DOI

1

Homogeneous isotropic superfluid turbulence in two dimensions: Inverse and forward cascades in the Hall-Vinen-Bekharevich-Khalatnikov model - Shukla, Vishwanath and Gupta, Anupam and Pandit, Rahul

PHYSICAL REVIEW B 92, (2015)

Abstract : We present the first direct-numerical-simulation study of the statistical properties of two-dimensional superfluid turbulence in the simplified, Hall-Vinen-Bekharevich-Khalatnikov two-fluid model. We show that both normalfluid and superfluid energy spectra can exhibit two power-law regimes, the first associated with an inverse cascade of energy and the second with the forward cascade of enstrophy. We quantify the mutual-friction-induced alignment of normal and superfluid velocities by obtaining probability distribution functions of the angle between them and the ratio of their moduli.

PHYSICAL REVIEW B 92, (2015)

Abstract : We present the first direct-numerical-simulation study of the statistical properties of two-dimensional superfluid turbulence in the simplified, Hall-Vinen-Bekharevich-Khalatnikov two-fluid model. We show that both normalfluid and superfluid energy spectra can exhibit two power-law regimes, the first associated with an inverse cascade of energy and the second with the forward cascade of enstrophy. We quantify the mutual-friction-induced alignment of normal and superfluid velocities by obtaining probability distribution functions of the angle between them and the ratio of their moduli.

DOI

2

Dislocation networks in He-4 crystals - Fefferman, A. D. and Souris, F. and Haziot, A. and Beamish, J. R. and Balibar, S.

PHYSICAL REVIEW B 89, (2014)

Abstract : The mechanical behavior of crystals is dominated by dislocation networks, their structure, and their interactions with impurities or thermal phonons. However, in classical crystals, networks are usually random with impurities often forming nonequilibrium clusters when their motion freezes at low temperature. Helium provides unique advantages for the study of dislocations: Crystals are free of all but isotopic impurities, the concentration of these can be reduced to the parts per 10(9) (ppb) level, and the impurities are mobile at all temperatures and therefore remain in equilibrium with the dislocations. We have achieved a comprehensive study of the mechanical response of He-4 crystals to a driving strain as a function of temperature, frequency, and strain amplitude. The quality of our fits to the complete set of data strongly supports our assumption of stringlike vibrating dislocations. It leads to a precise determination of the distribution of dislocation network lengths and to detailed information about the interaction between dislocations and both thermal phonons and He-3 impurities. The width of the dissipation peak associated with impurity binding is larger than predicted by a simple Debye model, and much of this broadening is due to the distribution of network lengths.

PHYSICAL REVIEW B 89, (2014)

Abstract : The mechanical behavior of crystals is dominated by dislocation networks, their structure, and their interactions with impurities or thermal phonons. However, in classical crystals, networks are usually random with impurities often forming nonequilibrium clusters when their motion freezes at low temperature. Helium provides unique advantages for the study of dislocations: Crystals are free of all but isotopic impurities, the concentration of these can be reduced to the parts per 10(9) (ppb) level, and the impurities are mobile at all temperatures and therefore remain in equilibrium with the dislocations. We have achieved a comprehensive study of the mechanical response of He-4 crystals to a driving strain as a function of temperature, frequency, and strain amplitude. The quality of our fits to the complete set of data strongly supports our assumption of stringlike vibrating dislocations. It leads to a precise determination of the distribution of dislocation network lengths and to detailed information about the interaction between dislocations and both thermal phonons and He-3 impurities. The width of the dissipation peak associated with impurity binding is larger than predicted by a simple Debye model, and much of this broadening is due to the distribution of network lengths.

DOI

3

Diagrammatic Monte Carlo study of the Fermi polaron in two dimensions - Vlietinck, Jonas and Ryckebusch, Jan and Van Houcke, Kris

PHYSICAL REVIEW B 89, (2014)

Abstract : We study the properties of the two-dimensional Fermi polaron model in which an impurity attractively interacts with a Fermi sea of particles in the zero-range limit. We use a diagrammatic Monte Carlo (DiagMC) method which allows us to sample a Feynman diagrammatic series to very high order. The convergence properties of the series and the role of multiple particle-hole excitations are discussed. We study the polaron and molecule energy as a function of the coupling strength, revealing a transition from a polaron to a molecule in the ground state. We find a value for the critical interaction strength which complies with the experimentally measured one and predictions from variational methods. For all considered interaction strengths, the polaron Z factor from the full diagrammatic series almost coincides with the one-particle-hole result. We also formally link the DiagMC and the variational approaches for the polaron problem at hand.

