Letters in mathematical physics, ISSN 1573-0530, 2013, Volume 104, Issue 2, pp. 141 - 156

We consider two-dimensional Bose–Einstein condensates with attractive interaction, described by the Gross–Pitaevskii functional. Minimizers of this functional...

symmetry breaking | Bose–Einstein condensation | Theoretical, Mathematical and Computational Physics | 82D50 | Statistical Physics, Dynamical Systems and Complexity | 35Q40 | Physics | Geometry | 46N50 | mass concentration | Gross–Pitaevskii functional | attractive interactions | Group Theory and Generalizations | Gross-Pitaevskii functional | Bose-Einstein condensation | NONLINEAR SCHRODINGER-EQUATIONS | POSITIVE SOLUTIONS | PHYSICS, MATHEMATICAL | VORTEX | UNIQUENESS | BOUND-STATES | COLLAPSE | GAS | BIFURCATION | SYMMETRY-BREAKING

symmetry breaking | Bose–Einstein condensation | Theoretical, Mathematical and Computational Physics | 82D50 | Statistical Physics, Dynamical Systems and Complexity | 35Q40 | Physics | Geometry | 46N50 | mass concentration | Gross–Pitaevskii functional | attractive interactions | Group Theory and Generalizations | Gross-Pitaevskii functional | Bose-Einstein condensation | NONLINEAR SCHRODINGER-EQUATIONS | POSITIVE SOLUTIONS | PHYSICS, MATHEMATICAL | VORTEX | UNIQUENESS | BOUND-STATES | COLLAPSE | GAS | BIFURCATION | SYMMETRY-BREAKING

Journal Article

Communications in partial differential equations, ISSN 1532-4133, 2014, Volume 40, Issue 7, pp. 1314 - 1335

We consider a general Euler-Korteweg-Poisson system in R 3 , supplemented with the space periodic boundary conditions, where the quantum hydrodynamics...

Convex integration | Weak solution | Primary: 35Q35, 35Q53 | Secondary: 76N10, 82D50 | Quantum hydrodynamics | Euler-Korteweg system | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | WAVES | FLUID-DYNAMICS | SUITABLE WEAK SOLUTIONS | EQUATIONS | MODEL | UNIQUE CONTINUATION | Fluid dynamics | Dynamics | Mathematical analysis | Dissipation | Inequalities | Dynamical systems | Density | Cauchy problem

Convex integration | Weak solution | Primary: 35Q35, 35Q53 | Secondary: 76N10, 82D50 | Quantum hydrodynamics | Euler-Korteweg system | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | WAVES | FLUID-DYNAMICS | SUITABLE WEAK SOLUTIONS | EQUATIONS | MODEL | UNIQUE CONTINUATION | Fluid dynamics | Dynamics | Mathematical analysis | Dissipation | Inequalities | Dynamical systems | Density | Cauchy problem

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 1420-9039, 2013, Volume 65, Issue 3, pp. 531 - 548

In this paper, the velocity profile of the normal component in the stationary flow of turbulent superfluid helium inside a cylindrical channel is determined,...

Quantized vortices | Engineering | Mathematical Methods in Physics | One-fluid model | 76F99 | Turbulent superfluid helium | 82D50 | Normal fluid profile | Theoretical and Applied Mechanics | 35G15 | Heat transfer | MATHEMATICS, APPLIED | SUPERFLUID TURBULENCE | EXTENDED IRREVERSIBLE THERMODYNAMICS | 4TH SOUND | PROPAGATION | Thermodynamics | Analysis

Quantized vortices | Engineering | Mathematical Methods in Physics | One-fluid model | 76F99 | Turbulent superfluid helium | 82D50 | Normal fluid profile | Theoretical and Applied Mechanics | 35G15 | Heat transfer | MATHEMATICS, APPLIED | SUPERFLUID TURBULENCE | EXTENDED IRREVERSIBLE THERMODYNAMICS | 4TH SOUND | PROPAGATION | Thermodynamics | Analysis

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 1420-9039, 2017, Volume 69, Issue 1, pp. 1 - 15

This work is the first of a series of papers devoted to the study of the influence of the anisotropy and polarization of the tangle of quantized vortex lines...

