Scaling of thermal conductivity of helium confined in pores

Nho, Kwangsik; Manousakis, Efstratios

doi:10.1103/physrevb.64.144513

Cited by 12 publications

(9 citation statements)

References 54 publications

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“…In all the cases mentioned above, due to the translational invariance, there are no surface, i.e., spatially varying effects. Monte Carlo simulations have been performed to study the thermal conductivity of the planar magnet lattice model in a bar-like geometry (H × H × L with L ≫ H) with open boundary conditions [28], aiming for a comparison with experimental results for 4 He at the superfluid transition confined to an array of pores [29]. The same problem has been addressed within the field-theoretical approach, studying Model F dynamics [2,30] in a L × L × ∞ geometry with Dirichlet boundary conditions (DBC, i.e., vanishing surface fields) for the order parameter [31].…”

Section: Introductionmentioning

confidence: 99%

Critical Dynamics in Thin Films

Gambassi

Dietrich

2006

J Stat Phys

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Critical dynamics in film geometry is analyzed within the field-theoretical approach. In particular we consider the case of purely relaxational dynamics (Model A) and Dirichlet boundary conditions, corresponding to the so-called ordinary surface universality class on both confining boundaries. The general scaling properties for the linear response and correlation functions and for dynamic Casimir forces are discussed. Within the Gaussian approximation we determine the analytic expressions for the associated universal scaling functions and study quantitatively in detail their qualitative features as well as their various limiting behaviors close to the bulk critical point. In addition we consider the effects of time-dependent fields on the fluctuation-induced dynamic Casimir force and determine analytically the corresponding universal scaling functions and their asymptotic behaviors for two specific instances of instantaneous perturbations. The universal aspects of nonlinear relaxation from an initially ordered state are also discussed emphasizing the different crossovers that occur during this evolution. The model considered is relevant to the critical dynamics of actual uniaxial ferromagnetic films with symmetry-preserving conditions at the confining surfaces and for Monte Carlo simulations of spin system with Glauber dynamics and free boundary conditions. Dynamic critical phenomena -confined geometry -finite-size scaling -magnetic properties of films -critical Casimir force

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Section: Introductionmentioning

confidence: 99%

Critical Dynamics in Thin Films

Gambassi

Dietrich

2006

J Stat Phys

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“…Indeed, the finite size scaling theory predicts, that a system confined to a barlike geometry, L · L · H where H → ∞, an observable O(t, L) scales as [32,33,34] …”

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confidence: 99%

“…However, when superconductivity is restricted to homogeneous domains of finite spatial extent L ab,c , the system is inhomogeneous and the resulting rounded transition uncovers a finite size effect [32,33,34] because the correlation lengths ξ ab,c = ξ ± ab0,c0 |t| −ν cannot grow beyond L ab,c , the respective extent of the homogenous domains. Hence, as long as ξ ab,c < L ab,c the critical properties of the fictitious homogeneous system can be explored.…”

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confidence: 99%

Magnetic field induced 3D–1D crossover in type-II superconductors

Schneider

2008

J. Phys.: Condens. Matter

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Abstract. We review and analyze magnetization and specific heat investigations on type-II superconductors which uncover remarkable evidence for the magnetic field induced finite size effect and the associated 3D to 1D crossover which enhances thermal fluctuations. Indeed, the correlation length transverse to the magnetic field H i , applied along the i-axis, cannot grow beyond the limiting magnetic length1/2 , related to the average distance between vortex lines. Noting that 1D is incompatible with the occurrence of a continuous phase transition at finite temperatures, the mean-field transition line H C2 (T ) is replaced by the 3D to 1D crossover line Hp (T ). Since the magnetic field induced finite size effect relies on thermal fluctuations and there enhancement originating from the 3D to 1D crossover, its observability is not be restricted to type-II superconductors with small correlation volume only, including YBa 2 Cu 4 O 8 , NdBa 2 Cu 3 O 7−δ , YBa 2 Cu 3 O 7−δ , and DyBa 2 Cu 3 O 7−δ , where 3D-xy critical behavior was already observed in zero field. Indeed, our analysis of the reversible magnetization of RbOs 2 O 6 and the specific heat of Nb 77 Zr 23 , Nb 3 Sn and NbSe 2 reveals that even in these low Tc superconductors with comparatively large correlation volume the 3D to 1D crossover is observable in sufficiently high magnetic fields. Consequently, below Tc and above H pi (T ) superconductivity is confined to cylinders with diameter L H i (1D) and there is no continuous phase transition in the (H, T ) -plane along the H c2 (T ) -line as predicted by the mean-field treatment. Moreover we observe that the thermodynamic vortex melting transition occurs in the 3D regime. While in YBa 2 Cu 4 O 8 , NdBa 2 Cu 3 O 7−δ , YBa 2 Cu 3 O 7−δ , and DyBa 2 Cu 3 O 7−δ it turns out to be driven by 3D-xy thermal fluctuations, the specific heat data of the conventional type-II superconductors Nb 77 Zr 23 , Nb 3 Sn and NbSe 2 point to Gaussian fluctuations. Because the vortex melting and the 3D-1D crossover line occur at universal values of the scaling variable their relationship is universal.

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“…This statement is supported by the fundamental studies of Ahlers (see, for example, [16]) and could be explained in terms of direct calculations of temperature variation due to the gravity effect. In order to proceed, we have to consider the limiting value of the cylinder length L over which the results of a study of the finite-size effect become independent of further increase of L. It was found [17,18] that there is no need to take the actual L ® ¥ limit, because it turns out that for L = 5D and larger (D is the diameter of a pore), the finite-size effect due to the finite value of L becomes insignificant.…”

Section: Helium-in-cylinrical-confinment Heat Capacity: Theoretical Pmentioning

confidence: 99%

“…The corresponding theoretical predictions could be suitable for comparison with actual Earth-based measurements [3,5,6]. Furthermore, the same theoretical approach is applicable for comparative study of the results of microgravity Confined Helium Experiment (CHEX) [1] conducted aboard the space shuttle and, hopefully, future experiments [17,20] which are scheduled to be carried out on the Low Temperature Microgravity Physics Facility (LTMPF) aboard the International Space Station.…”

Section: Helium-in-cylinrical-confinment Heat Capacity: Theoretical Pmentioning

confidence: 99%

Heat capacity of cylindrically confined helium: theoretical predictions versus experimental data

Chalyy

2004

Low Temperature Physics

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Different systems which could exhibit size-dependent second-order phase transitions have been studied experimentally during the last quarter century. The validity of the proposed theoretical results is verified by comparing high-resolution experimental data with an analytical evaluation of the heat capacity of confined 4 He. It is shown that the theoretical approach to the problem of the finite-size effect gives results that reasonably match the experimental data over a wide range of system sizes, from tens of nanometers up to a few micrometers for the cylindrical type of confinement geometry. The dependences of the shift of transition temperature on the cylinder size and boundary conditions are analyzed. The agreement of the results with finite-size scaling theory is confirmed.

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Scaling of thermal conductivity of helium confined in pores

Cited by 12 publications

References 54 publications

Critical Dynamics in Thin Films

Critical Dynamics in Thin Films

Magnetic field induced 3D–1D crossover in type-II superconductors

Heat capacity of cylindrically confined helium: theoretical predictions versus experimental data

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