PHYSICAL REVIEW B 89, (2014)

Abstract : We study the properties of the two-dimensional Fermi polaron model in which an impurity attractively interacts with a Fermi sea of particles in the zero-range limit. We use a diagrammatic Monte Carlo (DiagMC) method which allows us to sample a Feynman diagrammatic series to very high order. The convergence properties of the series and the role of multiple particle-hole excitations are discussed. We study the polaron and molecule energy as a function of the coupling strength, revealing a transition from a polaron to a molecule in the ground state. We find a value for the critical interaction strength which complies with the experimentally measured one and predictions from variational methods. For all considered interaction strengths, the polaron Z factor from the full diagrammatic series almost coincides with the one-particle-hole result. We also formally link the DiagMC and the variational approaches for the polaron problem at hand.

DOI

4

Belief-propagation-guided Monte-Carlo sampling - Decelle, Aurelien and Krzakala, Florent

PHYSICAL REVIEW B 89, (2014)

Abstract : A Monte-Carlo algorithm for discrete statistical models that combines the full power of the belief-propagation algorithm with the advantages of a heat-bath approach fulfilling the detailed balance is presented. First we extract randomly a subtree inside the interaction graph of the system. Second, given the boundary conditions, belief propagation is used as a perfect sampler to generate a configuration on the tree, and finally, the procedure is iterated. This approach is best adapted for locally treelike graphs and we therefore tested it on random graphs for hard models such as spin glasses, demonstrating its state-of-the art status in those cases.

PHYSICAL REVIEW B 89, (2014)

Abstract : A Monte-Carlo algorithm for discrete statistical models that combines the full power of the belief-propagation algorithm with the advantages of a heat-bath approach fulfilling the detailed balance is presented. First we extract randomly a subtree inside the interaction graph of the system. Second, given the boundary conditions, belief propagation is used as a perfect sampler to generate a configuration on the tree, and finally, the procedure is iterated. This approach is best adapted for locally treelike graphs and we therefore tested it on random graphs for hard models such as spin glasses, demonstrating its state-of-the art status in those cases.

DOI

5

Movement of dislocations dressed with He-3 impurities in He-4 crystals - Souris, Fabien and Fefferman, Andrew D. and Maris, Humphrey J. and Dauvois, Vincent and Jean-Baptiste, Philippe and Beamish, John R. and Balibar, Sebastien

PHYSICAL REVIEW B 90, (2014)

Abstract : Solid He-4 is a unique example of crystal where dislocations may move at macroscopic speeds with impurities attached to them. In He-4 crystals, the only impurities are He-3 atoms, whose concentration can be reduced to zero and measured down to the ppt (10(-12)) level. We present measurements of the mobility of dislocations dressed with He-3 impurities as a function of the crystal purity. They show that the damping of dislocation motion is proportional to the concentration of He-3 bound to these dislocations. It has allowed us to measure the He-3 binding energy E-B to dislocations without any ambiguity. Our results solve the controversy concerning E-B : We confirm our previously measured value 0.7 +/- 0.1 K, and we demonstrate that it cannot be 0.2 or 0.4 K as estimated by other authors. Finally, we present a simple model for the damping magnitude, where dissipation is due to the emission by moving He-3 impurities of transverse waves along the dislocation lines.

PHYSICAL REVIEW B 90, (2014)

Abstract : Solid He-4 is a unique example of crystal where dislocations may move at macroscopic speeds with impurities attached to them. In He-4 crystals, the only impurities are He-3 atoms, whose concentration can be reduced to zero and measured down to the ppt (10(-12)) level. We present measurements of the mobility of dislocations dressed with He-3 impurities as a function of the crystal purity. They show that the damping of dislocation motion is proportional to the concentration of He-3 bound to these dislocations. It has allowed us to measure the He-3 binding energy E-B to dislocations without any ambiguity. Our results solve the controversy concerning E-B : We confirm our previously measured value 0.7 +/- 0.1 K, and we demonstrate that it cannot be 0.2 or 0.4 K as estimated by other authors. Finally, we present a simple model for the damping magnitude, where dissipation is due to the emission by moving He-3 impurities of transverse waves along the dislocation lines.