Quantized vortices | Engineering | Mathematical Methods in Physics | 76F99 | Quantum turbulence | 82D50 | Theoretical and Applied Mechanics | Anisotropic and polarized turbulence | Inhomogeneous vortex tangle | 35G15 | LIQUID-HELIUM-II | ROTATION | MATHEMATICS, APPLIED | 2ND SOUND | EQUATIONS | EXTENDED IRREVERSIBLE THERMODYNAMICS | COUNTERFLOW | TANGLE | CONTINUUM THEORY | PROPAGATION | Thermodynamics | Turbulence | Anisotropy | Analysis

Quantized vortices | Engineering | Mathematical Methods in Physics | 76F99 | Quantum turbulence | 82D50 | Theoretical and Applied Mechanics | Anisotropic and polarized turbulence | Inhomogeneous vortex tangle | 35G15 | LIQUID-HELIUM-II | ROTATION | MATHEMATICS, APPLIED | 2ND SOUND | EQUATIONS | EXTENDED IRREVERSIBLE THERMODYNAMICS | COUNTERFLOW | TANGLE | CONTINUUM THEORY | PROPAGATION | Thermodynamics | Turbulence | Anisotropy | Analysis

Journal Article

Ricerche di Matematica, ISSN 0035-5038, 12/2019, Volume 68, Issue 2, pp. 315 - 331

In this paper, temperature waves (also known as second sound) are considered, with their respective coupling with waves in the order parameter describing the...

35G50 | 76F99 | 76Fxx | Probability Theory and Stochastic Processes | 82D50 | Mathematics | 80A20 | Geometry | Superfluid helium | Algebra | Analysis | Numerical Analysis | Lambda phase transition | Mathematics, general | Second sound | Quantum vortices | MATHEMATICS | MATHEMATICS, APPLIED | HEAT CURRENT

35G50 | 76F99 | 76Fxx | Probability Theory and Stochastic Processes | 82D50 | Mathematics | 80A20 | Geometry | Superfluid helium | Algebra | Analysis | Numerical Analysis | Lambda phase transition | Mathematics, general | Second sound | Quantum vortices | MATHEMATICS | MATHEMATICS, APPLIED | HEAT CURRENT

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 4/2017, Volume 56, Issue 2, pp. 1 - 40

We consider a gas of fermions at zero temperature and low density, interacting via a microscopic two-body potential which admits a bound state. The particles...

46N50 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 82D50 | Mathematics | 81Q10 | MATHEMATICS | HARTREE-FOCK THEORY | MATHEMATICS, APPLIED | LOW-DENSITY LIMIT | SUPERCONDUCTIVITY | GINZBURG-LANDAU THEORY | CONSTANT | CRITICAL-TEMPERATURE | HARDYS INEQUALITY | BCS THEORY | ELLIPTIC-OPERATORS | MICROSCOPIC DERIVATION

46N50 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 82D50 | Mathematics | 81Q10 | MATHEMATICS | HARTREE-FOCK THEORY | MATHEMATICS, APPLIED | LOW-DENSITY LIMIT | SUPERCONDUCTIVITY | GINZBURG-LANDAU THEORY | CONSTANT | CRITICAL-TEMPERATURE | HARDYS INEQUALITY | BCS THEORY | ELLIPTIC-OPERATORS | MICROSCOPIC DERIVATION

Journal Article

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

We study the time-dependent Bogoliubov–de-Gennes equations for generic translation-invariant fermionic many-body systems. For initial states that are close to...

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

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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

We consider the Bogolubov–Hartree–Fock functional for a fermionic many-body system with two-body interactions. For suitable interaction potentials that have a...

