERING LENGTHS | TEMPERATURE ZERO K | BCS THEORY

WEAK | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | MATERIALS SCIENCE, MULTIDISCIPLINARY | SPIN | CRITICAL TEMPERATURE | EQUATIONS | FERMIONS | CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY | POTENTIALS | COUPLING | INTERACTIONS | ENERGY GAP | TWO-BODY PROBLEM | SCATTERING LENGTHS | TEMPERATURE ZERO K | BCS THEORY

Journal Article

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Bogolubov–Hartree–Fock Theory for Strongly Interacting Fermions in the Low Density Limit

Mathematical Physics, Analysis and Geometry, ISSN 1385-0172, 6/2016, Volume 19, Issue 2, pp. 1 - 27

... Gerhard Br¨ aunlich 1 · Christian Hainzl 2 · Robert Seiringer 3 Received: 25 November 2015 / Accepted: 3 January 2016 / Published online: 8 June 2016 © The Author...

Low density limit | Theoretical, Mathematical and Computational Physics | 82D50 | BCS-theory | Physics | Geometry | 46N50 | Bogolubov-Hartree-Fock functional | Analysis | Group Theory and Generalizations | Gross-Pitaevskii functional | Applications of Mathematics | 81Q10 | Pairing | Bose-Einstein condensation | WEAK | MATHEMATICS, APPLIED | BCS | TEMPERATURE | CONDENSATION | PHYSICS, MATHEMATICAL

Low density limit | Theoretical, Mathematical and Computational Physics | 82D50 | BCS-theory | Physics | Geometry | 46N50 | Bogolubov-Hartree-Fock functional | Analysis | Group Theory and Generalizations | Gross-Pitaevskii functional | Applications of Mathematics | 81Q10 | Pairing | Bose-Einstein condensation | WEAK | MATHEMATICS, APPLIED | BCS | TEMPERATURE | CONDENSATION | PHYSICS, MATHEMATICAL

Journal Article