DOI

6

Dislocation densities and lengths in solid He-4 from elasticity measurements - Haziot, Ariel and Fefferman, Andrew D. and Beamish, John R. and Balibar, Sebastien

PHYSICAL REVIEW B 87, (2013)

Abstract : Measurements on solid He-4 show large softening of the shear modulus due to dislocations, behavior which has been described as giant plasticity. Dislocation networks may also be responsible for the unusual behavior seen in torsional oscillator and flow experiments. However, previous estimates of dislocation densities vary by many orders of magnitude, even in single crystals grown under similar conditions. By measuring the temperature and frequency dependencies of the elastic dissipation, we have determined dislocation densities and network lengths in 4He single crystals, both in coexistence with liquid and at higher pressures, and in polycrystals grown at constant density. In all cases, dislocation lengths are much longer and the networks are less connected than previous estimates. Even in polycrystals, the dislocation network is far too sparse to explain the torsional oscillator results in terms of superfluidity in a dislocation network. DOI:10.1103/PhysRevB.87.060509

PHYSICAL REVIEW B 87, (2013)

Abstract : Measurements on solid He-4 show large softening of the shear modulus due to dislocations, behavior which has been described as giant plasticity. Dislocation networks may also be responsible for the unusual behavior seen in torsional oscillator and flow experiments. However, previous estimates of dislocation densities vary by many orders of magnitude, even in single crystals grown under similar conditions. By measuring the temperature and frequency dependencies of the elastic dissipation, we have determined dislocation densities and network lengths in 4He single crystals, both in coexistence with liquid and at higher pressures, and in polycrystals grown at constant density. In all cases, dislocation lengths are much longer and the networks are less connected than previous estimates. Even in polycrystals, the dislocation network is far too sparse to explain the torsional oscillator results in terms of superfluidity in a dislocation network. DOI:10.1103/PhysRevB.87.060509

DOI

7

Critical dislocation speed in helium-4 crystals - Haziot, Ariel and Fefferman, Andrew D. and Souris, Fabien and Beamish, John R. and Maris, Humphrey J. and Balibar, Sebastien

PHYSICAL REVIEW B 88, (2013)

Abstract : Our experiments show that in He-4 crystals, the binding of He-3 impurities to dislocations does not necessarily imply their pinning. Indeed, in these crystals, there are two different regimes of the motion of dislocations when impurities bind to them. At low driving strain epsilon and frequency omega, where the dislocation speed is less than a critical value (45 mu m/s), dislocations and impurities apparently move together. Impurities really pin the dislocations only at higher values of epsilon omega. The critical speed separating the two regimes is two orders of magnitude smaller than the average speed of free He-3 impurities in the bulk crystal lattice. We obtained this result by studying the dissipation of dislocation motion as a function of the frequency and amplitude of a driving strain applied to a crystal at low temperature. Our results solve an apparent contradiction between some experiments, which showed a frequency-dependent transition temperature from a soft to a stiff state, and other experiments or models where this temperature was assumed to be independent of frequency. The impurity pinning mechanism for dislocations appears to be more complicated than previously assumed.

PHYSICAL REVIEW B 88, (2013)

Abstract : Our experiments show that in He-4 crystals, the binding of He-3 impurities to dislocations does not necessarily imply their pinning. Indeed, in these crystals, there are two different regimes of the motion of dislocations when impurities bind to them. At low driving strain epsilon and frequency omega, where the dislocation speed is less than a critical value (45 mu m/s), dislocations and impurities apparently move together. Impurities really pin the dislocations only at higher values of epsilon omega. The critical speed separating the two regimes is two orders of magnitude smaller than the average speed of free He-3 impurities in the bulk crystal lattice. We obtained this result by studying the dissipation of dislocation motion as a function of the frequency and amplitude of a driving strain applied to a crystal at low temperature. Our results solve an apparent contradiction between some experiments, which showed a frequency-dependent transition temperature from a soft to a stiff state, and other experiments or models where this temperature was assumed to be independent of frequency. The impurity pinning mechanism for dislocations appears to be more complicated than previously assumed.