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

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 8/2013, Volume 64, Issue 4, pp. 1387 - 1397

In this paper, we propose a thermodynamically consistent model for superfluid-normal phase transition in liquid helium, accounting for variations of...

Engineering | 82C26 | Thermodynamics | Mathematical Methods in Physics | Ginzburg–Landau equation | 74A15 | 82D50 | Second-order phase transitions | Theoretical and Applied Mechanics | Superfluids | Ginzburg-Landau equation | MATHEMATICS, APPLIED | PHASE-TRANSITIONS | EQUATIONS | ORDER-PARAMETER | Analysis

Engineering | 82C26 | Thermodynamics | Mathematical Methods in Physics | Ginzburg–Landau equation | 74A15 | 82D50 | Second-order phase transitions | Theoretical and Applied Mechanics | Superfluids | Ginzburg-Landau equation | MATHEMATICS, APPLIED | PHASE-TRANSITIONS | EQUATIONS | ORDER-PARAMETER | Analysis

Journal Article

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

We consider the low-density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the...

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

Letters in Mathematical Physics, ISSN 0377-9017, 6/2012, Volume 100, Issue 3, pp. 237 - 243

A positive temperature analogue of the scattering length of a potential V can be defined via integrating the difference of the heat kernels of −Δ and...

Geometry | 46N50 | Bose–Einstein condensation | Theoretical, Mathematical and Computational Physics | heat kernel | Schrödinger operator | 82D50 | Group Theory and Generalizations | 81Q10 | Statistical Physics, Dynamical Systems and Complexity | Physics | scattering length | Bose-Einstein condensation | Schrodinger operator | PHYSICS, MATHEMATICAL

Geometry | 46N50 | Bose–Einstein condensation | Theoretical, Mathematical and Computational Physics | heat kernel | Schrödinger operator | 82D50 | Group Theory and Generalizations | 81Q10 | Statistical Physics, Dynamical Systems and Complexity | Physics | scattering length | Bose-Einstein condensation | Schrodinger operator | PHYSICS, MATHEMATICAL

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 1420-9039, 2012, Volume 64, Issue 2, pp. 329 - 341

In this paper, we analyze a multi-temperature model for the description of second sound propagation with an application to superfluid helium. To this aim, we...

Hydrodynamic aspects of superfluidity | Engineering | Mathematical Methods in Physics | 35L60 | 80A17 | 76A25 | 74J30 | Multi-temperature mixture of fluids | 82D50 | Second sound propagation | Theoretical and Applied Mechanics | FLUIDS | MATHEMATICS, APPLIED | HELIUM II | HYPERBOLIC SYSTEMS | CONVEX ENTROPY | SHOCK-WAVES | TEMPERATURE | SUPERFLUID-HELIUM | CONSERVATION EQUATIONS | GAS | CONDUCTION | Analysis | Wave propagation | Fluids | Approximation | Sound propagation | Computational fluid dynamics | Fluid flow | Mathematical models | Inert | Helium

Hydrodynamic aspects of superfluidity | Engineering | Mathematical Methods in Physics | 35L60 | 80A17 | 76A25 | 74J30 | Multi-temperature mixture of fluids | 82D50 | Second sound propagation | Theoretical and Applied Mechanics | FLUIDS | MATHEMATICS, APPLIED | HELIUM II | HYPERBOLIC SYSTEMS | CONVEX ENTROPY | SHOCK-WAVES | TEMPERATURE | SUPERFLUID-HELIUM | CONSERVATION EQUATIONS | GAS | CONDUCTION | Analysis | Wave propagation | Fluids | Approximation | Sound propagation | Computational fluid dynamics | Fluid flow | Mathematical models | Inert | Helium

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 12/2007, Volume 17, Issue 4, pp. 559 - 567

For the BCS equation with local two-body interaction λV(x), we give a rigorous analysis of the asymptotic behavior of the critical temperature as γ»0. We...