DOI

8

Itinerant electrons in the Coulomb phase - Jaubert, L. D. C. and Piatecki, Swann and Haque, Masudul and Moessner, R.

PHYSICAL REVIEW B 85, (2012)

Abstract : We study the interplay between magnetic frustration and itinerant electrons. For example, howdoes the coupling to mobile charges modify the properties of a spin liquid, and does the underlying frustration favor insulating or conducting states? Supported by Monte Carlo simulations, our goal is in particular to provide an analytical picture of the mechanisms involved. The models under consideration exhibit Coulomb phases in two and three dimensions, where the itinerant electrons are coupled to the localized spins via double exchange interactions. Because of the Hund coupling, magnetic loops naturally emerge from the Coulomb phase and serve as conducting channels for the mobile electrons, leading to doping-dependent rearrangements of the loop ensemble in order to minimize the electronic kinetic energy. At low electron density rho, the double exchange coupling mainly tends to segment the very long loops winding around the system into smaller ones while it gradually lifts the extensive degeneracy of the Coulomb phase with increasing rho. For higher doping, the results are strongly lattice dependent, displaying loop crystals with a given loop length for some specific values of rho. By varying rho, they can melt into different mixtures of these loop crystals, recovering extensive degeneracy in the process. Finally, we contrast this to the qualitatively different behavior of analogous models on kagome or triangular lattices.

PHYSICAL REVIEW B 85, (2012)

Abstract : We study the interplay between magnetic frustration and itinerant electrons. For example, howdoes the coupling to mobile charges modify the properties of a spin liquid, and does the underlying frustration favor insulating or conducting states? Supported by Monte Carlo simulations, our goal is in particular to provide an analytical picture of the mechanisms involved. The models under consideration exhibit Coulomb phases in two and three dimensions, where the itinerant electrons are coupled to the localized spins via double exchange interactions. Because of the Hund coupling, magnetic loops naturally emerge from the Coulomb phase and serve as conducting channels for the mobile electrons, leading to doping-dependent rearrangements of the loop ensemble in order to minimize the electronic kinetic energy. At low electron density rho, the double exchange coupling mainly tends to segment the very long loops winding around the system into smaller ones while it gradually lifts the extensive degeneracy of the Coulomb phase with increasing rho. For higher doping, the results are strongly lattice dependent, displaying loop crystals with a given loop length for some specific values of rho. By varying rho, they can melt into different mixtures of these loop crystals, recovering extensive degeneracy in the process. Finally, we contrast this to the qualitatively different behavior of analogous models on kagome or triangular lattices.

DOI

9

He-4 crystal quality and rotational response in a transparent torsional oscillator - Fefferman, A. D. and Rojas, X. and Haziot, A. and Balibar, S. and West, J. T. and Chan, M. H. W.

PHYSICAL REVIEW B 85, (2012)

Abstract : We have studied natural purity He-4 single crystals and polycrystals between 10 and 600 mK using a torsional oscillator with a 2 cm(3) rigid cell made of sapphire with a smooth geometry. As the temperature was lowered, we observed sample-dependent but reproducible resonant frequency shifts that could be attributed to a supersolid fraction of order 0.1\%. However, these shifts were observed with single crystals, not with polycrystals. Our results indicate that, in our case, the rotational anomaly of solid helium is more likely due to a change in stiffness than to supersolidity. This interpretation would presumably require gliding of dislocations in more directions than previously thought.

PHYSICAL REVIEW B 85, (2012)

Abstract : We have studied natural purity He-4 single crystals and polycrystals between 10 and 600 mK using a torsional oscillator with a 2 cm(3) rigid cell made of sapphire with a smooth geometry. As the temperature was lowered, we observed sample-dependent but reproducible resonant frequency shifts that could be attributed to a supersolid fraction of order 0.1\%. However, these shifts were observed with single crystals, not with polycrystals. Our results indicate that, in our case, the rotational anomaly of solid helium is more likely due to a change in stiffness than to supersolidity. This interpretation would presumably require gliding of dislocations in more directions than previously thought.

DOI

10

Elastic effects in torsional oscillators containing solid helium - Beamish, J. R. and Fefferman, A. D. and Haziot, A. and Rojas, X. and Balibar, S.

PHYSICAL REVIEW B 85, (2012)

Abstract : A number of recent experiments have used torsional oscillators to study the behavior of solid helium. The oscillator frequencies increased at temperatures below 200 mK, an effect attributed to decoupling of a fraction of the helium mass-the signature of a ``supersolid'' phase. However, helium's shear modulus also increases below 200 mK and the frequency of a torsional oscillator depends on its elastic properties, as well as on its inertia. In many experiments helium is introduced via a hole in the torsion rod, where its shear modulus contributes to the stiffness of the rod. In oscillators with relatively large torsion rod holes, changes in the helium's shear modulus could produce the entire low temperature frequency shifts that have been interpreted as mass decoupling. For these oscillators we also find that the known elastic properties of helium in the torsion rod can explain the observed TO amplitude dependence (which has been interpreted as a critical velocity) and the TO dissipation peak. However, in other oscillators these elastic effects are small and the observed frequency changes must have a different origin.

PHYSICAL REVIEW B 85, (2012)

Abstract : A number of recent experiments have used torsional oscillators to study the behavior of solid helium. The oscillator frequencies increased at temperatures below 200 mK, an effect attributed to decoupling of a fraction of the helium mass-the signature of a ``supersolid'' phase. However, helium's shear modulus also increases below 200 mK and the frequency of a torsional oscillator depends on its elastic properties, as well as on its inertia. In many experiments helium is introduced via a hole in the torsion rod, where its shear modulus contributes to the stiffness of the rod. In oscillators with relatively large torsion rod holes, changes in the helium's shear modulus could produce the entire low temperature frequency shifts that have been interpreted as mass decoupling. For these oscillators we also find that the known elastic properties of helium in the torsion rod can explain the observed TO amplitude dependence (which has been interpreted as a critical velocity) and the TO dissipation peak. However, in other oscillators these elastic effects are small and the observed frequency changes must have a different origin.

DOI

11

Anomalous vortex-ring velocities induced by thermally excited Kelvin waves and counterflow effects in superfluids - Krstulovic, Giorgio and Brachet, Marc

PHYSICAL REVIEW B 83, (2011)

Abstract : Dynamical counterflow effects on vortex evolution under the truncated Gross-Pitaevskii equation are investigated. Standard longitudinal mutual-friction effects are produced and a dilatation of vortex rings is obtained at large counterflows. A strong temperature-dependent anomalous slowdown of vortex rings is observed and attributed to the presence of thermally excited Kelvin waves. This generic effect of finite-temperature superfluids is estimated using energy equipartition and orders of magnitude are given for weakly interacting Bose-Einstein condensates and superfluid (4)He. The relevance of thermally excited Kelvin waves is discussed in the context of quantum turbulence.

PHYSICAL REVIEW B 83, (2011)

Abstract : Dynamical counterflow effects on vortex evolution under the truncated Gross-Pitaevskii equation are investigated. Standard longitudinal mutual-friction effects are produced and a dilatation of vortex rings is obtained at large counterflows. A strong temperature-dependent anomalous slowdown of vortex rings is observed and attributed to the presence of thermally excited Kelvin waves. This generic effect of finite-temperature superfluids is estimated using energy equipartition and orders of magnitude are given for weakly interacting Bose-Einstein condensates and superfluid (4)He. The relevance of thermally excited Kelvin waves is discussed in the context of quantum turbulence.

DOI

12

Theory of nonequilibrium transport in the SU(N) Kondo regime - Mora, Christophe and Vitushinsky, Pavel and Leyronas, Xavier and Clerk, Aashish A. and Le Hur, Karyn

PHYSICAL REVIEW B 80, (2009)

Abstract : Using a Fermi-liquid approach, we provide a comprehensive treatment of the current and current noise through a quantum dot whose low-energy behavior corresponds to an SU(N) Kondo model, focusing on the case N=4 relevant to carbon nanotube dots. We show that for general N, one needs to consider the effects of higher-order Fermi-liquid corrections even to describe low-voltage current and noise. We also show that the noise exhibits complex behavior due to the interplay between coherent shot noise, and noise arising from interaction-induced scattering events. We also treat various imperfections relevant to experiments, such as the effects of asymmetric dot-lead couplings.