82D50 | Mathematics | Birman-Schwinger kemel | Abstract Harmonic Analysis | critical temperature | 46N50 | Gap equation | Fourier Analysis | degenerate symbols | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | 81Q10 | Differential Geometry | Dynamical Systems and Ergodic Theory | Birman-Schwinger kernel | MATHEMATICS | gap equation

82D50 | Mathematics | Birman-Schwinger kemel | Abstract Harmonic Analysis | critical temperature | 46N50 | Gap equation | Fourier Analysis | degenerate symbols | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | 81Q10 | Differential Geometry | Dynamical Systems and Ergodic Theory | Birman-Schwinger kernel | MATHEMATICS | gap equation

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 6/2008, Volume 84, Issue 2, pp. 99 - 107

We prove that the critical temperature for the BCS gap equation is given by $${T_c = \mu \left( \frac 8\pi {\rm e}^{\gamma -2} + o(1) \right) {\rm...

Geometry | 46N50 | Mathematical and Computational Physics | Birman–Schwinger principle | 82D50 | Group Theory and Generalizations | BCS equation | 81Q10 | superfluidity | Physics | Statistical Physics | scattering length | Scattering length | Birman-Schwinger principle | Superfluidity | WEAK | SUPERCONDUCTIVITY | GAS | STATE | PHYSICS, MATHEMATICAL | Football (College)

Geometry | 46N50 | Mathematical and Computational Physics | Birman–Schwinger principle | 82D50 | Group Theory and Generalizations | BCS equation | 81Q10 | superfluidity | Physics | Statistical Physics | scattering length | Scattering length | Birman-Schwinger principle | Superfluidity | WEAK | SUPERCONDUCTIVITY | GAS | STATE | PHYSICS, MATHEMATICAL | Football (College)

Journal Article

Revista Matemática Iberoamericana, ISSN 0213-2230, 2008, Volume 24, Issue 2, pp. 671 - 702

We derive the asymptotical dynamical law for Ginzburg-Landau vortices in the plane under the Schrödinger dynamics, as the Ginz\-burg-Landau parameter goes to...

Partial differential equations | General | Statistical mechanics, structure of matter | Nls equation | Vortex dynamics | Superfluids | MATHEMATICS | superfluids | GINZBURG-LANDAU EQUATION | NLS equation | FUNCTIONALS | MINIMIZERS | vortex dynamics | 35Q55 | 35B20 | 82D50 | 35B40

Partial differential equations | General | Statistical mechanics, structure of matter | Nls equation | Vortex dynamics | Superfluids | MATHEMATICS | superfluids | GINZBURG-LANDAU EQUATION | NLS equation | FUNCTIONALS | MINIMIZERS | vortex dynamics | 35Q55 | 35B20 | 82D50 | 35B40

Journal Article

16.
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Contribution of the normal component to the thermal resistance of turbulent liquid helium

Zeitschrift für angewandte Mathematik und Physik, ISSN 1420-9039, 2015, Volume 66, Issue 4, pp. 1853 - 1870

Previous results for the velocity profile of the normal component of helium II in counterflow are used to evaluate the viscous contribution to the effective...

Engineering | Mathematical Methods in Physics | Superfluid helium | Thermal resistance | 76F99 | 82D50 | Quantum turbulence | Theoretical and Applied Mechanics | Normal component | VISUALIZATION | TRANSITION | MATHEMATICS, APPLIED | CONDUCTIVITY | EXTENDED IRREVERSIBLE THERMODYNAMICS | DIFFUSION | COUNTERFLOW | PROPAGATION | Turbulence | Turbulent flow | Computational fluid dynamics | Fluid flow | Liquid helium | Estimates | Heat transfer

Engineering | Mathematical Methods in Physics | Superfluid helium | Thermal resistance | 76F99 | 82D50 | Quantum turbulence | Theoretical and Applied Mechanics | Normal component | VISUALIZATION | TRANSITION | MATHEMATICS, APPLIED | CONDUCTIVITY | EXTENDED IRREVERSIBLE THERMODYNAMICS | DIFFUSION | COUNTERFLOW | PROPAGATION | Turbulence | Turbulent flow | Computational fluid dynamics | Fluid flow | Liquid helium | Estimates | Heat transfer

Journal Article

Acta Mathematica Scientia, ISSN 0252-9602, 03/2016, Volume 36, Issue 2, pp. 317 - 324

Starting with the many-body Schrödinger Hamiltonian in ▪, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise...