PHYSICAL REVIEW B 80, (2009)

Abstract : Using a Fermi-liquid approach, we provide a comprehensive treatment of the current and current noise through a quantum dot whose low-energy behavior corresponds to an SU(N) Kondo model, focusing on the case N=4 relevant to carbon nanotube dots. We show that for general N, one needs to consider the effects of higher-order Fermi-liquid corrections even to describe low-voltage current and noise. We also show that the noise exhibits complex behavior due to the interplay between coherent shot noise, and noise arising from interaction-induced scattering events. We also treat various imperfections relevant to experiments, such as the effects of asymmetric dot-lead couplings.

DOI

13

Nonclassical rotational inertia fraction in a one-dimensional model of a supersolid - Sepulveda, Nestor and Josserand, Christophe and Rica, Sergio

PHYSICAL REVIEW B 77, (2008)

Abstract : We study the rotational inertia of a model of supersolid in the frame of the mean field Gross-Pitaevskii theory in one space dimension. We discuss the ground state of the model and the existence of a nonclassical inertia under rotation that models an annular geometry. An explicit formula for the nonclassical rotational inertia (NCRI) is deduced. It depends on the density profile of the ground state, in full agreement with former theories. We compare the NCRI computed through this theory with direct numerical simulations of rotating one-dimensional systems.

PHYSICAL REVIEW B 77, (2008)

Abstract : We study the rotational inertia of a model of supersolid in the frame of the mean field Gross-Pitaevskii theory in one space dimension. We discuss the ground state of the model and the existence of a nonclassical inertia under rotation that models an annular geometry. An explicit formula for the nonclassical rotational inertia (NCRI) is deduced. It depends on the density profile of the ground state, in full agreement with former theories. We compare the NCRI computed through this theory with direct numerical simulations of rotating one-dimensional systems.

DOI

14

Hydrodynamic boundary condition for superfluid flow - Pomeau, Yves and Roberts, David C.

PHYSICAL REVIEW B 77, (2008)

Abstract : We discuss the hydrodynamic boundary condition for a superfluid moving tangentially to a rough surface. Specifically, we argue that the scattering of quantum fluctuations off surface roughness affects the nature of the boundary condition, and that this has important consequences including a theorized critical speed and the presence of normal fluid at any nonzero speed, even if the boundary is held at zero temperature (i.e., a moving superfluid flow creates a sustained temperature difference between the superfluid and the boundary). This hydrodynamic boundary condition is relevant not only for superfluid helium experiments but also for experiments with trapped dilute Bose-Einstein condensates, in particular, those involving atomic waveguides near surfaces.

PHYSICAL REVIEW B 77, (2008)

Abstract : We discuss the hydrodynamic boundary condition for a superfluid moving tangentially to a rough surface. Specifically, we argue that the scattering of quantum fluctuations off surface roughness affects the nature of the boundary condition, and that this has important consequences including a theorized critical speed and the presence of normal fluid at any nonzero speed, even if the boundary is held at zero temperature (i.e., a moving superfluid flow creates a sustained temperature difference between the superfluid and the boundary). This hydrodynamic boundary condition is relevant not only for superfluid helium experiments but also for experiments with trapped dilute Bose-Einstein condensates, in particular, those involving atomic waveguides near surfaces.

DOI

15

Melting and freezing of embedded nanoclusters - Caupin, Frederic

PHYSICAL REVIEW B 77, (2008)

Abstract : Small crystals are known to melt at a different temperature than the bulk; it is usually lower for freestanding nanocrystals. However, the size-dependent melting temperature is often analyzed with approximate formulas, corresponding to the limits of metastability of the solid cluster, instead of accounting for nucleation at an intermediate temperature. In addition, the advent of nanofabrication of inclusions in a host matrix adds a parameter to the problem: the different interactions of the matrix with the solid and the liquid phases. We address the issue of freezing and melting of spherical inclusions with a thermodynamically consistent model for nucleation of the new phase. The role of the matrix is included in the model through the contact angle of the liquid-solid interface on the matrix material, which strongly affects the nucleation behavior. We emphasize how the matrix curvature modifies the classical result for heterogeneous nucleation on a plane surface. The proposed formulation is simple and universal and can be easily used to analyze measurements. We illustrate the procedure on two recent experiments.

PHYSICAL REVIEW B 77, (2008)

Abstract : Small crystals are known to melt at a different temperature than the bulk; it is usually lower for freestanding nanocrystals. However, the size-dependent melting temperature is often analyzed with approximate formulas, corresponding to the limits of metastability of the solid cluster, instead of accounting for nucleation at an intermediate temperature. In addition, the advent of nanofabrication of inclusions in a host matrix adds a parameter to the problem: the different interactions of the matrix with the solid and the liquid phases. We address the issue of freezing and melting of spherical inclusions with a thermodynamically consistent model for nucleation of the new phase. The role of the matrix is included in the model through the contact angle of the liquid-solid interface on the matrix material, which strongly affects the nucleation behavior. We emphasize how the matrix curvature modifies the classical result for heterogeneous nucleation on a plane surface. The proposed formulation is simple and universal and can be easily used to analyze measurements. We illustrate the procedure on two recent experiments.

DOI

16

Exciton-exciton scattering: Composite boson versus elementary boson - Combescot, M. and Betbeder-Matibet, O. and Combescot, R.

PHYSICAL REVIEW B 75, (2007)

Abstract : This paper shows the necessity of introducing a quantum object, the ``coboson,'' to properly describe, through a fermion scheme, any composite particle, such as the exciton, which is made of two fermions. Although commonly dealt with as elementary bosons, these composite bosons-cobosons in short-differ from them due to their composite nature which makes the handling of their many-body effects quite different from the existing treatments valid for elementary bosons. As a direct consequence of this composite nature, there is no correct way to describe the interaction between cobosons as a potential V. This is rather dramatic because, with the Hamiltonian not written as H=H-0+V, all the usual approaches to many-body effects fail. In particular, the standard form of the Fermi golden rule, written in terms of V, cannot be used to obtain the transition rates of two cobosons. To get them, we have had to construct an unconventional expression for this Fermi golden rule in which H only appears. Making use of this expression, we give here a detailed calculation of the time evolution of two excitons. We compare the results of this exact approach with the ones obtained by using an effective bosonic Hamiltonian in which the excitons are considered as elementary bosons with effective scatterings between them, these scatterings resulting from an elaborate mapping between the two-fermion space and the ideal boson space. We show that the relation between the inverse lifetime and the sum of the transition rates for elementary bosons differs from the one of the composite bosons by a factor of 1/2, so that it is impossible to find effective scatterings between bosonic excitons giving these two physical quantities correctly, whatever the mapping from composite bosons to elementary bosons is. The present paper thus constitutes a strong mathematical proof that, in spite of a widely spread belief, we cannot forget the composite nature of these cobosons, even in the extremely low-density limit of just two excitons. This paper also shows the (unexpected) cancellation in the Born approximation of the two-exciton transition rate for a finite value of the momentum transfer.

PHYSICAL REVIEW B 75, (2007)

Abstract : This paper shows the necessity of introducing a quantum object, the ``coboson,'' to properly describe, through a fermion scheme, any composite particle, such as the exciton, which is made of two fermions. Although commonly dealt with as elementary bosons, these composite bosons-cobosons in short-differ from them due to their composite nature which makes the handling of their many-body effects quite different from the existing treatments valid for elementary bosons. As a direct consequence of this composite nature, there is no correct way to describe the interaction between cobosons as a potential V. This is rather dramatic because, with the Hamiltonian not written as H=H-0+V, all the usual approaches to many-body effects fail. In particular, the standard form of the Fermi golden rule, written in terms of V, cannot be used to obtain the transition rates of two cobosons. To get them, we have had to construct an unconventional expression for this Fermi golden rule in which H only appears. Making use of this expression, we give here a detailed calculation of the time evolution of two excitons. We compare the results of this exact approach with the ones obtained by using an effective bosonic Hamiltonian in which the excitons are considered as elementary bosons with effective scatterings between them, these scatterings resulting from an elaborate mapping between the two-fermion space and the ideal boson space. We show that the relation between the inverse lifetime and the sum of the transition rates for elementary bosons differs from the one of the composite bosons by a factor of 1/2, so that it is impossible to find effective scatterings between bosonic excitons giving these two physical quantities correctly, whatever the mapping from composite bosons to elementary bosons is. The present paper thus constitutes a strong mathematical proof that, in spite of a widely spread belief, we cannot forget the composite nature of these cobosons, even in the extremely low-density limit of just two excitons. This paper also shows the (unexpected) cancellation in the Born approximation of the two-exciton transition rate for a finite value of the momentum transfer.