46N50 | attractive interactions | mean-field approximation | 82D50 | Gross-Pitaevskii functional | 35Q40 | Bose-Einstein condensation | Approximation | Mathematical analysis | Bose-Einstein condensates | Scattering | Ground state | Schroedinger equation | Hamiltonian functions | Two dimensional

46N50 | attractive interactions | mean-field approximation | 82D50 | Gross-Pitaevskii functional | 35Q40 | Bose-Einstein condensation | Approximation | Mathematical analysis | Bose-Einstein condensates | Scattering | Ground state | Schroedinger equation | Hamiltonian functions | Two dimensional

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 1420-9039, 2013, Volume 64, Issue 5, pp. 1571 - 1586

In this work, a hydrodynamical model of Superfluid Turbulence previously formulated is applied to study how the presence of a non-isotropic turbulent vortex...

Quantized vortices | Engineering | Mathematical Methods in Physics | Anisotropic superfluid turbulence | Perturbation method | Wave propagation | 82D50 | Second sound | 76Yxx | Theoretical and Applied Mechanics | LIQUID-HELIUM-II | DENSITY WAVES | MATHEMATICS, APPLIED | 2ND SOUND | HE-4 | 4TH SOUND | TANGLE | 3-DIMENSIONAL VORTEX DYNAMICS | EXTENDED THERMODYNAMICS | Turbulence | Anisotropy | Analysis | Computational fluid dynamics

Quantized vortices | Engineering | Mathematical Methods in Physics | Anisotropic superfluid turbulence | Perturbation method | Wave propagation | 82D50 | Second sound | 76Yxx | Theoretical and Applied Mechanics | LIQUID-HELIUM-II | DENSITY WAVES | MATHEMATICS, APPLIED | 2ND SOUND | HE-4 | 4TH SOUND | TANGLE | 3-DIMENSIONAL VORTEX DYNAMICS | EXTENDED THERMODYNAMICS | Turbulence | Anisotropy | Analysis | Computational fluid dynamics

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 11/1991, Volume 141, Issue 3, pp. 619 - 631

The thermodynamic functions and scaling exponents (including the Kolmogorov and Flory exponents) of a vortex filament in thermal equilibrium are calculated,...

TURBULENCE | MODEL | PHYSICS, MATHEMATICAL | LATTICE | 76M35 | 82D50 | 82B43 | 76F99

TURBULENCE | MODEL | PHYSICS, MATHEMATICAL | LATTICE | 76M35 | 82D50 | 82B43 | 76F99

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 7/2003, Volume 54, Issue 4, pp. 566 - 583

This work continues a study begun in previous works, where, using Extended Thermodynamics, a monofluid model of liquid helium II is formulated. The wave...

Extended Thermodynamics | Liquid helium II | 82D50 | 76S05 | Mathematics | 80A20 | Superfluids | Superfiuids | MATHEMATICS, APPLIED | superfluids | extended thermodynamics | ATTENUATION | MODEL | HEII | SUPERFLUIDITY | liquid helium II | Thermodynamics | Analysis | Knowledge-based systems

Extended Thermodynamics | Liquid helium II | 82D50 | 76S05 | Mathematics | 80A20 | Superfluids | Superfiuids | MATHEMATICS, APPLIED | superfluids | extended thermodynamics | ATTENUATION | MODEL | HEII | SUPERFLUIDITY | liquid helium II | Thermodynamics | Analysis | Knowledge-based systems

Journal Article

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